thephysicsofstartreck.htmLawrence Krauss 
 
is Ambrose Swasey Professor of Physics, Professor of Astronomy and Chairman of 
the Department of Physics at Case Western Reserve University. He is the author 
of two acclaimed books, Fear of Physics: A Guide for the Perplexed and The Fifth 
Essence: The Search for Dark Matter in the Universe, and over 120 scientific 
articles. He is the recipient of several international awards for his work, 
including the Presidential Investigator Award, given by President Reagan in 
1986. He lectures extensively to both lay and professional audiences and 
frequently appears on radio and television. 
 
Further praise for The Physics of Star Trek: 
 
'Always enlightening . . . this book is fun, and Mr Krauss has a nice touch with 
a tough subject . . . Krauss is smart, but speaks and writes the common tongue.' 

JAMES GORMAN, New York Times Book Review 
 
'Entertaining and fascinating.' 
Manchester Evening News 
 
'A brilliant book' 
STEVE FARRAR, Cambridge Evening News 
 
'Highly recommended' 
M. J. SIMPSON, SFX 
 
'Delightful. . . The Physics of Star Trek is an excellent guide to the Star Trek 
universe for an amateur scientist.' 
JOSEPH SILK, Times Higher 
 
"But I canna change the laws of physics, Captain!" 
(Scotty, to Kirk, innumerable times) 
CONTENTS
 
FOREWORD by Stephen Hawking. 3
PREFACE. 3
THE PHYSICS OF STAR TREK.. 5
SECTION ONE - A Cosmic Poker Game - In which the physics of inertial dampers and 
tractor beams paves the way for time travel, warp speed, deflector shields, 
wormholes, and other spacetime oddities. 5
CHAPTER ONE - NEWTON Antes. 6
CHAPTER TWO - EINSTEIN Raises. 9
CHAPTER THREE  HAWKING Shows His Hand. 16
CHAPTER FOUR  DATA Ends the Game. 25
SECTION TWO - Matter Matter Everywhere - In which the reader explores 
transporter beams, warp drives, dilithium crystals, matter-antimatter engines, 
and the holodeck. 27
CHAPTER FIVE - Atoms or Bits. 28
CHAPTER SIX - The Most Bang for Your Buck. 35
CHAPTER SEVEN - Holodecks and Holograms. 41
SECTION THREE - The Invisible Universe, or Things That Go Bump in the Night - In 
which we speak of things that may exist but are not yet seen extraterrestrial 
life, multiple dimensions, and an exotic zoo of other physics possibilities and 
impossibilities  45
CHAPTER EIGHT - The Search for Spock. 56
CHAPTER NINE - The Menagerie of Possibilities. 64
CHAPTER TEN - Impossibilities: The Undiscoverable Country. 73
EPILOGUE. 79
NOTES. 80
 
FOREWORD by Stephen Hawking 
I was very pleased that Data decided to call Newton, Einstein, and me for a game 
of poker aboard the Enterprise. Here was my chance to turn the tables on the two 
great men of gravity, particularly Einstein, who didn't believe in chance or in 
God playing dice. Unfortunately, I never collected my winnings because the game 
had to be abandoned on account of a red alert. I contacted Paramount studios 
afterward to cash in my chips, but they didn't know the exchange rate. 
Science fiction like Star Trek is not only good fun but it also serves a serious 
purpose, that of expanding the human imagination. We may not yet be able to 
boldly go where no man (or woman) has gone before, but at least we can do it in 
the mind. We can explore how the human spirit might respond to future 
developments in science and we can speculate on what those developments might 
be. There is a two-way trade between science fiction and science. Science 
fiction suggests ideas that scientists incorporate into their theories, but 
sometimes science turns up notions that are stranger than any science fiction. 
Black holes are an example, greatly assisted by the inspired name that the 
physicist John Archibald Wheeler gave them. Had they continued with their 
original names of "frozen stars" or "gravitationally completely collapsed 
objects," there wouldn't have been half so much written about them. 
One thing that Star Trek and other science fiction have focused attention on is 
travel faster than light. Indeed, it is absolutely essential to Star Trek's 
story line. If the Enterprise were restricted to flying just under the speed of 
light, it might seem to the crew that the round trip to the center of the galaxy 
took only a few years, but 80,000 years would have elapsed on Earth before the 
spaceship's return. So much for going back to see your family! 
Fortunately, Einstein's general theory of relativity allows the possibility for 
a way around this difficulty: one might be able to warp spacetime and create a 
shortcut between the places one wanted to visit. Although there are problems of 
negative energy, it seems that such warping might be within our capabilities in 
the future. There has not been much serious scientific research along these 
lines, however, partly, I think, because it sounds too much like science 
fiction. One of the consequences of rapid interstellar travel would be that one 
could also travel back in time. Imagine the outcry about the waste of taxpayers' 
money if it were known that the National Science Foundation were supporting 
research on time travel. For this reason, scientists working in this field have 
to disguise their real interest by using technical terms like "closed timelike 
curves" that are code for time travel. Nevertheless, today's science fiction is 
often tomorrow's science fact. The physics that underlies Star Trek is surely 
worth investigating. To confine our attention to terrestrial matters would be to 
limit the human spirit. 
PREFACE 
Why the physics of Star Trek? Gene Roddenberry's creation is, after all, science 
fiction, not science fact. Many of the technical wonders in the series therefore 
inevitably rest on notions that may be ill defined or otherwise at odds with our 
current understanding of the universe. I did not want to write a book that ended 
up merely outlining where the Star Trek writers went wrong. 
Yet I found that I could not get the idea of this book out of my head. I confess 
that it was really the transporter that seduced me. Thinking about the 
challenges that would have to be faced in devising such a fictional technology 
forces one to ponder topics ranging from computers and the information 
superhighway to particle physics, quantum mechanics, nuclear energy, telescope 
building, biological complexity, and even the possible existence of the human 
soul! Compound this with ideas such as warped space and time travel and the 
whole subject became irresistible. 
I soon realized that what made this so fascinating to me was akin to what keeps 
drawing fans to Star Trek today, almost thirty years after the series first 
aired. This is, as the omnipotent Star Trek prankster Q put it, "charting the 
unknown possibilities of existence." And, as I am sure Q would have agreed, it 
is even good fun to imagine them. 
As Stephen Hawking states in the foreword to this book, science fiction like 
Star Trek helps expand the human imagination. Indeed, exploring the infinite 
possibilities the future holdsincluding a world where humanity has overcome its 
myopic international and racial tensions and ventured out to explore the 
universe in peaceis part of the continuing wonder of Star Trek. And, as I see 
this as central to the continuing wonder of modern physics, it is these 
possibilities that I have chosen to concentrate on here. 
Based on an informal survey I carried out while walking around my university 
campus the other day, the number of people in the United States who would not 
recognize the phrase "Beam me up, Scotty" is roughly comparable to the number of 
people who have never heard of ketchup. When we consider that the Smithsonian 
Institution's exhibition on the starship Enterprise was the most popular display 
in their Air and Space Museummore popular than the real spacecraft thereI 
think it is clear that Star Trek is a natural vehicle for many people's 
curiosity about the universe. What better context to introduce some of the more 
remarkable ideas at the forefront of today's physics and the threshold of 
tomorrow's? I hope you find the ride as enjoyable as I have. 
Live long and prosper. 
THE PHYSICS OF STAR TREK
SECTION ONE - A Cosmic Poker Game - In which the physics of inertial dampers and 
tractor beams paves the way for time travel, warp speed, deflector shields, 
wormholes, and other spacetime oddities 
CHAPTER ONE - NEWTON Antes
 
"No matter where you go, there you are."
From a plaque on the starship Excelsior, in Star Trek VI: The Undiscovered 
Country,presumably borrowed from The Adventures of Buckaroo Banzai
 
You are at the helm of the starship Defiant (NCC-1764), currently in orbit 
around the planet Iconia, near the Neutral Zone. Your mission: to rendezvous 
with a nearby supply vessel at the other end of this solar system in order to 
pick up components to repair faulty transporter primary energizing coils. There 
is no need to achieve warp speeds; you direct the impulse drive to be set at 
full power for leisurely half-light-speed travel, which should bring you to your 
destination in a few hours, giving you time to bring the captain's log up to 
date. However, as you begin to pull out of orbit, you feel an intense pressure 
in your chest. Your hands are leaden, and you are glued to your seat. Your mouth 
is fixed in an evil-looking grimace, your eyes feel like they are about to burst 
out of their sockets, and the blood flowing through your body refuses to rise to 
your head. Slowly, you lose consciousness ... and within minutes you die. 
What happened? It is not the first signs of spatial "interphase" drift, which 
will later overwhelm the ship, or an attack from a previously cloaked Romulan 
vessel. Rather, you have fallen prey to something far more powerful. The 
ingenious writers of Star Trek, on whom you depend, have not yet invented 
inertial dampers, which they will introduce sometime later in the series. You 
have been defeated by nothing more exotic than Isaac Newton's laws of motionthe 
very first things one can forget about high school physics. 
OK, I know some trekkers out there are saying to themselves, "How lame! Don't 
give me Newton. Tell me things I really want to know, like 'How does warp drive 
work?' or 'What is the flash before going to warp speedis it like a sonic 
boom?' or 'What is a dilithium crystal anyway?'" All I can say is that we will 
get there eventually. Travel in the Star Trek universe involves some of the most 
exotic concepts in physics. But many different aspects come together before we 
can really address everyone's most fundamental question about Star Trek: "Is any 
of this really possible, and if so, how?" 
To go where no one has gone beforeindeed, before we even get out of Starfleet 
Headquarterswe first have to confront the same peculiarities that Galileo and 
Newton did over three hundred years ago. The ultimate motivation will be the 
truly cosmic question which was at the heart of Gene Roddenberry's vision of 
Star Trek and which, to me, makes this whole subject worth thinking about: "What 
does modem science allow us to imagine about our possible future as a 
civilization?" 
Anyone who has ever been in an airplane or a fast car knows the feeling of being 
pushed back into the seat as the vehicle accelerates from a standstill. This 
phenomenon works with a vengeance aboard a starship. The fusion reactions in the 
impulse drive produce huge pressures, which push gases and radiation backward 
away from the ship at high velocity. It is the backreaction force on the 
enginesfrom the escaping gas and radiationthat causes the engines to "recoil" 
forward. The ship, being anchored to the engines, also recoils forward. At the 
helm, you are pushed forward too, by the force of the captain's seat on your 
body. In turn, your body pushes back on the seat. 
Now, here's the catch. Just as a hammer driven at high velocity toward your head 
will produce a force on your skull which can easily be lethal, the captain's 
seat will kill you if the force it applies to you is too great. Jet pilots and 
NASA have a name for the force exerted on your body while you undergo high 
accelerations (as in a plane or during a space launch): G-forces. I can describe 
these by recourse to my aching back: As I am sitting at my computer terminal 
busily typing, I feel the ever-present pressure of my office chair on my 
buttocksa pressure that I have learned to live with (yet, I might add, that my 
buttocks are slowly reacting to in a very noncosmetic way). The force on my 
buttocks results from the pull of gravity, which if given free rein would 
accelerate me downward into the Earth. What stops me from acceleratingindeed, 
from moving beyond my seatis the ground exerting an opposite upward force on my 
house's concrete and steel frame, which exerts an upward force on the wood floor 
of my second-floor study, which exerts a force on my chair, which in turn exerts 
a force on the part of my body in contact with it. If the Earth were twice as 
massive but had the same diameter, the pressure on my buttocks would be twice as 
great. The upward forces would have to compensate for the force of gravity by 
being twice as strong. 
The same factors must be taken into account in space travel. If you are in the 
captain's seat and you issue a command for the ship to accelerate, you must take 
into account the force with which the seat will push you forward. If you request 
an acceleration twice as great, the force on you from the seat will be twice as 
great. The greater the acceleration, the greater the push. The only problem is 
that nothing can withstand the kind of force needed to accelerate to impulse 
speed quicklycertainly not your body. 
By the way, this same problem crops up in different contexts throughout Star 
Trekeven on Earth. At the beginning of Star Trek V: The Final Frontier, James 
Kirk is free-climbing while on vacation in Yosemite when he slips and falls. 
Spock, who has on his rocket boots, speeds to the rescue, aborting the captain's 
fall within a foot or two of the ground. Unfortunately, this is a case where the 
solution can be as bad as the problem. It is the process of stopping over a 
distance of a few inches which can kill you, whether or not it is the ground 
that does the stopping or Spock's Vulcan grip. 
Well before the reaction forces that will physically tear or break your body 
occur, other severe physiological problems set in. First and foremost, it 
becomes impossible for your heart to pump strongly enough to force the blood up 
to your head. This is why fighter pilots sometimes black out when they perform 
maneuvers involving rapid acceleration. Special suits have been created to force 
the blood up from pilots' legs to keep them conscious during acceleration. This 
physiological reaction remains one of the limiting factors in determining how 
fast the acceleration of present-day spacecraft can be, and it is why NASA, 
unlike Jules Verne in his classic From the Earth to the Moon, has never launched 
three men into orbit from a giant cannon. 
If I want to accelerate from rest to, say, 150,000 km/sec, or about half the 
speed of light, I have to do it gradually, so that my body will not be torn 
apart in the process. In order not to be pushed back into my seat with a force 
greater than 3G, my acceleration must be no more than three times the downward 
acceleration of falling objects on Earth. At this rate of acceleration, it would 
take some 5 million seconds, or about 2 1/2 months, to reach half light speed! 
This would not make for an exciting episode. 
To resolve this dilemma, sometime after the production of the first Constitution 
Class starshipthe Enterprise (NCC-1701)the Star Trek writers had to develop a 
response to the criticism that the accelerations aboard a starship would 
instantly turn the crew into "chunky salsa."1 They came up with "inertial 
dampers," a kind of cosmic shock absorber and an ingenious plot device designed 
to get around this sticky little problem. 
The inertial dampers are most notable in their absence. For example, the 
Enterprise was nearly destroyed after losing control of the inertial dampers 
when the microchip life-forms known as Nanites, as part of their evolutionary 
process, started munching on the ship's central-computer-core memory. Indeed, 
almost every time the Enterprise is destroyed (usually in some renegade 
timeline), the destruction is preceded by loss of the inertial dampers. The 
results of a similar loss of control in a Romulan Warbird provided us with an 
explicit demonstration that Romulans bleed green. 
Alas, as with much of the technology in the Star Trek universe, it is much 
easier to describe the problem the inertial dampers address than it is to 
explain exactly how they might do it. The First Law of Star Trek physics surely 
must state that the more basic the problem to be circumvented, the more 
challenging the required solution must be. For the reason we have come this far, 
and the reason we can even postulate a Star Trek future, is that physics is a 
field that builds on itself. A Star Trek fix must circumvent not merely some 
problem in physics but every bit of physical knowledge that has been built upon 
this problem. Physics progresses not by revolutions, which do away with ail that 
went before, but rather by evolutions, which exploit the best about what is 
already understood. Newton's laws will continue to be as true a million years 
from now as they are today, no matter what we discover at the frontiers of 
science. If we drop a ball on Earth, it will always fall. If I sit at this desk 
and write from here to eternity, my buttocks will always suffer the same 
consequences. 
Be that as it may, it would be unfair simply to leave the inertial dampers 
hanging without at least some concrete description of how they would have to 
operate. From what I have argued, they must create an artificial world inside a 
starship in which the reaction force that responds to the accelerating force is 
canceled. The objects inside the ship are "tricked" into acting as though they 
were not accelerating. I have described how accelerating gives you the same 
feeling as being pulled at by gravity. This connection, which was the basis of 
Einstein's general theory of relativity, is much more intimate than it may at 
first seem. Thus there is only one choice for the modus operandi of these 
gadgets: they must set up an artificial gravitational field inside the ship 
which "pulls" in the opposite direction to the reaction force, thereby canceling 
it out. 
Even if you buy such a possibility, other practical issues must be dealt with. 
For one thing, it takes some time for the inertial dampers to kick in when 
unexpected impulses arise. For example, when the Enterprise was bumped into a 
causality loop by the Bozeman as the latter vessel emerged from a temporal 
distortion, the crew was thrown all about the bridge (even before the breach in 
the warp core and the failure of the dampers). I have read in the Enterprise's 
technical specifications that the response time for the inertial dampers is 
about 60 milliseconds.2 Short as this may seem, it would be long enough to kill 
you if the same delay occurred during programmed periods of acceleration. To 
convince yourself, think how long it takes for a hammer to smash your head open, 
or how long it takes for the ground to kill you if you hit it after falling off 
of a cliff in Yosemite. Just remember that a collision at 10 miles per hour is 
equivalent to running full speed into a brick wall! The inertial dampers had 
better be pretty quick to respond. More than one trekker I know has remarked 
that whenever the ship is buffeted, no one ever gets thrown more than a few 
feet. 
Before leaving the familiar world of classical physics, I can't help mentioning 
another technological marvel that must confront Newton's laws in order to 
operate: the Enterprise's tractor beamhighlighted in the rescue of the Genome 
colony on Moab IV, when it deflected an approaching stellar core fragment, and 
in a similar (but failed) attempt to save Bre'el IV by pushing an asteroidal 
moon back into its orbit. On the face of it, the tractor beam seems simple 
enoughmore or less like an invisible rope or rodeven if the force exerted may 
be exotic. Indeed, just like a strong rope, the tractor beam often does a fine 
job of pulling in a shuttle craft, towing another ship, or inhibiting the escape 
of an enemy spacecraft. The only problem is that when we pull something with a 
rope, we must be anchored to the ground or to something else heavy. Anyone who 
has ever been skating knows what happens if you are on the ice and you try to 
push someone away from you. You do manage to separate, but at your own expense. 
Without any firm grounding, you are a helpless victim of your own inertia. 
It was this very principle that prompted Captain Jean-Luc Picard to order 
Lieutenant Riker to turn off the tractor beam in the episode "The Battle"; 
Picard pointed out that the ship they were towing would be carried along beside 
them by its own momentumits inertia. By the same token, if the Enterprise were 
to attempt to use the tractor beam to ward off the Stargazer, the resulting 
force would push the Enterprise backward as effectively as it would push the 
Stargazer forward. 
This phenomenon has already dramatically affected the way we work in space at 
present. Say, for example, that you are an astronaut assigned to tighten a bolt 
on the Hubble Space Telescope. If you take an electric screwdriver with you to 
do the job, you are in for a rude awakening after you drift over to the 
offending bolt. When you switch on the screwdriver as it is pressed against the 
bolt, you are as likely to start spinning around as the bolt is to turn. This is 
because the Hubble Telescope is a lot heavier than you are. When the screwdriver 
applies a force to the bolt, the reaction force you feel may more easily turn 
you than the bolt, especially if the bolt is still fairly tightly secured to the 
frame. Of course, if you are lucky enough, like the assassins of Chancellor 
Gorkon, to have gravity boots that secure you snugly to whatever you are 
standing on, then you can move about as efficiently as we are used to on Earth. 
Likewise, you can see what will happen if the Enterprise tries to pull another 
spacecraft toward it. Unless the Enterprise is very much heavier, it will move 
toward the other object when the tractor beam turns on, rather than vice versa. 
In the depths of space, this distinction is a meaningless semantic one. With no 
reference system nearby, who is to say who is pulling whom? However, if you are 
on a hapless planet like Moab IV in the path of a renegade star, it makes a 
great deal of difference whether the Enterprise pushes the star aside or the 
star pushes the Enterprise aside! 
One trekker I know claims that the way around this problem is already stated 
indirectly in at least one episode: if the Enterprise were to use its impulse 
engines at the same time that it turned its tractor beam on, it could, by 
applying an opposing force with its own engines, compensate for any recoil it 
might feel when it pushed or pulled on something. This trekker claims that 
somewhere it is stated that the tractor beam requires the impulse drive to be 
operational in order to work. I, however, have never noticed any instructions 
from Kirk or Picard to turn on the impulse engines at the same time the tractor 
beam is used. And in fact, for a society capable of designing and building 
inertial dampers, I don't think such a brute force solution would be necessary. 
Reminded of Geordi LaForge's need for a warp field to attempt to push back the 
moon at Bre'el IV, I think a careful, if presently unattainable, manipulation of 
space and time would do the trick equally well. To understand why, we need to 
engage the inertial dampers and accelerate to the modern world of curved space 
and time. 
CHAPTER TWO - EINSTEIN Raises
 
There once was a lady named Bright, 
Who traveled much faster than light. 
She departed one day, 
in a relative way, 
And returned on the previous night. 
Anonymous 
 
"Time, the final frontier"or so, perhaps, each Star Trek episode should begin. 
Thirty years ago, in the classic episode "Tomorrow Is Yesterday," the round-trip 
time travels of the Enterprise began. (Actually, at the end of an earlier 
episode, "The Naked Time," the Enterprise is thrown back in time three daysbut 
it is only a one-way trip.) The starship is kicked back to twentieth-century 
Earth as a result of a close encounter with a "black star" (the term "black 
hole" having not yet permeated the popular culture). Nowadays exotica like 
wormholes and "quantum singularities" regularly spice up episodes of Star Trek: 
Voyager, the latest series. Thanks to Albert Einstein and those who have 
followed in his footsteps, the very fabric of spacetime is filled with drama. 
While every one of us is a time traveler, the cosmic pathos that elevates human 
history to the level of tragedy arises precisely because we seem doomed to 
travel in only one directioninto the future. What wouldn't any of us give to 
travel into the past, relive glories, correct wrongs, meet our heroes, perhaps 
even avert disasters, or simply revisit youth with the wisdom of age? The 
possibilities of space travel beckon us every time we gaze up at the stars, yet 
we seem to be permanent captives in the present. The question that motivates not 
only dramatic license but a surprising amount of modern theoretical physics 
research can be simply put: Are we or are we not prisoners on a cosmic temporal 
freight train that cannot jump the tracks? 
The origins of the modern genre we call science fiction are closely tied to the 
issue of time travel. Mark Twain's early classic A Connecticut Yankee in King 
Arthur's Court is more a work of fiction than science fiction, in spite of the 
fact that the whole piece revolves around the time-travel adventures of a 
hapless American in medieval England. (Perhaps Twain did not dwell longer on the 
scientific aspects of time travel because of the promise he made to Picard 
aboard the Enterprise not to reveal his glimpse of the future once he returned 
to the nineteenth century by jumping through a temporal rift on Devidia II, in 
the episode "Time's Arrow.") But H. G. Wells's remarkable work The Time Machine 
completed the transition to the paradigm that Star Trek has followed. Wells was 
a graduate of the Imperial College of Science and Technology, in London, and 
scientific language permeates his discussions, as it does the discussions of the 
Enterprise crew. 
Surely among the most creative and compelling episodes in the Star Trek series 
are those involving time travel. I have counted no less than twenty-two episodes 
in the first two series which deal with this theme, and so do three of the Star 
Trek movies and a number of the episodes of Voyager and Deep Space Nine that 
have appeared as of this writing. 
Perhaps the most fascinating aspect of time travel as far as Star Trek is 
concerned is that there is no stronger potential for violation of the Prime 
Directive. The crews of Starfleet are admonished not to interfere with the 
present normal historical development of any alien society they visit. Yet by 
traveling back in time it is possible to remove the present altogether. Indeed, 
it is possible to remove history altogether! 
A famous paradox is to be found in both science fiction and physics: What 
happens if you go back in time and kill your mother before you were born? You 
must then cease to exist. But if you cease to exist, you could not have gone 
back and killed your mother. But if you didn't kill your mother, then you have 
not ceased to exist. Put another way: if you exist, then you cannot exist, while 
if you don't exist, you must exist. 
There are other, less obvious but equally dramatic and perplexing questions that 
crop up the moment you think about time travel. For example, at the resolution 
of "Time's Arrow," Picard ingeniously sends a message from the nineteenth to the 
twenty-fourth century by tapping binary code into Data's severed head, which he 
knows will be discovered almost five hundred years later and reattached to 
Data's body. As we watch, he taps the message, and then we cut to LaForge in the 
twenty-fourth century, as he succeeds in reattaching Data's head. To the viewer 
these events seem contemporaneous, but they are not; once Picard has tapped the 
message into Data's head, it lies there for half a millennium. But if I were 
carefully examining Data's head in the twenty-fourth century and Picard had not 
yet traveled back in time to change the future, would I see such a message? One 
might argue that if Picard hasn't traveled back in time yet, there can have been 
no effect on Data's head. Yet the actions that change Data's programming were 
performed in the nineteenth century regardless of when Picard traveled back in 
time to perform them. Thus they have already happened, even if Picard has not 
yet left! In this way, a cause in the nineteenth century (Picard tapping) can 
produce an effect in the twenty-fourth century (Data's circuitry change) before 
the cause in the twenty-fourth century (Picard leaving the ship) produces the 
effect in the nineteenth century (Picard's arrival in the cave where Data's head 
is located) which allowed the original cause (Picard tapping) to take place at 
all. 
Actually, if the above plot line is confusing, it is nothing compared to the 
Mother of all time paradoxes, which arises in the final episode of Star Trek: 
The Next Generation, when Picard sets off a chain of events that will travel 
back in time and destroy not just his own ancestry but all life on Earth. 
Specifically, a "subspace temporal distortion" involving "antitime" threatens to 
grow backward in time, eventually engulfing the amino acid protoplasm on the 
nascent Earth before the first proteins, which will be the building blocks of 
life, can form. This is the ultimate case of an effect producing a cause. The 
temporal distortion is apparently created in the future. If, in the distant 
past, the subspace temporal distortion was able to destroy the first life on 
Earth, then life on Earth could never have evolved to establish a civilization 
capable of creating the distortion in the future! 
The standard resolution of these paradoxes, at least among many physicists, is 
to argue a priori that such possibilities must not be allowed in a sensible 
universe, such as the one we presumably live in. However, the problem is that 
Einstein's equations of general relativity not only do not directly forbid such 
possibilities, they encourage them. 
Within thirty years of the development of the equations of general relativity, 
an explicit solution in which time travel could occur was developed by the 
famous mathematician Kurt Gdel, who worked at the Institute for Advanced Study 
in Princeton along with Einstein. In Star Trek language, this solution allowed 
the creation of a "temporal causality loop," such as the one the Enterprise got 
caught in after being hit by the Bozeman. The dryer terminology of modern 
physics labels this a "closed timelike curve." In either case, what it implies 
is that you can travel on a round-trip and return to your starting point in both 
space and time! Gdel's solution involved a universe that, unlike the one we 
happen to live in, is not expanding but instead is spinning uniformly. In such a 
universe, it turns out that one could in principle go back in time merely by 
traveling in a large circle in space. While such a hypothetical universe is 
dramatically different than the one in which we live, the mere fact that this 
solution exists at all indicates clearly that time travel is possible within the 
context of general relativity. 
There is a maxim about the universe which I always tell my students: That which 
is not explicitly forbidden is guaranteed to occur. Or, as Data said in the 
episode "Parallels," referring to the laws of quantum mechanics, "All things 
which can occur, do occur." This is the spirit with which I think one should 
approach the physics of Star Trek. We must consider the distinction not between 
what is practical and what is not, but between what is possible and what is not. 

This fact was not, of course, lost on Einstein himself, who wrote, "Kurt Gdel's 
[time machine solution raises] the problem [that] disturbed me already at the 
time of the building up of the general theory of relativity, without my having 
succeeded in clarifying it.... It will be interesting to weigh whether these 
[solutions] are not to be excluded on physical grounds."1 
The challenge to physicists ever since has been to determine what if any 
"physical grounds" exist that would rule out the possibility of time travel, 
which the form of the equations of general relativity appears to foreshadow. To 
discuss such things will require us to travel beyond the classical world of 
general relativity to a murky domain where quantum mechanics must affect even 
the nature of space and time. On the way, we, like the Enterprise, will 
encounter black holes and wormholes. But first we ourselves must travel back in 
time to the latter half of the nineteenth century. 
The marriage of space and time that heralded the modern era began with the 
marriage, in 1864, of electricity and magnetism. This remarkable intellectual 
achievement, based on the cumulative efforts of great physicists such as 
Andr-Marie Ampre, Charles-Augustin de Coulomb, and Michael Faraday, was capped 
by the brilliant British physicist James Clerk Maxwell. He discovered that the 
laws of electricity and magnetism not only displayed an intimate relationship 
with one another but together implied the existence of "electromagnetic waves," 
which should travel throughout space at a speed that one could calculate based 
on the known properties of electricity and magnetism. The speed turned out to be 
identical to the speed of light, which had previously been measured. 
Now, since the time of Newton there had been a debate about whether light was a 
wavethat is, a traveling disturbance in some background mediumor a particle, 
which travels regardless of the presence of a background medium. The observation 
of Maxwell that electromagnetic waves must exist and that their speed was 
identical to that of light ended the debate: light was an electromagnetic wave. 
Any wave is just a traveling disturbance. Well, if light is an electromagnetic 
disturbance, then what is the medium that is being disturbed as the wave 
travels? This became the hot topic for investigation at the end of the 
nineteenth century. The proposed medium had had a name since Aristotle. It was 
called the aether, and had thus far escaped any attempts at direct detection. In 
1887, however, Albert A. Michelson and Edward Morley, working at the 
institutions that later merged in 1967 to form my present home, Case Western 
Reserve University, performed an experiment guaranteed to detect not the aether 
but the aether's effects: Since the aether was presumed to fill all of space, 
the Earth was presumed to be in motion through it. Light traveling in different 
directions with respect to the Earth's motion through the aether ought therefore 
to show variations in speed. This experiment has since become recognized as one 
of the most significant of the last century, even though Michelson and Morley 
never observed the effect they were searching for. In fact, it is precisely 
because they failed to observe the effect of the Earth's motion through the 
aether that we remember their names today. (A. A. Michelson actually went on to 
become the first American Nobel laureate in physics for his experimental 
investigations into the speed of light, and I feel privileged to hold a position 
today which he held more than a hundred years ago. Edward Morley continued as a 
renowned chemist and determined the atomic weight of helium, among other 
things.) 
The nondiscovery of the aether did send minor ripples of shock throughout the 
physics community, but, like many watershed discoveries, its implications were 
fully appreciated only by a few individuals who had already begun to recognize 
several paradoxes associated with the theory of electromagnetism. Around this 
time, a young high school student who had been eight years old at the time of 
the Michelson-Morley experiment independently began to try to confront these 
paradoxes directly. By the time he was twenty-six, in the year 1905, Albert 
Einstein had solved the problem. But as also often occurs whenever great leaps 
are made in physics, Einstein's results created more questions than they 
answered. 
Einstein's solution, forming the heart of his special theory of relativity, was 
based on a simple but apparently impossible fact: the only way in which 
Maxwell's theory of electromagnetism could be self-consistent would be if the 
observed speed of light was independent of the observer's speed relative to the 
light. The problem, however, is that this completely defies common sense. If a 
probe is released from the Enterprise when the latter is traveling at impulse 
speed, an observer on a planet below will see the probe whiz past at a much 
higher speed than would a crew member looking out an observation window on the 
Enterprise. However, Einstein recognized that Maxwell's theory would be 
self-consistent only if light waves behaved differentlythat is, if their speed 
as measured by both observers remained identical, independent of the relative 
motion of the observers. Thus, if I shoot a phaser beam out the front of the 
Enterprise, and it travels away from the ship at the speed of light toward the 
bridge of a Romulan Warbird, which itself is approaching the Enterprise at an 
impulse speed of 3/4 the speed of light, those on the enemy bridge will observe 
the beam to be heading toward them just at the speed of light and not at 13/4 
times the speed of light. This sort of thing has confused some trekkers, who 
imagine that if the Enterprise is moving at near light speed and another ship is 
moving in the opposite direction at near light speed, the light from the 
Enterprise will never catch up with the other ship (and therefore the Enterprise 
will not be visible to it). Instead, those on the other ship will see the light 
from the Enterprise approaching at the speed of light. 
This realization alone was not what made Einstein's a household name. More 
important was the fact that he was willing to explore the implications of this 
realization, all of which on the surface seem absurd. In our normal experience, 
it is time and space that are absolute, while speed is a relative thing: how 
fast something is perceived to be moving depends upon how fast you yourself are 
moving. But as one approaches light speed, it is speed that becomes an absolute 
quantity, and therefore space and time must become relative! 
This comes about because speed is literally defined as distance traveled during 
some specific time. Thus, the only way observers in relative motion can measure 
a single light ray to traverse the same distancesay, 300 million 
metersrelative to each of them in, say, one second is if each of their 
"seconds" is different or each of their "meters" is different! It turns out that 
in special relativity, the "worst of both worlds" happensthat is, seconds and 
meters both become relative quantities. 
From the simple fact that the speed of light is measured to be the same for all 
observers, regardless of their relative motion, Einstein obtained the four 
following consequences for space, time, and matter: 
(a) Events that occur for one observer at the same time in two different places 
need not be simultaneous to another observer moving with respect to the first. 
Each person's "now" is unique to themselves. "Before" and "after" are relative 
for distant events. 
(b) All clocks on starships that are moving relative to me will appear to me to 
be ticking more slowly than my clock. Time is measured to slow down for objects 
in motion. 
(c) All yardsticks on starships that are moving relative to me will appear 
shorter than they would if they were standing still in my frame. Objects, 
including starships, are measured to contract if they are moving. 
(d)All massive objects get heavier the faster they travel. As they approach the 
speed of light, they become infinitely heavy. Thus, only massless objects, like 
light, can actually travel at the speed of light. 
This is not the place to review all of the wonderful apparent paradoxes that 
relativity introduces into the world. Suffice it to say that, like it or not, 
consequences (a) through (d) are truethat is, they have been tested. Atomic 
clocks have been carried aloft in high-speed aircraft and have been observed to 
be behind their terrestrial counterparts upon their return. In high-energy 
physics laboratories around the world, the consequences of the special theory of 
relativity are the daily bread and butter of experiment. Unstable elementary 
particles are made to move near the speed of light, and their lifetimes are 
measured to increase by huge factors. When electrons, which at rest are 2000 
times less massive than protons, are accelerated to near light speed, they are 
measured to carry a momentum equivalent to that of their heavier cousins. 
Indeed, an electron accelerated to 
.999999999999999999999999999999999999999999999999999999 99999999 times the speed 
of light would hit you with the same impact as a Mack truck traveling at normal 
speed. 
Of course, the reason all these implications of the relativity of space and time 
are so hard for us to accept at face value is that we happen to live and move at 
speeds far smaller than the speed of light. Each of the above effects becomes 
noticeable only when one is moving at "rel-ativistic" speeds. For example, even 
at half the speed of light, clocks would slow and yardsticks would shrink by 
only about 15 percent. On NASA's space shuttle, which moves at about 5 miles per 
second around the Earth, clocks tick less than one ten-millionth of a percent 
slower than their counterparts on Earth. 
However, in the high-speed world of the Enterprise or any other starship, 
relativity would have to be confronted on a daily basis. Indeed, in managing a 
Federation, one can imagine the difficulties of synchronizing clocks across a 
large segment of the galaxy when a great many of these clocks are moving at 
close to light speed. As a result, Starfleet apparently has a rule that normal 
impulse operations for starships are to be limited to a velocity of 0.25 cthat 
is, 1/4 light speed, or a mere 75,000 km/sec.2 
Even with such a rule, clocks on ships traveling at this speed will slow by 
slightly over 3 percent compared with clocks at Starfleet Command. This means 
that in a month of travel, clocks will have slowed by almost one day. If the 
Enterprise were to return to Starfleet Command after such a trip, it would be 
Friday on the ship but Saturday back home. I suppose the inconvenience would not 
be any worse than resetting your clocks after crossing the international date 
line when traveling to the Orient, except in this case the crew would actually 
be one. day younger after the round-trip, whereas on a round-trip to the Orient 
you gain one day going in one direction and lose one going in the other. 
You can now see how important warp drive is to the Enterprise. Not only is it 
designed to avoid the ultimate speed limitthe speed of lightand so allow 
practical travel across the galaxy, but it is also designed to avoid the 
problems of time dilation, which result when the ship is traveling close to 
light speed. 
I cannot overemphasize how significant these facts are. The fact that clocks 
slow down as one approaches the speed of light has been taken by science fiction 
writers (and indeed by all those who have dreamed of traveling to the stars) as 
opening the possibility that one might cross the vast distances between the 
stars in a human lifetimeat least a human lifetime for those aboard the 
spaceship. At close to the speed of light, a journey to, say, the center of our 
galaxy would take more than 25,000 years of Earth time. For those aboard the 
spaceship, if it were moving sufficiently close to light speed, the trip might 
take less than 10 yearsa long time, but not impossibly so. Nevertheless, while 
this might make individual voyages of discovery possible, it would make the task 
of running a Federation of civilizations scattered throughout the galaxy 
impossible. As the writers of Star Trek have correctly surmised, the fact that a 
10-year journey for the Enterprise would correspond to a 25,000-year period for 
Starfleet Command would wreak havoc on any command operation that hoped to 
organize and control the movements of many such craft. Thus it is absolutely 
essential that (a) light speed be avoided, in order not to put the Federation 
out of synchronization, and (b) faster-than-light speed be realized, in order to 
move practically about the galaxy. 
The kicker is that, in the context of special relativity alone, the latter 
possibility cannot be realized. Physics becomes full of impossibilities if super 
light speed is allowed. Not least among the problems is that because objects get 
more massive as they approach the speed of light, it takes progressively more 
and more energy to accelerate them by a smaller and smaller amount. As in the 
myth of the Greek hero Sisyphus, who was condemned to push a boulder uphill for 
all eternity only to be continually thwarted near the very top, all the energy 
in the universe would not be sufficient to allow us to push even a speck of 
dust, much less a starship, past this ultimate speed limit. 
By the same token, not just light but all massless radiation must travel at the 
speed of light. This means that the many types of beings of "pure energy" 
encountered by the Enterprise, and later by the Voyager, would have difficulty 
existing as shown. In the first place, they wouldn't be able to sit still. Light 
cannot be slowed down, let alone stopped in empty space. In the second place, 
any form of intelligent-energy being (such as the "photonic" energy beings in 
the Voyager series; the energy beings in the Beta Renna cloud, in The Next 
Generation; the Zetarians, in the original series; and the Dal'Rok, in Deep 
Space Nine), which is constrained to travel at the speed of light, would have 
clocks that are infinitely slowed compared to our own. The entire history of the 
universe would pass by in a single instant. If energy beings could experience 
anything, they would experience everything at once! Needless to say, before they 
could actually interact with corporeal beings the corporeal beings would be long 
dead. 
Speaking of time, I think it is time to introduce the Picard Maneuver. Jean-Luc 
became famous for introducing this tactic while stationed aboard the Stargazer. 
Even though it involves warp travel, or super light speed, which I have argued 
is impossible in the context of special relativity alone, it does so for just an 
instant and it fits in nicely with the discussions here. In the Picard Maneuver, 
in order to confuse an attacking enemy vessel, one's own ship is accelerated to 
warp speed for an instant. It then appears to be in two places at once. This is 
because, traveling faster than the speed of light for a moment, it overtakes the 
light rays that left it the instant before the warp drive was initiated. While 
this is a brilliant stategyand it appears to be completely consistent as far as 
it goes (that is, ignoring the issue of whether it is possible to achieve warp 
speed)I think you can see that it opens a veritable Pandora's can of worms. In 
the first place, it begs a question that has been raised by many trekkers over 
the years: How can the Enterprise bridge crew "see" objects approaching them at 
warp speed? Just as surely as the Stargazer overtook its own image, so too will 
all objects traveling at warp speed; one shouldn't be able to see the moving 
image of a warp-speed object until long after it has arrived. One can only 
assume that when Kirk, Picard, or Janeway orders up an image on the viewscreen, 
the result is an image assembled by some sort of long-range "subspace" (that is, 
super-light-speed communication) sensors. Even ignoring this apparent oversight, 
the Star Trek universe would be an interesting and a barely navigable one, full 
of ghost images of objects that long ago arrived where they were going at warp 
speed. 
Moving back to the sub-light-speed world: We are not through with Einstein yet. 
His famous relation between mass and energy, E=mc2, which is a consequence of 
special relativity, presents a further challenge to space travel at impulse 
speeds. As I have described it in chapter 1, a rocket is a device that propels 
material backward in order to move forward. As you might imagine, the faster the 
material is propelled backward, the larger will be the forward impulse the 
rocket will receive. Material cannot be propelled backward any faster than the 
speed of light. Even propelling it at light speed is not so easy: the only way 
to get propellant moving backward at light speed is to make the fuel out of 
matter and antimatter, which (as I describe in a later chapter) can completely 
annihilate to produce pure radiation moving at the speed of light. 
However, while the warp drive aboard the Enterprise uses such fuel, the impulse 
drive does not. It is powered instead by nuclear fusionthe same nuclear 
reaction that powers the Sun by turning hydrogen into helium. In fusion 
reactions, about 1 percent of the available mass is converted into energy. With 
this much available energy, the helium atoms that are produced can come 
streaming out the back of the rocket at about an eighth of the speed of light. 
Using this exhaust velocity for the propellant, we then can calculate the amount 
of fuel the Enterprise needs in order to accelerate to, say, half the speed of 
light. The calculation is not difficult, but I will just give the answer here. 
It may surprise you. Each time the Enterprise accelerates to half the speed of 
light, it must burn 81 TIMES ITS ENTIRE MASS in hydrogen fuel. Given that a 
Galaxy Class starship such as Picard's Enterprise-D would weigh in excess of 4 
million metric tons,3 this means that over 300 million metric tons of fuel would 
need to be used each time the impulse drive is used to accelerate the ship to 
half light speed! If one used a matter-antimatter propulsion system for the 
impulse drive, things would be a little better. In this case, one would have to 
burn merely twice the entire mass of the Enterprise in fuel for each such 
acceleration. 
It gets worse. The calculation I described above is correct for a single 
acceleration. To bring the ship to a stop at its destination would require the 
same factor of 81 times its mass in fuel. This means that just to go somewhere 
at half light speed and stop again would require fuel in the amount of 81x81= 
6561 TIMES THE ENTIRE SHIP'S MASS! Moreover, say that one wanted to achieve the 
acceleration to half the speed of light in a few hours (we will assume, of 
course, that the inertial dampers are doing their job of shielding the crew and 
ship from the tremendous G-forces that would otherwise ensue). The power 
radiated as propellant by the engines would then be about 1022 wattsor about a 
billion times the total average power presently produced and used by all human 
activities on Earth! 
Now, you may suggest (as a bright colleague of mine did the other day when I 
presented him with this argument) that there is a subtle loophole. The argument 
hinges on the requirement that you carry your fuel along with the rocket. What 
if, however, you harvest your fuel as you go along? After all, hydrogen is the 
most abundant element in the universe. Can you not sweep it up as you move 
through the galaxy? Well, the average density of matter in our galaxy is about 
one hydrogen atom per cubic centimeter. To sweep up just one gram of hydrogen 
per second, even moving at a good fraction of the speed of light, would require 
you to deploy collection panels with a diameter of over 25 miles. And even 
turning all this matter into energy for propulsion would provide only about a 
hundred-millionth of the needed propulsion power! 
To paraphrase the words of the Nobel prizewinning physicist Edward Purcell, 
whose arguments I have adapted and extended here: 
If this sounds preposterous to you, you are right. Its preposterousness follows 
from the elementary laws of classical mechanics and special relativity. The 
arguments presented here are as inescapable as the fact that a ball will fall 
when you drop it at the Earth's surface. Rocket-propelled space travel through 
the galaxy at near light speed is not physically practical, now or ever! 
So, do I end the book here? Do we send back our Star Trek memorabilia and ask 
for a refund? Well, we are still not done with Einstein. His final, perhaps 
greatest discovery holds out a glimmer of hope after all. 
Fast rewind back to 1908: Einstein's discovery of the relativity of space and 
time heralds one of those "Aha!" experiences that every now and then forever 
change our picture of the universe. It was in the fall of 1908 that the 
mathematical physicist Hermann Minkowski wrote these famous words: "Henceforth, 
space by itself, and time by itself, are doomed to fade away into mere shadows, 
and only a kind of union of the two will preserve an independent reality." 
What Minkowski realized is that even though space and time are relative for 
observers in relative motionyour clock can tick slower than mine, and my 
distances can be different from yoursif space and time are instead merged as 
part of a four-dimensional whole (three dimensions of space and one of time), an 
"absolute" objective reality suddenly reappears. 



The leap of insight Minkowski had can be explained by recourse to a world in 
which everyone has monocular vision and thus no direct depth perception. If you 
were to close one eye, so that your depth perception was reduced, and I were to 
hold a ruler up for you to see, and I then told someone else, who was observing 
from a different angle, to close one eye too, the ruler I was holding up would 
appear to the other observer to be a different length than it would appear to be 
to youas the following bird's-eye view shows. 
Each observer in the example above, without the direct ability to discern depth, 
will label "length" (L or L') to be the two-dimensional projection onto his or 
her plane of vision of the actual three-dimensional length of the ruler. Now, 
because we know that space has three dimensions, we are not fooled by this 
trick. We know that viewing something from a different angle does not change its 
real length, even if it changes its apparent length. Minkowski showed that the 
same idea can explain the various paradoxes of relativity, if we now instead 
suppose that our perception of space is merely a three-dimensional slice of what 
is actually a four-dimensional manifold in which space and time are joined. Two 
different observers in relative motion perceive different three-dimensional 
slices of the underlying four-dimensional space in much the same way that the 
two rotated observers pictured here view different two-dimensional slices of a 
three-dimensional space. 
Minkowski imagined that the spatial distance measured by two observers in 
relative motion is a projection of an underlying four-dimensional spacetime 
distance onto the three-dimensional space that they can sense; and, similarly, 
that the temporal "distance" between two events is a projection of the 
four-dimensional spacetime distance onto their own timeline. Just as rotating 
something in three dimensions can mix up width and depth, so relative motion in 
four-dimensional space can mix up different observers' notions of "space" and 
"time." Finally, just as the length of an object does not change when we rotate 
it in space, the four-dimensional spacetime distance between two events is 
absoluteindependent of how different observers in relative motion assign 
"spatial" and "temporal" distances. 
So the crazy invariance of the speed of light for all observers provided a key 
clue to unravel the true nature of the four-dimensional universe of spacetime in 
which we actually live. Light displays the hidden connection between space and 
time. Indeed, the speed of light defines the connection. 
It is here that Einstein returned to save the day for Star Trek. Once Minkowski 
had shown that spacetime in special relativity was like a four-dimensional sheet 
of paper, Einstein spent the better part of the next decade flexing his 
mathematical muscles until he was able to bend that sheet, which in turn allows 
us to bend the rules of the game. As you may have guessed, light was again the 
key. 
CHAPTER THREE  HAWKING Shows His Hand
"How little do you mortals understand time. Must you be so linear, Jean-Luc?"
Q to Picard, in "All Good Things... .
 
The planet Vulcan, home to Spock, actually has a venerable history in 
twentieth-century physics. A great puzzle in astrophysics in the early part of 
this century was the fact that the perihelion of Mercurythe point of its 
closest approach to the Sunwas precess-ing around the Sun each Mercurian year 
by a very small amount in a way that was not consistent with Newtonian gravity. 
It was suggested that a new planet existed inside Mercury's orbit which could 
perturb it in such a way as to fix the problem. (In fact, the same solution to 
an anomaly in the orbit of Uranus had earlier led to the discovery of the planet 
Neptune.) The name given to the hypothetical planet was Vulcan. 
Alas, the mystery planet Vulcan is not there. Instead, Einstein proposed that 
the flat space of Newton and Minkowski had to be given up for the curved 
spacetime of general relativity. In this curved space, Mercury's orbit would 
deviate slightly from that predicted by Newton, explaining the observed 
discrepancy. While this removed the need for the planet Vulcan, it introduced 
possibilities that are much more exciting. Along with curved space come black 
holes, wormholes, and perhaps even warp speeds and time travel. 
Indeed, long before the Star Trek writers conjured up warp fields, Einstein 
warped spacetime, and, like the Star Trek writers, he was armed with nothing 
other than his imagination. Instead of imagining twenty-second-century starship 
technology, however, Einstein imagined an elevator. He was undoubtedly a great 
physicist, but he probably never would have sold a screenplay. 
Nonetheless, his arguments remain intact when translated aboard the Enterprise. 
Because light is the thread that weaves together space and time, the 
trajectories of light rays give us a map of spacetime just as surely as warp and 
weft threads elucidate the patterns of a tapestry. Light generally travels in 
straight lines. But what if a Romulan commander aboard a nearby Warbird shoots a 
phaser beam at Picard as he sits on the bridge of his captain's yacht Calypso, 
having just engaged the impulse drive (we will assume the inertial dampers are 
turned off for this example)? Picard would accelerate forward, narrowly missing 
the brunt of the phaser blast. When viewed in Picard's frame of reference, 
things would look like the figure at the top of the following page. 

So, for Picard, the trajectory of the phaser ray would be curved. What else 
would Picard notice? Well, recalling the argument in the first chapter, as long 
as the inertial dampers are turned off, he would be thrust back in his seat. In 
fact, I also noted there that if Picard was being accelerated forward at the 
same rate as gravity causes things to accelerate downward at the Earth's 
surface, he would feel exactly the same force pushing him back against his seat 
that he would feel pushing him down if he were standing on Earth. In fact, 
Einstein argued that Picard (or his equivalent in a rising elevator) would never 
be able to perform any experiment that could tell the difference between the 
reaction force due to his acceleration and the pull of gravity from some nearby 
heavy object outside the ship. Because of this, Einstein boldly went where no 
physicist had gone before, and reasoned that whatever phenomena an accelerating 
observer experienced would be identical to the phenomena an observer in a 
gravitational field experienced. 
Our example implies the following: Since Picard observes the phaser ray bending 
when he is accelerating away from it, the ray must also bend in a gravitational 
field. But if light rays map out spacetime, then spacetime must bend in a 
gravitational field. Finally, since matter produces a gravitational field, then 
matter must bend spacetime! 
Now, you may argue that since light has energy, and mass and energy are related 
by Einstein's famous equation, then the fact that light bends in a gravitational 
field is no big surpriseand certainly doesn't seem to imply that we have to 
believe that spacetime itself need be curved. After all, the paths that matter 
follows bend too (try throwing a ball in the air). Galileo could have shown, had 
he known about such objects, that the trajectories of baseballs and Pathfinder 
missiles bend, but he never would have mentioned curved space. 
Well, it turns out that you can calculate how much a light ray should bend if 
light behaved the same way a baseball does, and then you can go ahead and 
measure this bending, as Sir Arthur Stanley Eddington did in 1919 when he led an 
expedition to observe the apparent position of stars on the sky very near the 
Sun during a solar eclipse. Remarkably, you would find, as Eddington did, that 
light bends exactly twice as much as Galileo might have predicted if it behaved 
like a baseball in flat space. As you may have guessed, this factor of 2 is just 
what Einstein predicted if spacetime was curved in the vicinity of the Sun and 
light (or the planet Mercury, for that matter) was locally traveling in a 
straight line in this curved space! Suddenly, Einstein's was a household name. 
Curved space opens up a whole universe of possibilities, if you will excuse the 
pun. Suddenly we, and the Enterprise, are freed from the shackles of the kind of 
linear thinking imposed on us in the context of special relativity, which Q, for 
one, seemed to so abhor. One can do many things on a curved manifold which are 
impossible on a flat one. For example, it is possible to keep traveling in the 
same direction and yet return to where you beganpeople who travel around the 
world do it all the time. 
The central premise of Einstein's general relativity is simple to state in 
words: the curvature of spacetime is directly determined by the distribution of 
matter and energy contained within it. Einstein's equations, in fact, provide 
simply the strict mathematical relation between curvature on the one hand and 
matter and energy on the other: 
 
      Left-hand side
      {CURVATURE}=Right-hand side
      {Matter and Energy}

 
What makes the theory so devilishly difficult to work with is this simple 
feedback loop: The curvature of spacetime is determined by the distribution of 
matter and energy in the universe, but this distribution is in turn governed by 
the curvature of space. It is like the chicken and the egg. Which was there 
first? Matter acts as the source of curvature, which in turn determines how 
matter evolves, which in turn alters the curvature, and so on. 
Indeed, this may be perhaps the most important single aspect of general 
relativity as far as Star Trek is concerned. The complexity of the theory means 
that we still have not yet fully understood all its consequences; therefore we 
cannot rule out various exotic possibilities. It is these exotic possibilities 
that are the grist of Star Trek's mill. In fact, we shall see that all these 
possibilities rely on one great unknown that permeates everything, from 
wormholes and black holes to time machines. 
The first implication of the fact that spacetime need not be flat which will be 
important to the adventures of the Enterprise is that time itself becomes an 
even more dynamic quantity than it was in special relativity. Time can flow at 
different rates for different observers even if they are not moving relative to 
each other. Think of the ticks of a clock as the ticks on a ruler made of 
rubber. If I were to stretch or bend the ruler, the spacing between the ticks 
would differ from point to point. If this spacing represents the ticks of a 
clock, then clocks located in different places can tick at different rates. In 
general relativity, the only way to "bend" the ruler is for a gravitational 
field to be present, which in turn requires the presence of matter. 
To translate this into more pragmatic terms: if I put a heavy iron ball near a 
clock, it should change the rate at which the clock ticks. Or more practical 
still, if I sleep with my alarm clock tucked next to my body's rest mass, I will 
be awakened a little later than I would otherwise, at least as far as the rest 
of the world is concerned. 
A famous experiment done in the physics laboratories at Harvard University in 
1960 first demonstrated that time can depend on where you are. Robert Pound and 
George Rebka showed that the frequency of gamma radiation measured at its 
source, in the basement of the building, differed from the frequency of the 
radiation when it was received 74 feet higher, on the building's roof (with the 
detectors having been carefully calibrated so that any observed difference would 
not be detector-related). The shift was an incredibly small amount about 1 part 
in a million billion. If each cycle of the gamma-ray wave is like the tick of an 
atomic clock, this experiment implies that a clock in the basement will appear 
to be running more slowly than an equivalent atomic clock on the roof. Time 
slows on the lower floor because this is closer to the Earth than the roof is, 
so the gravitational field, and hence the spacetime curvature, is larger there. 
As small as this effect was, it was precisely the value predicted by general 
relativity, assuming that spacetime is curved near the Earth. 
The second implication of curved space is perhaps even more exciting as far as 
space travel is concerned. If space is curved, then a straight line need not be 
the shortest distance between two points. Here's an example. Consider a circle 
on a piece of paper. Normally, the shortest distance between two points A and B 
located on opposite sides of the circle is given by the line connecting them 
through the center of the circle: 

 


If, instead, one were to travel around the circle to get from A to B, the 
journey would be about 1 1/2 times as long. However, let me draw this circle on 
a rubber sheet, and distort the central region: 

 


Now, when viewed in our three-dimensional perspective, it is clear that the 
journey from A to B taken through the center of the region will be much longer 
than that taken by going around the circle. Note that if we took a snapshot of 
this from above, so we would have only a two-dimensional perspective, the line 
from A to B through the center would look like a straight line. More relevant 
perhaps, if a tiny bug (or two-dimensional beings, of the type encountered by 
the Enterprise) were to follow the trajectory from A to B through the center by 
crawling along the surface of the sheet, this trajectory would appear to be 
straight. The bug would be amazed to find that the straight line through the 
center between A and B was no longer the shortest distance between these two 
points. If the bug were intelligent, it would be forced to the conclusion that 
the two-dimensional space it lived in was curved. Only by viewing the embedding 
of this sheet in the underlying three-dimensional space can we observe the 
curvature directly. 
Now, remember that we live within a four-dimensional spacetime that can be 
curved, and we can no more perceive the curvature of this space directly than 
the bug crawling on the surface of the sheet can detect the curvature of the 
sheet. I think you know where I am heading: If, in curved space, the shortest 
distance between two points need not be a straight line, then it might be 
possible to traverse what appears along the line of sight to be a huge distance, 
by finding instead a shorter route through curved spacetime. 
These properties I have described are the stuff that Star Trek dreams are made 
of. Of course, the question is: How many of these dreams may one day come true? 
 
WORMHOLES: FACT AND FANCY: The Bajoran wormhole in Deep Space Nine is perhaps 
the most famous wormhole in Star Trek, although there have been plenty of 
others, including the dangerous wormhole that Scotty could create by imbalancing 
the matter-antimatter mix in the Enterprise's warp drive; the unstable Barzan 
wormhole, through which a Ferengi ship was lost in the Next Generation episode 
"The Price"; and the temporal wormhole that the Voyager encountered in its 
effort to get back home from the far edge of the galaxy. 
The idea that gives rise to wormholes is exactly the one I just described. If 
spacetime is curved, then perhaps there are different ways of connecting two 
points so that the distance between them is much shorter than that which would 
be measured by traveling in a "straight line" through curved space. Because 
curved-space phenomena in four dimensions are impossible to visualize, we once 
again resort to a two-dimensional rubber sheet, whose curvature we can observe 
by embedding it in three-dimensional space. 
If the sheet is curved on large scales, one might imagine that it looks 
something like this: 
 
 



Clearly, if we were to poke a pencil down at A and stretch the sheet until we 
touched B, and then sewed together the two parts of the sheet, like so: 
we would create a path from A to B that was far shorter than the path leading 
around the sheet from one point to another. Notice also that the sheet appears 
flat near A and also near B. The curvature that brings these two points close 
enough together to warrant joining them by a tunnel is due to the global bending 
of the sheet over large distances. A little bug (even an intelligent one) at A, 
confined to crawl on the sheet, would have no idea that B was as "close" as it 
was, even if it could do some local experiments around A to check for a 
curvature of the sheet. 
As you have no doubt surmised, the tunnel connecting A and B in this figure is a 
two-dimensional analogue of a three-dimensional wormhole, which could, in 
principle, connect distant regions of space-time. As exciting as this 
possibility is, there are several deceptive aspects of the picture which I want 
to bring to your attention. In the first place, even though the rubber sheet is 
shown embedded in a three-dimensional space in order for us to "see" the 
curvature of the sheet, the curved sheet can exist without the three-dimensional 
space around it needing to exist. Thus, while a wormhole could exist joining A 
and B, there is no sense in which A and B are "close" without the wormhole being 
present. It is not as if one is free to leave the rubber sheet and move from A 
to B through the three-dimensional space in which the sheet is embedded. If the 
three-dimensional space is not there, the rubber sheet is all there is to the 
universe. 
Thus, imagine that you were part of an infinitely advanced civilization (but not 
as advanced as the omnipotent Q beings, who seem to transcend the laws of 
physics) that had the power to build wormholes in space. Your wormhole building 
device would effectively be like the pencil in the example I just gave. If you 
had the power to produce huge local curvatures in space, you would have to poke 
around blindly in the hope that somehow you could connect two regions of space 
that, until the instant a wormhole was established, would remain very distant 
from each other. In no way whatsoever would these two regions be close together 
until the wormhole produced a bridge. The bridge-building process itself is what 
changes the global nature of spacetime. 
Because of this, making a wormhole is not to be taken lightly. When Premier 
Bhavani of Barzan visited the Enterprise to auction off the rights to the Barzan 
wormhole, she exclaimed, "Before you is the first and only stable wormhole known 
to exist!" Alas, it wasn't stable; indeed, the only wormholes whose mathematical 
existence has been consistently established in the context of general relativity 
are transitory. Such wormholes are created as two microscopic "singularities" 
regions of spacetime where, the curvature becomes infinitely sharp find each 
other and momentarily join. However, in a time shorter than the time it would 
take a space traveler to pass through such a worm-hole, it closes up, leaving 
once again two disconnected singularities. The unfortunate explorer would be 
crushed to bits in one singularity or the other before being able to complete 
the voyage through the wormhole. 
The problem of how to keep the mouth of a wormhole open has been hideously 
difficult to resolve in mathematical detail, but is quite easily stated in 
physical terms: Gravity sucks! Any kind of normal matter or energy will tend to 
collapse under its own gravitational attraction unless something else stops it. 
Similarly, the mouth of a wormhole will pinch off in nothing flat under normal 
circumstances. 
So, the trick is to get rid of the normal circumstances. In recent years, the 
Caltech physicist Kip Thorne, among others, has argued that the only way to keep 
wormholes open is to thread them with "exotic material." By this is meant 
material that will be measured, at least by certain observers, to have 
"negative" energy. As you might expect (although naive expectations are 
notoriously suspect in general relativity), such material would tend to "blow" 
not "suck," as far as gravity is concerned. 
Not even a diehard trekker might be willing to suspend disbelief long enough to 
accept the idea of matter with "negative energy"; however, as noted, in curved 
space one's normal expectations are often suspect. When you compound this with 
the exotica forced upon us by the laws of quantum mechanics, which govern the 
behavior of matter on small scales, quite literally almost all bets are off. 
 
BLACK HOLES AND DR. HAWKING: Enter Stephen Hawking. He first became well known 
among physicists working on general relativity for his part in proving general 
theorems related to singularities in spacetime, and then, in the 1970s, for his 
remarkable theoretical discoveries about the behavior of black holes. These 
objects are formed from material that has collapsed so utterly that the local 
gravitational field at their surface prevents even light from escaping. 
Incidentally, the term "black hole," which has so captivated the popular 
imagination, was coined by the theoretical physicist John Archibald Wheeler of 
Princeton University, in the late fall of 1967. The date here is very 
interesting, because, as far as I can determine, the first Star Trek episode to 
refer to a black hole, which it called a "black star," was aired in 1967 before 
Wheeler ever used the term in public. When I watched this episode early in the 
preparation of this book, I found it amusing that the Star Trek writers had 
gotten the name wrong. Now I realize that they very nearly invented it! 
Black holes are remarkable objects for a variety of reasons. First, all black 
holes eventually hide a spacetime singularity at their center, and anything that 
falls into the black hole must inevitably encounter it. At such a singularityan 
infinitely curved "cusp" in spacetimethe laws of physics as we know them break 
down. The curvature near the singularity is so large over such a small region 
that the effects of gravity are governed by the laws of quantum mechanics. Yet 
no one has yet been able to write down a theory that consistently accommodates 
both general relativity (that is, gravity) and quantum mechanics. Star Trek 
writers correctly recognized this tension between quantum mechanics and gravity, 
as they usually refer to all spacetime singularities as "quantum singularities." 
One thing is certain, however: by the time the gravitational field at the center 
of a black hole reaches a strength large enough for our present picture of 
physics to break down, any ordinary physical object will be torn apart beyond 
recognition. Nothing could survive intact. 
You may notice that I referred to a black hole as "hiding" a singularity at its 
center. The reason is that at the outskirts of a black hole is a mathematically 
defined surface we call the "event horizon," which shields our view of what 
happens to objects that fall into the hole. Inside the event horizon, everything 
must eventually hit the ominous singularity. Outside the event horizon, objects 
can escape. While an observer unlucky enough to fall into a black hole will 
notice nothing special at all as he or she (soon to be "it") crosses the event 
horizon, an observer watching the process from far away sees something very 
different. Time slows down for the observer freely falling in the vicinity of 
the event horizon, relative to an observer located far away. As a result, the 
falling observer appears from the outside to slow down as he or she nears the 
event horizon. The closer the falling observer gets to the event horizon, the 
slower is his or her clock relative to the outside observer's. While it may take 
the falling observer a few moments (local time) to cross the event 
horizonwhere, I repeat, nothing special happens and nothing special sitsit 
will take an eternity as observed by someone on the outside. The infalling 
object appears to become frozen in time. 
Moreover, the light emitted by any infalling object gets harder and harder to 
see from the outside. As an object approaches the event horizon, the object gets 
dimmer and dimmer (because the observable radiation from it gets shifted to 
frequencies below the visible). Finally, even if you could see, from the 
outside, the object's transit of the event horizon (which you cannot, in any 
finite amount of time), the object would disappear completely once it passed the 
horizon, because any light it emitted would be trapped inside, along with the 
object. Whatever falls inside the event horizon is lost forever to the outside 
world. It appears that this lack of communication is a one-way street: an 
observer on the outside can send signals into the black hole, but no signal can 
ever be returned. 
For these reasons, the black holes encountered in Star Trek tend to produce 
impossible results. The fact that the event horizon is not a tangible object, 
but rather a mathematical marker that we impose on our description of a black 
hole to delineate the region inside from that outside, means that the horizon 
cannot have a "crack," as required by the crew of the Voyager when they 
miraculously escape from a black hole's interior. (Indeed, this notion is so 
absurd that it makes it onto my ten-best list of Star Trek mistakes described in 
the last chapter.) And the "quantum singularity life-forms" encountered by the 
crew of the Enterprise as they, and a nearby Romulan Warbird, travel backward 
and forward in time have a rather unfortunate nesting place for their young: 
apparently they place them inside natural black holes (which they incorrectly 
mistake the "artificial" quantum singularity inside the Romulan engine core 
for). This may be a safe nursery, but it must be difficult to retrieve your 
children afterward. I remind you that nothing inside a black hole can ever 
communicate with anything outside one. 
Nevertheless, black holes, for all their interesting properties, need not be 
that exotic. The only black holes we have any evidence for in the universe today 
result from the collapse of stars much more massive than the Sun. These 
collapsed objects are so dense that a teaspoon of material inside would weigh 
many tons. However, it is another remarkable property of black holes that the 
more massive they are, the less dense they need be when they form. For example, 
the density of the black hole formed by the collapse of an object 100 million 
times as massive as our Sun need only be equal to the density of water. An 
object of larger mass will collapse to form a black hole at a point when it is 
even less dense. If you keep on extrapolating, you will find that the density 
required to form a black hole with a mass equal to the mass of the observable 
universe would be roughly the same as the average density of matter in the 
universe! We may be living inside a black hole. 
In 1974, Stephen Hawking made a remarkable discovery about the nature of black 
holes. They aren't completely black! Instead, they will emit radiation at a 
characteristic temperature, which depends on their mass. While the nature of 
this radiation will give no information whatsoever on what fell into the black 
hole, the idea that radiation could be emitted from a black hole was 
nevertheless astounding, and appeared to violate a number of theoremssome of 
which Hawking had earlier provedholding that matter could only fall into black 
holes, not out of them. This remains true, except for the source of the 
black-hole radiation, which is not normal matter. Instead, it is empty space, 
which can behave quite exoticallyespecially in the vicinity of a black hole. 
Ever since the laws of quantum mechanics were made consistent with the special 
theory of relativity, shortly after the Second World War, we have known that 
empty space is not so empty. It is a boiling, bubbling sea of quantum 
fluctuations. These fluctuations periodically spit out elementary particle 
pairs, which exist for time intervals so short that we cannot measure them 
directly, and then disappear back into the vacuum from which they came. The 
uncertainty principle of quantum mechanics tells us that there is no way to 
directly probe empty space over such short time intervals and thus no way to 
preclude the brief existence of these so-called virtual particles. But although 
they cannot be measured directly, their presence does affect certain physical 
processes that we can measure, such as the rate and energy of transitions 
between certain energy levels in atoms. The predicted effect of virtual 
particles agrees with observations as well as any prediction known in physics. 
This brings us back to Hawking's remarkable result about black holes. Under 
normal circumstances, when a quantum fluctuation creates a virtual particle 
pair, the pair will annihilate and disappear back into the vacuum in a time 
short enough so that the violation of conservation of energy (incurred by the 
pair's creation from nothing) is not observable. However, when a virtual 
particle pair pops out in the curved space near a black hole, one of the 
particles may fall into the hole, and then the other can escape and be observed. 
This is because the particle that falls into the black hole can in principle 
lose more energy in the process than the amount required to create it from 
nothing. It thus contributes "negative energy" to the black hole, and the black 
hole's own energy is therefore decreased. This satisfies the energy-conservation 
law's balance-sheet, making up for the energy that the escaping particle is 
observed to have. This is how the black hole emits radiation. Moreover, as the 
black hole's own energy decreases bit by bit in this process, there is a 
concomitant decrease in its mass. Eventually, it may completely evaporate, 
leaving behind only the radiation it produced in its lifetime. 
Hawking and many others have gone beyond a consideration of quantum fluctuations 
of matter in a background curved space to something even more exotic and less 
well defined. If quantum mechanics applies not merely to matter and radiation 
but to gravity as well, then on sufficiently small scales quantum fluctuations 
in spacetime itself must occur. Unfortunately, we have no workable theory for 
dealing with such processes, but this has not stopped a host of tentative 
theoretical investigations of phenomena that might result. One of the most 
interesting speculations is that quantum mechanical processes might allow the 
spontaneous creation not just of particles but of whole new baby universes. The 
quantum mechanical formalism describing how this might occur is, at least 
mathematically, very similar to the wormhole solutions discovered in ordinary 
general relativity. Via such "Euclidean" wormholes, a temporary "bridge" is 
created, from which a new universe springs. The possibilities of Euclidean 
wormhole processes and baby universes are sufficiently exciting that quantum 
fluctuations were mentioned during Hawking's poker game with Einstein and Newton 
in the Next Generation episode "Descent."1 If the Star Trek writers were 
confused, they had a right to be. These issues are unfortunately currently very 
murky. Until we discover the proper mathematical framework to treat such quantum 
gravitational processes, all such discussions are shots in the dark. 
What is most relevant to us here is not the phenomenon of black-hole 
evaporation, or even baby universes, as interesting as they may be, but rather 
the discovery that quantum fluctuations of empty space can, at least in the 
presence of strong gravitational fields, become endowed with properties 
reminiscent of those required to hold open a worm-hole. The central question, 
which also has no definitive answer yet, is whether quantum fluctuations near a 
wormhole can behave sufficiently exotically to allow one to keep a wormhole 
open. 
(By the way, once again, I find the Star Trek writers remarkably prescient in 
their choice of nomenclature. The Bajoran and Barzan wormholes are said to 
involve "verteron" fields. I have no idea whether this name was plucked out of a 
hat or not. However, since virtual particlesthe quantum fluctuations in 
otherwise empty spaceare currently the best candidate for Kip Thorne's "exotic 
matter," I think the Star Trek writers deserve credit for their intuition, if 
that's what it was.) 
More generally, if quantum fluctuations in the vacuum can be exotic, is it 
possible that some other nonclassical configuration of matter and 
radiationlike, say, a warp core breach, or perhaps Scotty's "intermix" 
imbalance in the warp drivemight also fill the bill? Questions such as this 
remain unanswered. While by no means circumventing the incredible implausibility 
of stable wormholes in the real universe, they do leave open the larger question 
of whether wormhole travel is impossible or merely almost impossible. The 
wormhole issue is not just one of science fact versus science fiction: it is a 
key that can open doors which many would prefer to leave closed. 
 
TIME MACHINES REVISITED: Wormholes, as glorious as they would be for tunneling 
through vast distances in space, have an even more remarkable potential, 
glimpsed most recently in the Voyager episode "Eye of the Needle." In this 
episode, the Voyager crew discovered a small wormhole leading back to their own 
"alpha quadrant" of the galaxy. After communicating through it, they found to 
their horror that it led not to the alpha quadrant they knew and loved but to 
the alpha quadrant of a generation earlier. The two ends of the wormhole 
connected space at two different times! 
Well, this is another one of those instances in which the Voyager writers got it 
right. If wormholes exist, they can and will be time machines! This startling 
realization has grown over the last decade, as various theorists, for lack of 
anything more interesting to do, began to investigate the physics of wormholes a 
little more seriously. Worm-hole time machines are easy to design: perhaps the 
simplest example (due again to Kip Thorne) is to imagine a wormhole with one end 
fixed and the other end moving at a fast but sublight speed through a remote 
region of the galaxy. In principle, this is possible even if the length of the 
wormhole remains unchanged. In my earlier two-dimensional wormhole drawing, just 
drag the bottom half of the sheet to the left, letting space "slide" past the 
bottom mouth of the wormhole while this mouth stays fixed relative to the 
wormhole's other mouth: 

 


Because the bottom mouth of the wormhole will be moving with respect to the 
space in which it is situated, while the top mouth will not, special relativity 
tells us that clocks will tick at different rates at each mouth. On the other 
hand, if the length of the wormhole remains fixed, then as long as one is inside 
the wormhole the two ends appear to be at rest relative to each other. In this 
frame, clocks at either end should be ticking at the same rate. Now slide the 
bottom sheet back to where it used to be, so that the bottom mouth of the 
wormhole ends up back where it started relative to the background space. Let's 
say that this process takes a day, as observed by someone near the bottom mouth. 
But for an observer near the top mouth, this same process could appear to have 
taken ten days. If this second observer were to peer through the top mouth to 
look at the observer located near the bottom mouth, he would see on the wall 
calendar next to the observer a date nine days earlier! If he now decides to go 
through the worm-hole for a visit, he will travel backward in time. 
If stable wormholes exist, we must therefore concede that time machines are 
possible. We now return finally to Einstein's remarks early in the last chapter. 
Can time travel, and thus stable wormholes, and thus exotic matter with negative 
energy, be "excluded on physical grounds"? 
Wormholes are after all merely one example of time machines that have been 
proposed in the context of general relativity. Given our previous discussion 
about the nature of the theory, it is perhaps not so surprising that time travel 
becomes a possibility. Let's recall the heuristic description of Einstein's 
equations which I gave earlier: 
 
      Left-hand side
      {CURVATURE}=Right-hand side
      {Matter and Energy}

 
The left-hand side of this equation fixes the geometry of spacetime. The 
right-hand side fixes the matter and energy distribution. Generally we would 
ask: For a given distribution of matter and energy, what will be the resulting 
curvature of space? But we can also work backward: For any given geometry of 
space, including one with "closed timelike curves"that is, the "causality 
loops," which allow you to return to where you began in space and time, like the 
loop the Enterprise was caught in before, during, and after crashing into the 
Boze-manEinstein's equations tell you exactly what distribution of matter and 
energy must be present. So in principle you can design any kind of time-travel 
universe you want; Einstein's equations will tell you what matter and energy 
distribution is necessary. The key question then simply becomes: Is such a 
matter and energy distribution physically possible? 
We have already seen how this question arises in the context of wormholes. 
Stable wormholes require exotic matter with negative energy. Kurt Gdel's 
time-machine solution in genera! relativity involves a universe with constant 
uniform energy density and zero pressure which spins but does not expand. More 
recently, a proposed time machine involving "cosmic strings" was shown to 
require a negative-energy configuration. In fact, it was recently proved that 
any configuration of matter in general relativity which might allow time travel 
must involve exotic types of matter with negative energy as viewed by at least 
one observer. 
It is interesting that almost all the episodes in Star Trek involving time 
travel or temporal distortions also involve some catastrophic form of energy 
release, usually associated with a warp core breach. For example, the temporal 
causality loop in which the Enterprise was trapped resulted only after (although 
the concepts of "before" and "after" lose their meaning in a causality loop) a 
collision with the Bozeman, which caused the warp core to breach and thereby 
caused the destruction of the Enterprise, a series of events that kept repeating 
over and over, until finally in one cycle the crew managed to avoid the 
collision. The momentary freezing of time aboard the Enterprise, discovered by 
Picard, Data, Troi, and LaForge in the episode "Timescape," also appears to have 
been produced by a nascent warp core breach combined with a failure of the 
engine core aboard a nearby Romulan vessel. In "Time Squared," a vast "energy 
vortex" propelled Picard back in time. In the original example of Star Trek time 
travel, "The Naked Time," the Enterprise was thrown back three days following a 
warp core implosion. And the mammoth spacetime distortion in the final episode 
of The Next Generation, which travels backward in time and threatens to engulf 
the entire universe, was caused by the simultaneous explosion of three different 
temporal versions of the Enterprise, which converged at the same point in space. 

So, time travel in the real universe, as in the Star Trek universe, seems to 
hinge on the possibility of exotic configurations of matter. Could some 
sufficiently advanced alien civilization construct a stable wormhole? Or can we 
characterize all mass distributions that might lead to time travel and then 
exclude them, as a set, "on physical grounds," as Einstein might have wished? To 
date, we do not know the answer. Some specific time machinessuch as Gdel's, 
and the cosmic-string-based systemhave been shown to be unphysical. While 
wormhole time travel has yet to be definitively ruled out, preliminary 
investigations suggest that the quantum gravitational fluctuations themselves 
may cause wormholes to self-destruct before they could lead to time travel. 
Until we have a theory of quantum gravity, the final resolution of the issue of 
time travel is likely to remain unresolved. Nevertheless, several brave 
individuals, including Stephen Hawking, have already tipped their hand. Hawking 
is convinced that time machines are impossible, because of the obvious paradoxes 
that might result, and he has proposed a "chronology-protection conjecture," to 
wit: "The laws of physics do not allow the appearance of closed timelike 
curves." 
I am personally inclined to agree with Hawking in this case. Nevertheless, 
physics is not done by fiat. As I have stated earlier, general relativity often 
outwits our naive expectations. As a warning, I provide two historical 
precedents. Twice before (that I know of), eminent theorists have argued that a 
proposed phenomenon in general relativity should be dismissed because the laws 
of physics must forbid it: 
1. When the young astrophysicist Subrahmanyan Chandrasekhar proposed that 
stellar cores more massive than 1.4 times the mass of the Sun cannot, after 
burning all their nuclear fuel, settle down as white dwarfs but must continue to 
collapse due to gravity, the eminent physicist Sir Arthur Eddington dismissed 
the result in public, stating, "Various accidents may intervene to save the 
star, but I want more protection than that. I think there should be a law of 
nature to prevent a star from behaving in this absurd way!" At the time, much of 
the astrophysics community sided with Eddington. A half century later, 
Chandrasekhar shared the Nobel Prize for his insights, which have long since 
been verified. 
2. Slightly over 20 years after Eddington dismissed Chandrasekhar's claim, a 
remarkably similar event ocurred at a conference in Brussels. J. Robert 
Oppenheimer, the distinguished American theoretical physicist and father of the 
atomic bomb, had calculated that objects called neutron starsleft over after 
supernovae and even more dense than white dwarfscould not be larger than about 
twice the mass of the Sun without collapsing further to form what we would now 
call a black hole. The equally distinguished John Archibald Wheeler argued that 
this result was impossible, for precisely the reason Eddington had given for his 
earlier rejection of Chandrasekhar's claim: somehow the laws of physics must 
protect objects from such an absurd fate. Within a decade, Wheeler would 
completely capitulate and, ironically, would become known as the man who gave 
black holes their name. 
CHAPTER FOUR  DATA Ends the Game
 
For I dipt into the future, far as human eye could see, Saw the Vision of the 
world, and all the wonder that would be. 
From "Locksley Hall, " by Alfred Lord Tennyson (posted aboard the starship 
Voyager,) 
 
Whether or not the Star Trek future can include a stable worm-hole, and whether 
or not the Enterprise crew could travel back in time to nineteenth-century San 
Francisco, the real stakes in this cosmic poker game derive from one of the 
questions that led us to discuss curved spacetime in the first place: Is warp 
drive possible? For, barring the unlikely possibility that our galaxy is riddled 
with stable wormholes, it is abundantly clear from our earlier discussions that 
without something like it, most of the galaxy will always remain beyond our 
reach. It is finally time to address this vexing question. The answer is a 
resounding "Maybe!" 
Once again we are guided by the linguistic perspicacity of the Star Trek 
writers. I have described how no rocket propulsion mechanism can ever get around 
the three roadblocks to interstellar travel set up by special relativity: First, 
nothing can travel faster than the speed of light in empty space. Second, 
objects that travel near the speed of light will have clocks that are slowed 
down. Third, even if a rocket could accelerate a spacecraft to near the speed of 
light, the fuel requirements would be prohibitive. 
The idea is not to use any sort of rocket at all for propulsion, but instead to 
use spacetime itselfby warping it. General relativity requires us to be a 
little more precise in our statements about motion. Instead of saying that 
nothing can travel faster than the speed of light, we must state that nothing 
can travel locally any faster than the speed of light. This means that nothing 
can travel faster than the speed of light with respect to local distance 
markers. However, if spacetime is curved, local distance markers need not be 
global ones. 
Let me use the universe itself as an example. Special relativity tells me that 
all observers who are at rest with respect to their local surroundings will have 
clocks that tick at the same rate. Thus, as I move throughout the universe, I 
can periodically stop and place clocks at regular intervals in space and expect 
that they will all keep the same time. General relativity does not change this 
result. Clocks that are locally at rest will all keep the same time. However, 
general relativity allows spacetime itself to expand. Objects on opposite sides 
of the observable universe are flying apart at almost the speed of light, yet 
they remain at rest relative to their local surroundings. In fact, if the 
universe is expanding uniformly and if it is large enoughboth of which appear 
to be the casethere exist objects we cannot yet see which are at this very 
moment moving away from us far faster than the speed of light, even though any 
civilizations in these far reaches of the universe can be locally at rest with 
respect to their surroundings. 
The curvature of space therefore produces a loophole in special relativistic 
argumentsa loophole large enough to drive a Federation starship through. If 
spacetime itself can be manipulated, objects can travel locally at very slow 
velocities, yet an accompanying expansion or contraction of space could allow 
huge distances to be traversed in short time intervals. We have already seen how 
an extreme manipulationnamely, cutting and pasting distant parts of the 
universe together with a wormholemight create shortcuts through space-time. 
What is argued here is that even if we do not resort to this surgery, 
faster-than-light travel might globally be possible, even if it is not locally 
possible. 
A proof in principle of this idea was recently developed by a physicist in 
Wales, Miguel Alcubierre, who for fun decided to explore whether a consistent 
solution in general relativity could be derived which would correspond to "warp 
travel." He was able to demonstrate that it was possible to tailor a spacetime 
configuration wherein a spacecraft could travel between two points in an 
arbitrarily short time. Moreover, throughout the journey the spacecraft could be 
moving with respect to its local surroundings at speeds much less than the speed 
of light, so that clocks aboard the spacecraft would remain synchronized with 
those at its place of origin and at its destination. General relativity appears 
to allow us to have our cake and eat it too. 
The idea is straightforward. If spacetime can locally be warped so that it 
expands behind a starship and contracts in front of it, then the craft will be 
propelled along with the space it is in, like a surfboard on a wave. The craft 
will never travel locally faster than the speed of light, because the light, 
too, will be carried along with the expanding wave of space. 
One way to picture what is happening is to imagine yourself on the starship. If 
space suddenly expands behind you by a huge amount, you will find that the 
starbase you just left a few minutes ago is now many light-years away. 
Similarly, if space contracts in front of you, you will find that the starbase 
you are heading for, which formerly was a few light-years away, is now close to 
you, within reach by normal rocket propulsion in a matter of minutes. 
It is also possible to arrange the geometry of spacetime in this solution so 
that the huge gravitational fields necessary to expand and contract space in 
this way are never large near the ship or any of the star-bases. In the vicinity 
of the ship and the bases, space can be almost flat, and therefore clocks on the 
ship and the starbases remain synchronized. Somewhere in between the ship and 
the bases, the tidal forces due to gravity will be immense, but that's OK as 
long as we aren't located there. 
This scenario must be what the Star Trek writers intended when they invented 
warp drive, even if it bears little resemblance to the technical descriptions 
they have provided. It fulfills all the requirements we listed earlier for 
successful controlled intergalactic space travel: (1) faster-than-light travel, 
(2) no time dilation, and (3) no resort to rocket propulsion. Of course, we have 
begged a pretty big question thus far. By making spacetime itself dynamical, 
general relativity allows the creation of "designer spacetimes," in which almost 
any type of motion in space and time is possible. However, the cost is that the 
theory relates these spacetimes to some underlying distribution of matter and 
energy. Thus, for the desired spacetime to be "physical," the underlying 
distribution of matter and energy must be attainable. I will return to this 
question shortly. 
First, however, the wonder of such "designer spacetimes" is that they allow us 
to return to Newton's original challenge and to create iner-tial dampers and 
tractor beams. The idea is identical to warp drive. If spacetime around the ship 
can be warped, then objects can move apart or together without experiencing any 
sense of local acceleration, which you will recall was Newton's bane. To avoid 
the incredible accelerations required to get to impulse sublight speeds, one 
must resort to the same spacetime shenanigans as one does to travel at warp 
speeds. The distinction between impulse drive and warp drive is thus diminished. 
Similarly, to use a tractor beam to pull a heavy object like a planet, one 
merely has to expand space on the other side of the planet and contract it on 
the near side. Simple! 
Warping space has other advantages as well. Clearly, if spacetime becomes 
strongly curved in front of the Enterprise, then any light rayor phaser beam, 
for that matterwill be deflected away from the ship. This is doubtless the 
principle behind deflector shields. Indeed, we are told that the deflector 
shields operate by "coherent graviton emission." Since gravitons are by 
definition particles that transmit the force of gravity, then "coherent graviton 
emission" is nothing other than the creation of a coherent gravitational field. 
A coherent gravitational field is, in modern parlance, precisely what curves 
space! So once again the Star Trek writers have at least settled upon the right 
language. 
I would imagine that the Romulans' cloaking device might operate in a similar 
manner. In fact, an Enterprise that has its deflector shield deployed should be 
very close to a cloaked Enterprise. After all, the reason we see something that 
doesn't shine of its own accord is that it reflects light, which travels back to 
us. Cloaking must somehow warp space so that incident light rays bend around a 
Warbird instead of being reflected from it. The distinction between this and 
deflecting light rays away from the Enterprise is thus pretty subtle. In this 
connection, a question that puzzled many trekkers until the Next Generation 
episode "The Pegasus" aired was, Why didn't the Federation employ cloaking 
technology? It would certainly seem, in light of the above, that any 
civilization that could develop deflector shields could develop cloaking 
devices. And as we learned in "The Pegasus," the Federation was limited in its 
development of cloaking devices by treaty rather than by technology. (Indeed, as 
became evident in "All Good Things ...," the last episode of the Next 
Generation, the Federation eventually seems to have allowed cloaking on 
starships.) 
Finally, given this general-relativistic picture of warp drive, warp speeds take 
on a somewhat more concrete meaning. The warp speed would be correlated to the 
contraction and expansion factor of the spatial volume in front of and behind 
the ship. Warp-speed conventions have never been particularly stable: between 
the first and second series, Gene Roddenberry apparently decided that warp 
speeds should be recalibrated so that nothing could exceed warp 10. This meant 
that warp speed could not be a simple logarithmic scale, with, say, warp 10 
being 210 = 1024 x light speed. According to the Next Generation Technical 
Manual, warp 9.6, which is the highest normal rated speed for the Enterprise-D, 
is 1909 x the speed of light, and warp 10 is infinite. It is interesting to note 
that in spite of this recalibration, objects (such as the Borg cube) are 
periodically sighted which go faster than warp 10, so I suppose one shouldn't 
concern oneself unduly about understanding the details. 
Well, so much for the good news.... 
Having bought into warp drive as a nonimpossibility (at least in principle), we 
finally have to face up to the consequences for the right-hand side of 
Einstein's equationsnamely, for the distribution of matter and energy required 
to produce the requisite curvature of space-time. And guess what? The situation 
is almost worse than it was for wormholes. Observers traveling at high speed 
through a wormhole can measure a negative energy. For the kind of matter needed 
to produce a warp drive, even an observer at rest with respect to the 
star-shipthat is, someone on boardwill measure a negative energy. 
This result is not too surprising. At some level, the exotic solutions of 
general relativity required to keep wormholes open, allow time travel, and make 
warp drive possible all imply that on some scales matter must gravitationally 
repel other matter. There is a theorem in general relativity that this condition 
is generally equivalent to requiring the energy of matter to be negative for 
some observers. 
What is surprising, perhaps, is the fact, mentioned earlier, that quantum 
mechanics, when combined with special relativity, implies that at least on 
microscopic scales the local distribution of energy can be negative. Indeed, as 
I noted in chapter 3, quantum fluctuations often have this property. The key 
question, which remains unanswered to date, is whether the laws of physics as we 
know them will allow matter to have this property on a macroscopic scale. It is 
certainly true that currently we haven't the slightest idea of how one could 
create such matter in any physically realistic way. 
However, ignore for the moment the potential obstacles to creating such 
material, and suppose that it will someday be possible to create exotic matter, 
by using some sophisticated quantum mechanical engineering of matter or of empty 
space. Even so, the energy requirements to do any of the remarkable playing 
around with spacetime described here would likely make the power requirement for 
accelerating to impulse speed seem puny. Consider the mass of the Sun, which is 
about a million times the mass of the Earth. The gravitational field at the 
surface of the Sun is sufficient to bend light by less than 1/1000 of a degree. 
Imagine the extreme gravitational fields that would have to be generated near a 
starship to deflect an oncoming phaser beam by 90! (This is one of the many 
reasons why the famous "slingshot effect" first used in the classic episode 
"Tomorrow Is Yesterday" to propel the Enterprise backward in time, again in Star 
Trek IV: The Voyage Home, and also mentioned in the Next Generation episode 
"Time Squared"is completely impossible. The gravitational field near the 
surface of the Sun is minuscule in terms of the kind of gravitational effects 
required to perturb spacetime in the ways we have discussed here.) One way to 
estimate how much energy would have to be generated is to imagine producing a 
black hole the size of the Enterprisesince certainly a black hole of this size 
would produce a gravitational field that could significantly bend any light beam 
that traveled near it. The mass of such a black hole would be about 10 percent 
of the mass of the Sun. Expressed in energy units, it would take more than the 
total energy produced by the Sun during its entire lifetime to generate such a 
black hole. 
So where do we stand at the end of this game? We know enough about the nature of 
spacetime to describe explicitly how one might, at least in principle, utilize 
curved space to achieve many of the essentials of interstellar space travel  la 
Star Trek. We know that without such exotic possibilities we will probably never 
voyage throughout the galaxy. On the other hand, we have no idea whether the 
physical conditions needed to achieve any of these things are realizable in 
practice or even allowed in principle. Finally, even if they were, it is clear 
that any civilization putting these principles into practice would have to 
harness energies vastly in excess of anything imaginable today. 
I suppose one might take the optimistic view that these truly remarkable wonders 
are at least not a priori impossible. They merely hinge on one remote 
possibility: the ability to create and sustain exotic matter and energy. There 
is reason for hope, but I must admit that I remain skeptical. Like my colleague 
Stephen Hawking, I believe that the paradoxes involved in round-trip time travel 
rule it out for any sensible physical theory. Since virtually the same 
conditions of energy and matter are required for warp travel and deflector 
shields, I'm not anticipating them eitherthough I have been wrong before. 
Nevertheless, I am still optimistic. What to me is really worth celebrating is 
the remarkable body of knowledge that has brought us to this fascinating 
threshold. We live in a remote corner of one of 100 billion galaxies in the 
observable universe. And like insects on a rubber sheet, we live in a universe 
whose true form is hidden from direct view. Yet in the course of less than 
twenty generationsfrom Newton to todaywe have utilized the simple laws of 
physics to illuminate the depths of space and time. It is likely that we may 
never be able to board ships headed for the stars, but even imprisoned on this 
tiny blue planet we have been able to penetrate the night sky to reveal 
remarkable wonders, and there is no doubt more to come. If physics cannot give 
us what we need to roam the galaxy, it is giving us what we need to bring the 
galaxy to us. 
SECTION TWO - Matter Matter Everywhere - In which the reader explores 
transporter beams, warp drives, dilithium crystals, matter-antimatter engines, 
and the holodeck 
CHAPTER FIVE - Atoms or Bits
"Reg, transporting really is the safest way to travel."
Geordi LaForge to Lieutenant Reginald Barclay, in "Realm of Fear" 
 
Life imitates art. Lately, I keep hearing the same question: "Atoms or 
bitswhere does the future lie?" Thirty years ago, Gene Roddenberry dealt with 
this same speculation, driven by another imperative. He had a beautiful design 
for a starship, with one small problem: like a penguin in the water, the 
Enterprise could glide smoothly through the depths of space, but like a penguin 
on the ground it clearly would have trouble with its footing if it ever tried to 
land. More important perhaps, the meager budget for a weekly television show 
precluded landing a huge starship every week. 
How then to solve this problem? Simple: make sure the ship would never need to 
land. Find some other way to get the crew members from the ship to a planet's 
surface. No sooner could you say, "Beam me up" than the transporter was born. 
Perhaps no other piece of technology, save for the warp drive, so colors every 
mission of every starship of the Federation. And even those who have never 
watched a Star Trek episode recognize the magic phrase on the preceding page. It 
has permeated our popular culture. I recently heard about a young man who, while 
inebriated, drove through a red light and ran into a police cruiser that 
happened to be lawfully proceeding through the intersection. At his hearing, he 
was asked if he had anything to say. In well-founded desperation, he replied, 
"Yes, your honor," stood up, took out his wallet, flipped it open, and muttered 
into it, "Beam me up, Scotty!" 
The story is probably apochryphal, but it is testimony to the impact that this 
hypothetical technology has had on our culturean impact all the more remarkable 
given that probably no single piece of science fiction technology aboard the 
Enterprise is so utterly implausible. More problems of practicality and 
principle would have to be overcome to create such a device than you might 
imagine. The challenges involve the whole spectrum of physics and mathematics, 
including information theory, quantum mechanics, Einstein's relation between 
mass and energy, elementary particle physics, and more. 
Which brings me to the atoms versus bits debate. The key question the 
transporter forces us to address is the following: Faced with the task of 
moving, from the ship to a planet's surface, roughly 1028 (1 followed by 28 
zeroes) atoms of matter combined in a complex pattern to make up an individual 
human being, what is the fastest and most efficient way to do it? This is a very 
timely question, because we are facing exactly the same quandary as we consider 
how best to disseminate the complex pattern of roughly 1026 atoms in an average 
paperback book. A potentially revolutionary concept, at least so claimed by 
various digital-media gurus, is that the atoms themselves are often secondary. 
What matters more are the bits. 
Consider, for example, a library book. A library buys one copyor, for some 
lucky authors, several copiesof a book, which it stores and lends out for use 
by one individual at a time. However, in a digital library the same information 
can be stored as bits. A bit is a 1 or a 0, which is combined in groups of 
eight, called bytes, to represent words or numbers. This information is stored 
in the magnetic memory cores of computers, in which each bit is represented as 
either a magnetized (1) or unmagnetized (0) region. Now an arbitrarily large 
number of users can access the same memory location on a computer at essentially 
the same time, so in a digital library every single person on Earth who might 
otherwise have to buy a book can read it from a single source. Clearly, in this 
case, having on hand the actual atoms that make up the book is less significant, 
and certainly less efficient, than storing the bits (although it will play havoc 
with authors' royalties). 
So, what about people? If you are going to move people around, do you have to 
move their atoms or just their information? At first you might think that moving 
the information is a lot easier; for one thing, information can travel at the 
speed of light. However, in the case of people, you have two problems you don't 
have with books: first, you have to extract the information, which is not so 
easy, and then you have to recombine it with matter. After all, people, unlike 
books, require the atoms. 
The Star Trek writers seem never to have got it exactly clear what they want the 
transporter to do. Does the transporter send the atoms and the bits, or just the 
bits? You might wonder why I make this point, since the Next Generation 
Technical Manual describes the process in detail: First the transporter locks on 
target. Then it scans the image to be transported, "dematerializes" it, holds it 
in a "pattern buffer" for a while, and then transmits the "matter stream," in an 
"annular confinement beam," to its destination. The transporter thus apparently 
sends out the matter along with the information. 
The only problem with this picture is that it is inconsistent with what the 
transporter sometimes does. On at least two well-known occasions, the 
transporter has started with one person and beamed up two. In the famous classic 
episode "The Enemy Within," a transporter malfunction splits Kirk into two 
different versions of himself, one good and one evil. In a more interesting, and 
permanent, twist, in the Next Generation episode "Second Chances," we find out 
that Lieutenant Riker was earlier split into two copies during transportation 
from the planet Nervala IV to the Potemkin. One version returned safely to the 
Potemkin and one was reflected back to the planet, where he lived alone for 
eight years. 
If the transporter carries both the matter stream and the information signal, 
this splitting phenomenon is impossible. The number of atoms you end up with has 
to be the same as the number you began with. There is no possible way to 
replicate people in this manner. On the other hand, if only the information were 
beamed up, one could imagine combining it with atoms that might be stored aboard 
a star-ship and making as many copies as you wanted of an individual. 
A similar problem concerning the matter stream faces us when we consider the 
fate of objects beamed out into space as "pure energy." For example, in the Next 
Generation episode "Lonely among Us," Picard chooses at one point to beam out as 
pure energy, free from the constraints of matter. After this proves a dismal and 
dangerous experience, he manages to be retrieved, and his corporeal form is 
restored from the pattern buffer. But if the matter stream had been sent out 
into space, there would have been nothing to restore at the end. 
So, the Star Trek manual notwithstanding, I want to take an agnostic viewpoint 
here and instead explore the myriad problems and challenges associated with each 
possibility: transporting the atoms or the bits. 
 
WHEN A BODY HAS NO BODY: Perhaps the most fascinating question about beamingone 
that is usually not even addressedis, What comprises a human being? Are we 
merely the sum of all our atoms? More precisely, if I were to re-create each 
atom in your body, in precisely the same chemical state of excitation as your 
atoms are in at this moment, would I produce a functionally identical person who 
has exactly all your memories, hopes, dreams, spirit? There is every reason to 
expect that this would be the case, but it is worth noting that it flies in the 
face of a great deal of spiritual belief about the existence of a "soul" that is 
somehow distinct from one's body. What happens when you die, after all? Don't 
many religions hold that the "soul" can exist after death? What then happens to 
the soul during the transport process? In this sense, the transporter would be a 
wonderful experiment in spirituality. If a person were beamed aboard the 
Enterprise and remained intact and observably unchanged, it would provide 
dramatic evidence that a human being is no more than the sum of his or her 
parts, and the demonstration would directly confront a wealth of spiritual 
beliefs. 
For obvious reasons, this issue is studiously avoided in Star Trek. However, in 
spite of the purely physical nature of the dematerialization and transport 
process, the notion that some nebulous "life force" exists beyond the confines 
of the body is a constant theme in the series. The entire premise of the second 
and third Star Trek movies, The Wrath of Khan and The Search for Spock, is that 
Spock, at least, has a "katra" a living spiritwhich can exist apart from the 
body. More recently, in the Voyager series episode "Cathexis," the "neural 
energy"akin to a life forceof Chakotay is removed and wanders around the ship 
from person to person in an effort to get back "home." 
I don't think you can have it both ways. Either the "soul," the "katra," the 
"life force," or whatever you want to call it is part of the body, and we are no 
more than our material being, or it isn't. In an effort not to offend religious 
sensibilities, even a Vulcan's, I will remain neutral in this debate. 
Nevertheless, I thought it worth pointing out before we forge ahead that even 
the basic premise of the transporterthat the atoms and the bits are all there 
isshould not be taken lightly. 
 
THE PROBLEM WITH BITS: Many of the problems I will soon discuss could be avoided 
if one were to give up the requirement of transporting the atoms along with the 
information. After all, anyone with access to the Internet knows how easy it is 
to transport a data stream containing, say, the detailed plans for a new car, 
along with photographs. Moving the actual car around, however, is nowhere near 
as easy. Nevertheless, two rather formidable problems arise even in transporting 
the bits. The first is a familiar quandary, faced, for example, by the last 
people to see Jimmy Hoffa alive: How are we to dispose of the body? If just the 
information is to be transported, then the atoms at the point of origin must be 
dispensed with and a new set collected at the reception point. This problem is 
quite severe. If you want to zap 1028 atoms, you have quite a challenge on your 
hands. Say, for example, that you simply want to turn all this material into 
pure energy. How much energy would result? Well, Einstein's formula E = mc2 
tells us. If one suddenly transformed 50 kilograms (a light adult) of material 
into energy, one would release the energy equivalent of somewhere in excess of a 
thousand 1-megaton hydrogen bombs. It is hard to imagine how to do this in an 
environmentally friendly fashion. 
There is, of course, another problem with this procedure. If it is possible, 
then replicating people would be trivial. Indeed, it would be much easier than 
transporting them, since the destruction of the original subject would then not 
be necessary. Replication of inanimate objects in this manner is something one 
can live with, and indeed the crew members aboard starships do seem to live with 
this. However, replicating living human beings would certainly be cause for 
trouble ( la Riker in "Second Chances"). Indeed, if recombinant DNA research 
today has raised a host of ethical issues, the mind boggles at those which would 
be raised if complete individuals, including memory and personality, could be 
replicated at will. People would be like computer programs, or drafts of a book 
kept on disk. If one of them gets damaged or has a bug, you could simply call up 
a backup version. 
 
OK, KEEP THE ATOMS: The preceding arguments suggest that on both practical and 
ethical grounds it might be better to imagine a transporter that carries a 
matter stream along with the signal, just as we are told the Star Trek 
transporters do. The problem then becomes, How do you move the atoms? Again, the 
challenge turns out to be energetics, although in a somewhat more subtle way. 
What would be required to "dematerialize" something in the transporter? To 
answer this, we have to consider a little more carefully a simpler question: 
What is matter? All normal matter is made up of atoms, which are in turn made up 
of very dense central nuclei surrounded by a cloud of electrons. As you may 
recall from high school chemistry or physics, most of the volume of an atom is 
empty space. The region occupied by the outer electrons is about ten thousand 
times larger than the region occupied by the nucleus. 
Why, if atoms are mostly empty space, doesn't matter pass through other matter? 
The answer to this is that what makes a wall solid is not the existence of the 
particles but of the electric fields between the particles. My hand is stopped 
from going through my desk when I slam it down primarily because of the electric 
repulsion felt by the electrons in the atoms in my hand due to the presence of 
the electrons in the atoms of the desk and not because of the lack of available 
space for the electrons to move through. 
These electric fields not only make matter corporeal, in the sense of stopping 
objects from passing through one another, but they also hold the matter 
together. To alter this normal situation, one must therefore overcome the 
electric forces between atoms. Overcoming these forces will require work, which 
takes energy. Indeed, this is how all chemical reactions work. The configuration 
of individual sets of atoms and their binding to one another are altered through 
the exchange of energy. For example, if one injects some energy into a mixture 
of ammonium nitrate and fuel oil, the molecules of the two materials can 
rearrange, and in the process the "binding energy" holding the original 
materials can be released. This release, if fast enough, will cause a large 
explosion. 
The binding energy between atoms is, however, minuscule compared to the binding 
energy of the particlesprotons and neutrons that make up the incredibly dense 
nuclei of atoms. The forces holding these particles together in a nucleus result 
in binding energies that are millions of times stronger than the atomic binding 
energies. Nuclear reactions therefore release significantly more energy than 
chemical reactions, which is why nuclear weapons are so powerful. 
Finally, the binding energy that holds together the elementary particles, called 
quarks, which make up the protons and neutrons themselves is yet larger than 
that holding together the protons and neutrons in nuclei. In fact, it is 
currently believedbased on all calculations we can perform with the theory 
describing the interactions of quarks that it would take an infinite amount of 
energy to completely separate the quarks making up each proton or neutron. 
Based on this argument, you might expect that breaking matter completely apart 
into quarks, its fundamental constituents, would be impossibleand it is, at 
least at room temperature. However, the same theory that describes the 
interactions of quarks inside protons and neutrons tells us that if we were to 
heat up the nuclei to about 1000 billion degrees (about a million times hotter 
than the temperature at the core of the Sun), then not only would the quarks 
inside lose their binding energies but at around this temperature matter will 
suddenly lose almost all of its mass. Matter will turn into radiationor, in the 
language of our transporter, matter will dematerialize. 
So, all you have to do to overcome the binding energy of matter at its most 
fundamental level (indeed, at the level referred to in the Star Trek technical 
manual) is to heat it up to 1000 billion degrees. In energy units, this implies 
providing about 10 percent of the rest mass of protons and neutrons in the form 
of heat. To heat up a sample the size of a human being to this level would 
require therefore, about 10 percent of the energy needed to annihilate the 
materialor the energy equivalent of a hundred 1-megaton hydrogen bombs. 
One might suggest, given this daunting requirement, that the scenario I have 
just described is overkill. Perhaps we don't have to break down matter to the 
quark level. Perhaps a dematerialization at the proton and neutron level, or 
maybe even the atomic level, is sufficient for the purposes of the transporter. 
Certainly the energy requirements in this case would be vastly less, even if 
formidable. Unfortunately, hiding this problem under the rug exposes one that is 
more severe. For once you have the matter stream, made now of individual protons 
and neutrons and electrons, or perhaps whole atoms, you have to transport 
itpresumably at a significant fraction of the speed of light. 
Now, in order to get particles like protons and neutrons to move near the speed 
of light, one must give them an energy comparable to their rest-mass energy. 
This turns out to be about ten times larger than the amount of energy required 
to heat up and "dissolve" the protons into quarks. Nevertheless, even though it 
takes more energy per particle to accelerate the protons to near light speed, 
this is still easier to accomplish than to deposit and store enough energy 
inside the protons for long enough to heat them up and dissolve them into 
quarks. This is why today we can build, albeit at great cost, enormous particle 
acceleratorslike Fermilab's Tevatron, in Batavia, Illinoiswhich can accelerate 
individual protons up to more than 99.9 percent of the speed of light but we 
have not yet managed to build an accelerator that can bombard protons with 
enough energy to "melt" them into their constituent quarks. In fact, it is one 
of the goals of physicists designing the next generation of large 
acceleratorsincluding one device being built at Brookhaven National Laboratory, 
on Long Islandto actually achieve this "melting" of matter. 
Yet again I am impressed with the apt choice of terminology by the Star Trek 
writers. The melting of protons into quarks is what we call in physics a phase 
transition. And lo and behold, if one scours the Next Generation Technical 
Manual for the name of the transporter instruments that dematerialize matter, 
one finds that they are called "phase transition coils." 
So the future designers of transporters will have a choice. Either they must 
find an energy source that will temporarily produce a power that exceeds the 
total power consumed on the entire Earth today by a factor of about 10,000, in 
which case they could make an atomic "matter stream" capable of moving along 
with the information at near the speed of light, or they could reduce the total 
energy requirements by a factor of 10 and discover a way to heat up a human 
being instantaneously to roughly a million times the temperature at the center 
of the Sun. 
 
IF THIS IS THE INFORMATION SUPERHIGHWAY, WE'D BETTER GET IN THE FAST LANE: As I 
write this on my Power PC-based home computer, I marvel at the speed with which 
this technology has developed since I bought my first Macintosh a little over a 
decade ago. I remember that the internal memory in that machine was 128 
kilobytes, as opposed to the 16 megabytes in my current machine and the 128 
megabytes in the fast workstation I have in my office in Case Western Reserve's 
Physics Department. Thus, in a decade my computer internal-memory capabilities 
have increased by a factor of 1000! This increase has been matched by an 
increase in the capacity of my hard-drive memory. My first machine had no hard 
drive at all and thus had to work from floppy disks, which held 400 kilobytes of 
information. My present home machine has a 500-megabyte hard driveagain, an 
increase of more than a factor of 1000 in my storage capabilities. The speed of 
my home system has also greatly increased in the last decade. For doing actual 
detailed numerical calculations, I estimate that my present machine is almost a 
hundred times faster than my first Macintosh. My office workstation is perhaps 
ten times faster still, performing close to half a billion instructions per 
second! 
Even at the cutting edge, the improvement has been impressive. The fastest 
computers used for general-purpose computing have increased in speed and memory 
capability by a factor of about 100 in the past decade. And I am not including 
here computers built for special-purpose work: these little marvels can have 
effective speeds exceeding tens of billions of instructions per second. In fact, 
it has been shown that in principle certain special-purpose devices must be 
built using biological, DNA-based systems, which could be orders of magnitude 
faster. 
One might wonder where all this is heading, and whether we can extrapolate the 
past rapid growth to the future. Another valid question is whether we need to 
keep up this pace. I find already that the rate-determining step in the 
information superhighway is the end user. We can assimilate only so much 
information. Try surfing the Internet for a few hours, if you want a graphic 
example of this. I often wonder why, with the incredible power at my disposal, 
my own productivity has not increased nearly as dramatically as my computer's. I 
think the answer is clear. I am not limited by my computer's capabilities but by 
my own capabilities. It has been argued that for this reason computing machines 
could be the next phase of human evolution. It is certainly true that Data, even 
without emotions, is far superior to his human crewmates in most respects. And, 
as determined in "The Measure of a Man," he is a genuine life-form. 
But I digress. The point of noting the growth of computer capability in the last 
decade is to consider how it compares with what we would need to handle the 
information storage and retrieval associated with the transporter. And of 
course, it doesn't come anywhere close. 
Let's make a simple estimate of how much information is encoded in a human body. 
Start with our standard estimate of 1028 atoms. For each atom, we first must 
encode its location, which requires three coordinates (the x, y, and z 
positions). Next, we would have to record the internal state of each atom, which 
would include things like which energy levels are occupied by its electrons, 
whether it is bound to a nearby atom to make up a molecule, whether the molecule 
is vibrating or rotating, and so forth. Let's be conservative and assume that we 
can encode all the relevant information in a kilobyte of data. (This is roughly 
the amount of information on a double-spaced typewritten page.) That means we 
would need roughly 1028 kilobytes to store a human pattern in the pattern 
buffer. I remind you that this is a 1 followed by 28 zeros. 
Compare this with, say, the total information stored in all the books ever 
written. The largest libraries contain several million volumes, so let's be very 
generous and say that there are a billion different books in existence (one 
written for every five people now alive on the planet). Say each book contains 
the equivalent of a thousand typewritten pages of information (again on the 
generous side)or about a megabyte. Then all the information in all the books 
ever written would require about 1012, or about a million million, kilobytes of 
storage. This is about sixteen orders of magnitudeor about one ten-millionth of 
a billionthsmaller than the storage capacity needed to record a single human 
pattern! When numbers get this large, it is difficult to comprehend the enormity 
of the task. Perhaps a comparison is in order. The storage requirements for a 
human pattern are ten thousand times as large, compared to the information in 
all the books ever written, as the information in all the books ever written is 
compared to the information on this page. 
Storing this much information is, in an understatement physicists love to use, 
nontrivial. At present, the largest commercially available single hard disks 
store about 10 gigabytes, or 10,000 thousand megabytes, of information. If each 
disk is about 10 cm thick, then if we stacked all the disks currently needed to 
store a human pattern on top of one another, they would reach a third of the way 
to the center of the galaxyabout 10,000 light-years, or about 5 years' travel 
in the Enterprise at warp 9! 
Retrieving this information in real time is no less of a challenge. The fastest 
digital information transfer mechanisms at present can move somewhat less than 
about 100 megabytes per second. At this rate, it would take about 2000 times the 
present age of the universe (assuming an approximate age of 10 billion years) to 
write the data describing a human pattern to tape! Imagine then the dramatic 
tension: Kirk and McCoy have escaped to the surface of the penal colony at Rura 
Penthe. You don't have even the age of the universe to beam them back, but 
rather just seconds to transfer a million billion billion megabytes of 
information in the time it takes the jailor to aim his weapon before firing. 
I think the point is clear. This task dwarfs the ongoing Human Genome Project, 
whose purpose is to scan and record the complete human genetic code contained in 
microscopic strands of human DNA. This is a multibillion-dollar endeavor, being 
carried out over at least a decade and requiring dedicated resources in many 
laboratories around the world. So you might imagine that I am mentioning it 
simply to add to the transporter-implausibility checklist. However, while the 
challenge is daunting, I think this is one area that could possibly be up to 
snuff in the twenty-third century. My optimism stems merely from extrapolating 
the present growth rate of computer technology. Using my previous yardstick of 
improvement in storage and speed by a factor of 100 each decade, and dividing it 
by 10 to be conservativeand given that we are about 21 powers of 10 short of 
the mark nowone might expect that 210 years from now, at the dawn of the 
twenty-third century, we will have the computer technology on hand to meet the 
information-transfer challenge of the transporter. 
I say this, of course, without any idea of how. It is clear that in order to be 
able to store in excess of 1028 kilobytes of information in any human-scale 
device, each and every atom of the device will have to be exploited as a memory 
site. The emerging notions of biological computers, in which molecular dynamics 
mimics digital logical processes and the 1025 or so particles in a macroscopic 
sample all act simultaneously, seem to me to be the most promising in this 
regard. 
I should also issue one warning. I am not a computer scientist. My cautious 
optimism may therefore merely be a reflection of my ignorance. However, I take 
some comfort in the example of the human brain, which is light-years ahead of 
any existing computational system in complexity and comprehensiveness. If 
natural selection can develop such a fine information storage and retrieval 
device, I believe that there is still a long way we can go. 
 
THAT QUANTUM STUFF: For some additional cold water of reality, two words: 
quantum mechanics. At the microscopic level necessary to scan and re-create 
matter in the transporter, the laws of physics are governed by the strange and 
exotic laws of quantum mechanics, whereby particles can behave like waves and 
waves can behave like particles. I am not going to give a course in quantum 
mechanics here. However, the bottom line is as follows: on microscopic scales, 
that which is being observed and that which is doing the observation cannot be 
separated. To make a measurement is to alter a system, usually forever. This 
simple law can be parameterized in many different ways, but is probably most 
famous in the form of the Heisenberg uncertainty principle. This fundamental 
lawwhich appears to do away with the classical notion of determinism in 
physics, although in fact at a fundamental level it doesn'tdivides the physical 
world into two sets of observable quantities: the yin and the yang, if you like. 
It tells us that no matter what technology is invented in the future, it is 
impossible to measure certain combinations of observables with arbitrarily high 
accuracy. On microscopic scales, one might measure the position of a particle 
arbitrarily well. However, Heisenberg tells us that we then cannot know its 
velocity (and hence precisely where it will be in the next instant) very well at 
all. Or, we might ascertain the energy state of an atom with arbitrary 
precision. Yet in this case we cannot determine exactly how long it will remain 
in this state. The list goes on. 
These relations are at the heart of quantum mechanics, and they will never go 
away. As long as we work on scales where the laws of quantum mechanics 
applywhich, as far as all evidence indicates, is at least larger than the scale 
at which quantum gravitational effects become significant, or at about 10-33 
cmwe are stuck with them. 
There is a slightly flawed yet very satisfying physical argument that gives some 
heuristic understanding of the uncertainty principle. Quantum mechanics endows 
all particles with a wavelike behavior, and waves have one striking property: 
they are disturbed only when they encounter objects larger than their wavelength 
(the distance between successive crests). You have only to observe water waves 
in the ocean to see this behavior explicitly. A pebble protruding from the 
surface of the water will have no effect on the pattern of the surf pounding the 
shore. However, a large boulder will leave a region of calm water in its wake. 
So, if we want to "illuminate" an atomthat is, bounce light off it so that we 
can see where it iswe have to shine light of a wavelength small enough so that 
it will be disturbed by the atom. However, the laws of quantum mechanics tell us 
that waves of light come in small packets, or quanta, which we call photons (as 
in starship "photon torpedoes," which in fact are not made of photons). The 
individual photons of each wavelength have an energy inversely related to their 
wavelength. The greater the resolution we want, the smaller the wavelength of 
light we must use. But the smaller the wavelength, the larger the energy of the 
packets. If we bombard an atom with a high-energy photon in order to observe it, 
we may ascertain exactly where the atom was when the photon hit it, but the 
observation process itself that is, hitting the atom with the photonwill 
clearly transfer significant energy to the atom, thus changing its speed and 
direction of motion by some amount. 
It is therefore impossible to resolve atoms and their energy configurations with 
the accuracy necessary to re-create exactly a human pattern. Residual 
uncertainty in some of the observables is inevitable. What this would mean for 
the accuracy of the final product after transport is a detailed biological 
question I can only speculate upon. 
This problem was not lost on the Star Trek writers, who were aware of the 
inevitable constraints of quantum mechanics on the transporter. 
Possessing something physicists can't usually call uponnamely, artistic 
licensethey introduced "Heisenberg compensators," which allow "quantum 
resolution" of objects. When an interviewer asked the Star Trek technical 
consultant Michael Okuda how Heisenberg compensators worked, he merely replied, 
"Very well, thank you!" 
Heisenberg compensators perform another useful plot function. One may wonder, as 
I have, why the transporter is not also a replicator of life-forms. After all, a 
replicator exists aboard starships that allows glasses of water or wine to 
magically appear in each crew member's quarters on voice command. Well, it seems 
that replicator technology can operate only at "molecular-level resolution" and 
not "quantum resolution." This is supposed to explain why replication of living 
beings is not possible. It may also explain why the crew continually complains 
that the replicator food is never quite the same as the real thing, and why 
Riker, among others, prefers to cook omelets and other delicacies the 
old-fashioned way. 
 
SEEING IS BELIEVING: One last challenge to transportingas if one more were 
needed. Beaming down is hard enough. But beaming up may be even more difficult. 
In order to transport a crew member back to the ship, the sensors aboard the 
Enterprise have to be able to spot the crew member on the planet below. More 
than that, they need to scan the individual prior to dematerialization and 
matter-stream transport. So the Enterprise must have a telescope powerful enough 
to resolve objects on and often under a planet's surface at atomic resolution. 
In fact, we are told that normal operating range for the transporter is 
approximately 40,000 kilometers, or about three times the Earth's diameter. This 
is the number we shall use for the following estimate. 
Everyone has seen photographs of the domes of the world's great telescopes, like 
the Keck telescope in Hawaii (the world's largest), or the Mt. Palomar telescope 
in California. Have you ever wondered why bigger and bigger telescopes are 
designed? (It is not just an obsession with bignessas some people, including 
many members of Congress, like to accuse science of.) Just as larger 
accelerators are needed if we wish to probe the structure of matter on ever 
smaller scales, larger telescopes are needed if we want to resolve celestial 
objects that are fainter and farther away. The reasoning is simple: Because of 
the wave nature of light, anytime it passes through an opening it tends to 
diffract, or spread out a little bit. When the light from a distant point source 
goes through the telescopic lens, the image will be spread out somewhat, so that 
instead of seeing a point source, you will see a small, blurred disk of light. 
Now, if two point sources are closer together across the line of sight than the 
size of their respective disks, it will be impossible to resolve them as 
separate objects, since their disks will overlap in the observed image. 
Astronomers call such disks "seeing disks." The bigger the lens, the smaller the 
seeing disk. Thus, to resolve smaller and smaller objects, telescopes must have 
bigger and bigger lenses. 
There is another criterion for resolving small objects with a telescope. The 
wavelength of light, or whatever radiation you use as a probe, must be smaller 
than the size of the object you are trying to scan, according to the argument I 
gave earlier. Thus, if you want to resolve matter on an atomic scale, which is 
about several billionths of a centimeter, you must use radiation that has a 
wavelength of less than about one-billionth of a centimeter. If you select 
electromagnetic radiation, this will require the use of either X rays or gamma 
rays. Here a problem arises right away, because such radiation is harmful to 
life, and therefore the atmosphere of any Class M planet will filter it out, as 
our own atmosphere does. The transporter will therefore have to use 
nonelectromagnetic probes, like neutrinos or gravitons. These have their own 
problems, but enough is enough.... 
In any case, one can perform a calculation, given that the Enterprise is using 
radiation with a wavelength of less than a billionth of a centimeter and 
scanning an object 40,000 kilometers away with atomic-scale resolution. I find 
that in order to do this, the ship would need a telescope with a lens greater 
than approximately 50,000 kilometers in diameter! Were it any smaller, there 
would be no possible way even in principle to resolve single atoms. I think it 
is fair to say that while the Enterprise-D is one large mother, it is not that 
large. 
As promised, thinking about transporters has led us into quantum mechanics, 
particle physics, computer science, Einstein's mass-energy relation, and even 
the existence of the human soul. We should therefore not be too disheartened by 
the apparent impossibility of building a device to perform the necessary 
functions. Or, to put it less negatively, building a transporter would require 
us to heat up matter to a temperature a million times the temperature at the 
center of the Sun, expend more energy in a single machine than all of humanity 
presently uses, build telescopes larger than the size of the Earth, improve 
present computers by a factor of 1000 billion billion, and avoid the laws of 
quantum mechanics. It's no wonder that Lieutenant Barclay was terrified of 
beaming! I think even Gene Roddenberry, if faced with this challenge in real 
life, would probably choose instead to budget for a landable starship. 
CHAPTER SIX - The Most Bang for Your Buck
Nothing Unreal Exists. 
Kir-kin-tha's First Law of Metaphysics (Star Trek IV: The Voyage Home,) 
 
If you are driving west on Interstate 88 out of Chicago, by the time you are 30 
miles out of town, near Aurora, the hectic urban sprawl gives way to the gentle 
Midwestern prairie, which stretches forward and flat as far as you can see. 
Located slightly north of the interstate at this point is a ring of land marked 
by what looks like a circular moat. Inside the property, you may see buffalo 
grazing and many species of ducks and geese in a series of ponds. 
Twenty feet below the surface, it is a far cry from the calm pastoral atmosphere 
above ground. Four hundred thousand times a second, an intense beam of 
antiprotons strikes a beam of protons head on, producing a shower of hundreds or 
thousands of secondary particles: electrons, positrons, pions, and more. 
This is the Fermi National Accelerator Laboratory, or Fermilab for short. It 
contains the world's highest-energy particle accelerator. But more germane for 
our purposes is the fact that it is also the world's largest repository of 
antiprotons. Here, antimatter is not the stuff of science fiction. It is the 
bread and butter of the thousands of research scientists who use the Fermilab 
facilities. 
It is in this sense that Fermilab and the U.S.S. Enterprise bear a certain 
kinship. Antimatter is crucial to the functioning of a starship: it powers the 
warp drive. As I mentioned earlier, there is no more efficient way to power a 
propulsion system (though the warp drive is not, in fact, based on rocket 
propulsion). Antimatter and matter, when they come into contact, can completely 
annihilate and produce pure radiation, which travels out at the speed of light. 
Obviously, great pains must be taken to make sure that antimatter is "contained" 
whenever it is stored in bulk. When antimatter containment systems fail aboard 
starships, as when the Enterprise's system failed after its collision with the 
Bozeman, or when the containment system aboard the Yamato failed due to the 
Iconian computer weapon, total destruction inevitably follows soon afterward. In 
fact, antimatter containment would be so fundamental to starship operation that 
it is hard to understand why Federation Lieutenant Commander Deanna Troi was 
ignorant of the implications of containment loss when she temporarily took over 
command of the Enterprise in the Next Generation episode "Disaster," after the 
ship collided with two "quantum filaments." The fact that she was formally 
trained only as a psychologist should have been no excuse! 
The antimatter containment system aboard starships is plausible, and in fact 
uses the same principle that allows Fermilab to store antiprotons for long 
periods. Antiprotons and antielectrons (called positrons) are electrically 
charged particles. In the presence of a magnetic field, charged particles will 
move in circular orbits. Thus, if the particles are accelerated in electric 
fields, and then a magnetic field of appropriate strength is applied, the 
antiparticles will travel in circles of prescribed sizes. In this way, for 
example, they can travel around inside a doughnut-shaped container without ever 
touching the walls. This principle is also used in so-called Tokomak devices to 
contain the high-temperature plasmas in studies of controlled nuclear fusion. 
The Antiproton Source for the Fermilab collider contains a large ring of 
magnets. Once antiprotons are produced, in medium-energy collisions, they are 
steered into this ring, where they can be stored until they are needed for the 
highest-energy collisions, which take place in the Tevatronthe Fermilab 
high-energy collider. The Teva-tron is a much larger ring, about four miles in 
circumference. Protons are injected into the ring and accelerated in one 
direction, and antiprotons are accelerated in the other. If the magnetic field 
is carefully adjusted, these two beams of particles can be kept apart throughout 
most of the tunnel. At specified points, however, the two beams converge and the 
collisions are studied. 
Besides containment, another problem faces us immediately if we want to use a 
matter-antimatter drive: where to get the antimatter. As far as we can tell, the 
universe is made mostly of matter, not antimatter. We can confirm that this is 
the case by examining the content of high-energy cosmic rays, many of which 
originate well outside our own galaxy. Some antiparticles should be created 
during the collisions of high-energy cosmic rays with matter, and if one 
explores the cosmic-ray signatures over wide energy ranges, the antimatter 
signal is completely consistent with this phenomenon alone; there is no evidence 
of a primordial antimatter component. 
Another possible sign of antimatter in the universe would be the annihilation 
signature of antiparticle-particle collisions. Wherever the two coexist, one 
would expect to see the characteristic radiation emitted during the annihilation 
process. Indeed, this is exactly how the Enterprise searched for the Crystalline 
Entity after it had destroyed a new Federation outpost. Apparently the Entity 
left behind a trace antiproton trail. By looking for the annihilation radiation, 
the Enterprise trailed the Entity and overtook it before it could attack another 
planet. 
While the Star Trek writers got this idea right, they got the details wrong. Dr. 
Marr and Data search for a sharp "gamma radiation" spike at "10 keV"a reference 
to 10 kilo-electron volts, which is a unit of energy of radiation. 
Unfortunately, this is the wrong scale of energy for the annihilation of protons 
and antiprotons, and in fact corresponds to no known annihilation signal. The 
lightest known particle with mass is the electron. If electrons and positrons 
annihilate, they produce a sharp spike of gamma radiation at 511 keV, 
corresponding to the mass of the electron. Protons and antiprotons would produce 
a sharp spike at an energy corresponding to the rest energy of the proton, or 
about 1 GeV (Giga-electron volt)roughly a hundred thousand times the energy 
searched for by Marr and Data. (Incidentally, 10 keV is in the X-ray band of 
radiation, not the gamma-ray band, which generally corresponds to radiation in 
excess of about 100 keV, but this is perhaps too fine a detail to complain 
about.) 
In any case, astronomers and physicists have looked for diffuse background 
signals near 511 keV and in the GeV range as signals of substantial 
matter-antimatter conflagrations but have not found such signals. This and the 
cosmic-ray investigations indicate that even if substantial distributions of 
antimatter were to exist in the universe, they would not be interspersed with 
ordinary matter. 
As most of us are far more comfortable with matter than antimatter, it may seem 
quite natural that the universe should be made of the former and not the latter. 
However, there is nothing natural at all about this. In fact, the origin of the 
excess of matter over antimatter is one of the most interesting unsolved 
problems in physics today, and is a subject of intense research at the present 
time. This excess is very relevant to our existence, and thus to Star Trek's, so 
it seems appropriate to pause to review the problem here. 
When quantum mechanics was first developed, it was applied successfully to 
atomic physics phenomena; in particular, the behavior of electrons in atoms was 
wonderfully accounted for. However, it was clear that one of the limitations of 
this testing ground was that such electrons have velocities that are generally 
much smaller than the speed of light. How to accommodate the effects of special 
relativity with quantum mechanics remained an unsolved problem for almost two 
decades. Part of the reason for the delay was that unlike special relativity, 
which is quite straightforward in application, quantum mechanics required not 
just a whole new world view but a vast array of new mathematical techniques. The 
best young minds in physics were fully occupied in the first three decades of 
this century with exploring this remarkable new picture of the universe. 
One of those minds was Paul Adrien Maurice Dirac. Like his successor Stephen 
Hawking, and later Data, he would one day hold the Lucasian Professorship in 
Mathematics at Cambridge University. Educated by Lord Rutherford, and later 
training with Niels Bohr, Dirac was better prepared than most to extend quantum 
mechanics to the realm of the ultrafast. In 1928, like Einstein before him, he 
wrote down an equation that would change the world. The Dirac equation correctly 
describes the relativistic behavior of electrons in fully quantum mechanical 
terms. 
Shortly after writing down this equation, Dirac realized that to retain 
consistency, the mathematics required another particle of equal but opposite 
charge to the electron to exist in nature. Of course, such a particle was known 
alreadynamely, the proton. However, Dirac's equation suggested that this 
particle should have the same mass as the electron, whereas the proton is almost 
two thousand times heavier. This discrepancy between observation and the "naive" 
interpretation of the mathematics remained a puzzle for four years, until the 
American physicist Carl Anderson discovered, among the cosmic rays bombarding 
the Earth, a new particle whose mass was identical to the electron's but whose 
charge was the oppositethat is, positive. This "antielectron" soon became known 
as the positron. 
Since then, it has become clear that one of the inevitable consequences of the 
merger of special relativity and quantum mechanics is that all particles in 
nature must possess antiparticles, whose electric charge (if any) and various 
other properties should be the opposite of their particle partners. If all 
particles possess antiparticles, then which particles we call particles and 
which we call antiparticles is completely arbitrary, as long as no physical 
process displays any bias for particles over antiparticles. In the classical 
world of electromagnetism and gravity, no such biased process exists. 
Now we are left in a quandary. If particles and antiparticles are on an 
identical footing, why should the initial conditions of the universe have 
determined that what we call particles should comprise the dominant form of 
matter? Surely a more sensible, or at least a more symmetric, initial condition 
would be that in the beginning the number of particles and antiparticles would 
have been identical. In this case, we must explain how the laws of physics, 
which apparently do not distinguish particles from antiparticles, could somehow 
contrive to produce more of one type than the other. Either there exists a 
fundamental quantity in the universethe ratio of particles to 
antiparticleswhich was fixed at the beginning of time and about which the laws 
of physics apparently have nothing to say, or we must explain the paradoxical 
subsequent dynamical creation of more matter than antimatter. 
In the 1960s, the famous Soviet scientist and later dissident Andrei Sakharov 
made a modest proposal. He argued that it was possible, if three conditions were 
fulfilled in the laws of physics during the early universe, to dynamically 
generate an asymmetry between matter and antimatter even if there was no 
asymmetry to start with. At the time this proposal was made, there were no 
physical theories that satisfied the conditions Sakharov laid down. However, in 
the years since, particle physics and cosmology have both made great strides. 
Now we have many theories that can, in principle, explain directly the observed 
difference in abundance between matter and antimatter in nature. Unfortunately, 
they all require new physics and new elementary particles in order to work; 
until nature points us in the right direction, we will not know which of them to 
choose from. Nevertheless, many physicists, myself included, find great solace 
in the possibility that we may someday be able to calculate from first 
principles exactly why the matter fundamental to our existence itself exists. 
Now, if we had the correct theory, what number would it need to explain? In the 
early universe, what would the extra number of protons compared to antiprotons 
need to have been in order to explain the observed excess of matter in the 
universe today? We can get a clue to this number by comparing the abundance of 
protons today to the abundance of photons, the elementary particles that make up 
light. If the early universe began with an equal number of protons and 
antiprotons, these would annihilate, producing radiationthat is, photons. Each 
proton-antiproton annihilation in the early universe would produce, on average, 
one pair of photons. However, assuming there was a small excess of protons over 
antiprotons, then not all the protons would be annihilated. By counting the 
number of protons left over after the annihilations were completed, and 
comparing this with the number of photons produced by those annihilations (that 
is, the number of photons in the background radiation left over from the big 
bang), we can get an idea of the fractional excess of matter over antimatter in 
the early universe. 
We find that there is roughly one proton in the universe today for every 10 
billion photons in the cosmic background radiation. This means that the original 
excess of protons over antiprotons was only about 1 part in 10 billion! That is, 
for every 10 billion antiprotons in the early universe, there were 10 billion 
and 1 protons! Even this minuscule excess (accompanied by a similar excess in 
neutrons and electrons over their antiparticles) would have been sufficient to 
have produced all the observed matter in the universethe stars, galaxies, 
planetsand all that we have come to know and love. 
That is how we think the universe got to be made of matter and not antimatter. 
Aside from its intrinsic interest, the moral of this story for Star Trek is that 
if you want to make a matter-antimatter drive, you cannot harvest the antimatter 
out in space, because there isn't very much. You will probably have to make it. 
To find out how to do this, we return to the buffalo roaming on the Midwestern 
plain above the Fermilab accelerator. When thinking about the logistics of this 
problem, I decided to contact the director of Fermilab, John Peoples, Jr., who 
led the effort to design and build its Antiproton Source, and ask if he could 
help me determine how many antiprotons one could produce and store per dollar in 
today's dollars. He graciously agreed to help by having several of his staff 
provide me with the necessary information to make reasonable estimates. 
Fermilab produces antiprotons in medium-energy collisions of protons with a 
lithium target. Every now and then these collisions will produce an antiproton, 
which is then directed into the storage ring beneath the buffalo. When operating 
at average efficiency, Fermilab can produce about 50 billion antiprotons an hour 
in this way. Assuming that the Antiproton Source is operating about 75 percent 
of the time throughout the year, this is about 6000 hours of operation per year, 
so Fermilab produces about 300,000 billion antiprotons in an average year. 
The cost of those components of the Fermilab accelerator that relate directly to 
producing antiprotons is about $500 million, in 1995 dollars. Amortizing this 
over an assumed useful lifetime of 25 years gives $20 million per year. The 
operating cost for personnel (engineers, scientists, staff) and machinery is 
about $8 million a year. Next, there is the cost of the tremendous amount of 
electricity necessary to produce the particle beams and to store the 
antiprotons. At current Illinois rates, this costs about $5 million a year. 
Finally, related administrative costs are about $15 million a year. The total 
comes to some $48 million a year to produce the 300,000 billion antiprotons that 
Fermilab annually uses to explore the fundamental structure of matter in the 
universe. This works out to about 6 million antiprotons for a dollar! 
Now, this cost is probably higher than it would need to be. Fermilab produces a 
high-energy beam of antiprotons, and if we required only the antiprotons and not 
such high energies we might cut the cost, perhaps by a factor of about 2 to 4. 
So, to be generous, let's assume that using today's technology, one might be 
able to get from 10 million to 20 million antiprotons for a buck, wholesale. 
The next question is almost too obvious: How much bang for this buck? If we 
convert entirely the mass of one dollar's worth of antiprotons into energy, we 
would release approximately 1/1000 of a joule, which is the amount of energy 
required to heat up about 1/4 of a gram of water by about 1/1000 of a degree 
Celsius. This is nothing to write home about. 
Perhaps a better way to picture the potential capabilities of the Fermilab 
Antiproton Source as the nucleus of a warp core is to consider the energy that 
might be generated by utilizing every antiproton produced by the Source in real 
time. The Antiproton Source can produce 50 billion antiprotons an hour. If all 
these antiprotons were converted into energy, this would result in a power 
generation of about 1/1000 of a watt! Put another way, you would need about 
100,000 Fermilab Antiproton Sources to power a single lightbulb! Given the total 
annual cost of $48 million to run the Antiproton Source, it would cost at the 
present time more than the annual budget of the U.S. government to light up your 
living room in this way. 
The central problem is that as things stand today it requires far more energy to 
produce an antiproton than you would get out by converting its rest mass back 
into energy. The energy lost during the production process is probably at least 
a million times more than the energy stored in the antiproton mass. Some much 
more effective means would be needed for antimatter production before we could 
ever think of using matter-antimatter drives to propel us to the stars. 
It is also clear that if the Enterprise were to make its own antimatter, vast 
new technologies of scale would be needednot just for cost reduction, but for 
space reduction. If accelerator techniques were to be utilized, machines that 
generate far more energy per meter than those of today would be necessary. I 
might add that this is currently a subject of intense research here on 
late-twentieth-century Earth. If particle accelerators, which are our only tools 
for directly exploring the fundamental structure of matter, are not to become 
too costly for even international consortiums to build, new technologies for 
accelerating elementary particles must be developed. (We have already seen that 
our own government has decided that it is too expensive to build a 
next-generation accelerator in this country, so a European group will be 
building one in Geneva, designed to come on line at the beginning of the next 
century.) Past trends in the efficiency of energy generation per meter of 
accelerator suggest that a tenfold improvement may be possible every decade or 
two. So perhaps in several centuries it will not be unreasonable to imagine a 
starship-size, antimatter-producing accelerator. Given the current reluctance of 
governments to support expensive fundamental research at this scale, one might 
not be so optimistic, but in two centuries a lot of political changes can occur. 

Even if one were to make antimatter on board ship, however, one would still have 
to deal with the fact that to produce each antiproton would invariably use up 
much more energy than one would get out afterward. Why would one want to expend 
this energy on antimatter production, when one might turn it directly into 
propulsion? 
The Star Trek writers, always on the ball, considered this problem. Their answer 
was simple. While energy available in other forms could be used for impulse 
propulsion and hence sublight speeds, only matter-antimatter reactions could be 
used to power the warp drive. And because warp drive could remove a ship from 
danger much more effectively than impulse drive, the extra energy expended to 
produce antimatter might be well worth it in a pinch. The writers also 
sidestepped the accelerator-based antimatter-production problems by inventing a 
new method of antimatter production. They proposed hypothetical "quantum charge 
reversal devices," which would simply flip the charge of elementary particles, 
so that one could start with protons and neutrons and end up with antiprotons 
and antineutrons. According to the Next Generation Technical Manual, while this 
process is incredibly power-intensive, there is a net energy loss of only 24 
percentorders of magnitude less than the losses described above for accelerator 
use. 
While all this is very attractive, unfortunately simply flipping the electric 
charge of a proton is not enough. Consider, for example, that both neutrons and 
antineutrons are neutral. Antiparticles have all the opposite "quantum numbers" 
(labels describing their properties) of their matter partners. Since the quarks 
that make up protons possess many labels other than electric charge, one would 
have to have many other "quantum reversal devices" to complete the transition 
from matter to antimatter. 
In any case, we are told in the technical manual that, except for emergency 
antimatter production aboard starships, all Starfleet antimatter is produced at 
Starfleet fueling facilities. Here antiprotons and antineutrons are combined to 
form the nuclei of anti-heavy hydrogen. What is particularly amusing is that the 
Starfleet engineers then add antielectrons (positrons) to these electrically 
charged nuclei to make neutral anti-heavy-hydrogen atomsprobably because 
neutral antiatoms sound easier to handle than electrically charged anti-nuclei 
to the Star Trek writers. (In fact no antiatoms have yet been created in the 
laboratoryalthough recent reports out of Harvard suggest that we are on the 
threshold of producing an antihydrogen atom in this decade.) Unfortunately, this 
raises severe containment problems, since magnetic fields, which are absolutely 
essential for handling substantial amounts of antimatter without catastrophe, 
work only for electrically charged objects! Ah well, back to the drawing board.
The total antimatter fuel capacity of a starship is approximately 3000 cubic 
meters, stored in various storage pods (on Deck 42 in the Enterprise-D). This is 
claimed to be sufficient for a 3-year mission. Just for fun, let's estimate how 
much energy one could get out of this much antimatter if it were stored as 
anti-heavy-hydrogen nuclei. I will assume that the nuclei are transported as a 
rarefied plasma, which would probably be easier to contain magnetically than a 
liquid or solid. In this case, 3000 cubic meters could correspond to about 5 
million grams of material. If 1 gram per second were consumed in annihilation 
reactions, this would produce a power equivalent to the total power expended on 
a daily basis by the human race at the present time. As I indicated earlier in 
discussing warp drive, one must be prepared to produce at least this much power 
aboard a starship. One could continue using the fuel at this rate for 5 million 
seconds, or about 2 months. Assuming that a starship utilizes the 
matter-antimatter drive for 5 percent of the time during its missions, one might 
then get the required 3 years' running time out of this amount of material. Also 
of some relevance to the amount of antimatter required for energy production is 
another fact (one that the Star Trek writers have chosen to forget from time to 
time): matter-antimatter annihilation is an all-or-nothing proposition. It is 
not continuously tunable. As you change the ratio of matter to antimatter in the 
warp drive, you will not change the absolute power-generation rate. The relative 
power versus fuel used will decrease only if some fuel is wastedthat is, if 
some particles of matter fail to find antimatter to annihilate with, or if they 
merely collide without annihilating. In a number of episodes ("The Naked Time," 
"Galaxy's Child," "Skin of Evil") the matter-antimatter ratio is varied, and in 
the Star Trek technical manual this ratio is said to vary continuously from 25:1 
to 1:1 as a function of warp speed, with the 1:1 ratio being used at warp 8 or 
higher. For speeds higher than warp 8, the amount of reactants is increased, 
with the ratio remaining unchanged. Changing the amount of reactants and not the 
ratio should be the proper procedure throughout, as even Starfleet cadets should 
know. Wesley Crusher made this clear when he pointed out, in the episode "Coming 
of Age," that the Starfleet exam question on matter-antimatter ratios was a 
trick question and that there was only one possible rationamely, 1:1. 
Finally, the Star Trek writers added one more crucial component to the 
matter-antimatter drive. I refer to the famous dilithium crystals 
(coincidentally invented by the Star Trek writers long before the Fer-milab 
engineers decided upon a lithium target in their Antiproton Source). It would be 
unthinkable not to mention them, since they are a centerpiece of the warp drive 
and as such figure prominently in the economics of the Federation and in various 
plot developments. (For example, without the economic importance of dilithium, 
the Enterprise would never have been sent to the Halkan system to secure its 
mining rights, and we would never have been treated to the "mirror universe," in 
which the Federation is an evil empire!) 
What do these remarkable figments of the Star Trek writers' imaginations do? 
These crystals (known also by their longer formula 2<5>6 dilithium 2<:>1 
diallosilicate 1:9:1 heptoferranide) can regulate the matter-antimatter 
annihilation rate, because they are claimed to be the only form of matter known 
which is "porous" to antimatter. 
I liberally interpret this as follows: Crystals are atoms regularly arrayed in a 
lattice; I assume therefore that the antihydrogen atoms are threaded through the 
lattices of the dilithium crystals and therefore remain a fixed distance both 
from atoms of normal matter and one another. In this way, dilithium could 
regulate the antimatter density, and thus the matter-antimatter reaction rate. 
The reason I am bothering to invent this hypothetical explanation of the utility 
of a hypothetical material is that once again, I claim, the Star Trek writers 
were ahead of their time. A similar argument, at least in spirit, was proposed 
many years after Star Trek introduced dilithium-mediated matter-antimatter 
annihilation, in order to justify an equally exotic process: cold fusion. During 
the cold-fusion heyday, which lasted about 6 months, it was claimed that by 
putting various elements together chemically one could somehow induce the nuclei 
of the atoms to react much more quickly than they might otherwise and thus 
produce the same fusion reactions at room temperature that the Sun requires 
great densities and temperatures in excess of a million degrees to generate. 
One of the many implausibilities of the cold-fusion arguments which made 
physicists suspicious is that chemical reactions and atomic binding take place 
on scales of the order of the atomic size, which is a factor of 10,000 larger 
than the size of the nuclei of atoms. It is difficult to believe that reactions 
taking place on scales so much larger than nuclear dimensions could affect 
nuclear reaction rates. Nevertheless, until it was realized that the announced 
results were irreproducible by other groups, a great many people spent a great 
deal of time trying to figure out how such a miracle might be possible. 
Since the Star Trek writers, unlike the cold-fusion advocates, never claimed to 
be writing anything other than science fiction, I suppose we should be willing 
to give them a little extra slack. After all, dilithium-mediated reactions 
merely aid what is undoubtedly the most com-pellingly realistic aspect of 
starship technology: the matter-antimatter drives. And I might add that 
crystalstungsten in this case, not dilithiumare indeed used to moderate, or 
slow down, beams of anti-electrons (positrons) in modern-day experiments; here 
the antielec-trons scatter off the electric field in the crystal and lose 
energy. 
There is no way in the universe to get more bang for your buck than to take a 
particle and annihilate it with its antiparticle to produce pure radiation 
energy. It is the ultimate rocket-propulsion technology, and will surely be used 
if ever we carry rockets to their logical extremes. The fact that it may take 
quite a few bucks to do it is a problem the twenty-third-century politicians can 
worry about. 
CHAPTER SEVEN - Holodecks and Holograms
 
"Oh, we are us, sir. They are also us. So, indeed, we are both us." 
Data to Picard and Riker, in "We'll Always Have Paris" 
 
When Humphrey Bogart said to Ingrid Bergman at the Casablanca airport, "We'll 
always have Paris," he meant, of course, the memory of Paris. When Picard said 
something similar to Jenice Manheim at the holodeck re-creation of the Caf des 
Artistes, he may have intended it more literally. Thanks to the holodeck, 
memories can be relived, favorite places revisited, and lost loves 
rediscoveredalmost. 
The holodeck is one of the most fascinating pieces of technology aboard the 
Enterprise. To anyone already familiar with the nascent world of virtual 
reality, either through video games or the more sophisticated modern high-speed 
computers, the possibilities offered by the holodeck are particularly enticing. 
Who wouldn't want to enter completely into his or her own fantasy world at a 
moment's notice? 
It is so seductive, in fact, that I have little doubt that it would be far more 
addictive than it is made out to be in the series. We get some inkling of 
"holodeck addiction" (or "holodiction") in the episodes "Hollow Pursuits" and 
"Galaxy's Child." In the former, everyone's favorite neurotic officer, 
Lieutenant Reginald Barclay, becomes addicted to his fantasy vision of the 
senior officers aboard the Enterprise, and would rather interact with them on 
the holodeck than anywhere else on the ship. In the latter, when Geordi LaForge, 
who has begun a relationship with a holodeck representation of Dr. Leah Brahms, 
the designer of the ship's engines, meets the real Dr. Brahms, things become 
complicated- 
Given the rather cerebral pastimes the crew generally engage in on the holodeck, 
one may imagine that the hormonal instincts driving twentieth-century humanity 
have evolved somewhat by the twenty-third century (although if this is the case, 
Will Riker is not representative of his peers). Based on what I know of the 
world of today, I would have expected that sex would almost completely drive the 
holodeck. (Indeed, the holodeck would give safe sex a whole new meaning.) I am 
not being facetious here. The holodeck represents what is so enticing about 
fantasy, particularly sexual fantasy: actions without consequences, pleasure 
without pain, and situations that can be repeated and refined at will. 
The possible hidden pleasures of the holodeck are merely alluded to from time to 
time in the series. For example, after Geordi has barged in rather rudely on 
Reg's private holodeck fantasy, he admits, "I've spent a few hours on the 
holodeck myself. Now, as far as I'm concerned, what you do on the holodeck is 
your own business, as long as it doesn't interfere with your work." If that 
doesn't sound like a twentieth-century admonition against letting the pleasures 
of the flesh get the better of one, I don't know what does. 
I have little doubt that our century's tentative explorations of virtuai reality 
are leading us in the direction of something very much like the holodeck, at 
least in spirit. Perhaps my concerns will appear as quaint in the twenty-third 
century as the warning cries that accompanied the invention of television a half 
century ago. After all, though cries continue because of the surfeit of 
televised sex and violence, without television there would be no Star Trek. 
The danger that we will become a nation of couch potatoes would not apply in a 
world full of personal holodecks, or perhaps holodecks down at the mall; 
engaging in holodeck play is far from passive. However, I still find the 
prospect of virtual reality worrisome, precisely because though it appears real, 
it is much less scary than real life. The attraction of a world of direct 
sensual experience without consequences could be overwhelming. 
Nevertheless, every new technology has bad as well as good sides and will force 
adjustments in our behavior. It's probably clear from the tone of this book that 
I believe technology has on the whole made our lives better rather than worse. 
The challenge of adjusting to it is just one part of the challenge of being part 
of an evolving human society. 
Be that as it may, the holodeck differs in one striking way from most of the 
virtual-reality technologies currently under development. At present, through 
the use of devices that you strap on and that influence your vision and sensory 
input, virtual reality is designed to put the "scene" inside you. The holodeck 
takes a more inventive tack: it puts you inside the scene. It does this in part 
by inventive use of holography and in part by replication. 
The principles on which holography is based were first elucidated in 1947, well 
before the technology was available to fully exploit it, by the British 
physicist Dennis Gabor, who subsequently won the Nobel Prize for his work. By 
now, most people are familiar with the use of three-dimensional holographic 
images on credit cards, and even on the covers of books, like this one. The word 
"hologram" derives from the Greek words for "whole" and "to write." Unlike 
normal photographs, which merely record two-dimensional representations of 
three-dimensional reality, holograms give you the whole picture. In fact, it is 
possible with holography to re-create a three-dimensional image that you can 
walk around and view from all sides, as if it were the original object. The only 
way to tell the difference is to try touching it. Only then will you find that 
there is nothing there to touch. 
How can a two-dimensional piece of film, which is what stores the holographic 
image, record the full information of a three-dimensional image? To answer this 
we have to think a little about exactly what it is we see when we see something, 
and what a photograph actually records. 
We see objects either because they emit or reflect light, which then arrives at 
our eyes. When a three-dimensional object is illuminated, it scatters light in 
many different directions because of this three-dimensionality. If we could 
somehow reproduce the exact pattern of divergent light created when light is 
scattered by the actual object, then our eyes would not be able to distinguish 
the difference between the actual object and the divergent-light pattern sans 
object. By moving our head, for example, we would be able to see features that 
were previously obscured, because the entire pattern of scattered light from all 
parts of the object would have been re-created. 
How can we first store and then later re-create all this information? We can 
gain some insight into this question by thinking about what a normal 
photographwhich stores and later re-creates a two-dimensional imageactually 
records. When we take a picture, we expose a light-sensitive material to the 
incoming light, which arrives through the lens of the camera. This 
light-sensitive material, when exposed to various chemicals, will darken in 
proportion to the intensity of the light that impinged upon it. (I am discussing 
black-and-white film here, but the extension to color film is simpleone just 
coats the film with three different substances, each of which is sensitive to a 
different primary color of light.) 
So, the total information content recorded on a photographic film is the 
intensity of light arriving at each point on the film. When we develop the film, 
those points on it that were exposed to a greater intensity of light will react 
with the development chemicals to become darker, while those not so exposed will 
remain lighter. The resulting image on the film is a "negative" two-dimensional 
projection of the original light field. We can project light through this 
negative onto a light-sensitive sheet of paper to create the final photograph. 
When we look at it, light hitting the lighter areas of the photograph will be 
predominantly reflected, while light hitting the darker areas will be absorbed. 
Thus, looking at the light reflected from the photograph produces a 
two-dimensional intensity pattern on our retinas, which then allows us to 
interpret this pattern. 
The question then becomes, what more is there to record than just the intensity 
of light at each point? Once again, we rely on the fact that light is a wave. 
Because of this fact, more than just intensity is needed to characterize its 
configuration. Consider the light wave shown below: 
 
 

At position A, the wave, which in this case represents the strength of the 
electric field, has its maximum value, corresponding to an electric field with 
strength EA pointing upward. At point B, the field is exactly the same strength 
but is pointing downward. Now, if you are sensitive only to the intensity of the 
light wave, you will find that the field has the same intensity at A as it does 
at B. However, as you can see, position B represents a different part of the 
wave from position A. This "position" along the wave is called the phase. It 
turns out that you can specify all the information associated with a wave at a 
given point by giving its intensity and its phase. So, to record all the 
information about the light waves scattered by a three-dimensional object, you 
have to find a way of recording on a piece of film both the intensity and the 
phase of the scattered light. 
This is simple to do. If you split a light beam into two parts and shine one 
part directly onto the film and let the other part scatter off the object before 
illuminating the film, then either one of two things can happen. If the two 
light waves are "in phase"that is, both have crests coinciding at some point 
Athen the amplitude of the resulting wave at A will be twice the amplitude of 
either individual wave, as shown in the figure below: 

 


On the other hand, if the two waves are out of phase at point A, then they will 
cancel each other out, and the resulting "wave" at A will have zero amplitude: 



  

So now, if the film at point A is photographic film, which records intensity 
only, the pattern recorded will be the "interference pattern" of the two 
wavesthe reference beam and the beam of light scattered by the object. This 
pattern contains not only the information about the intensity of the scattered 
light from the object, but information about its phases as well. If one is 
clever, one can extract this information to re-create a three-dimensional image 
of the object that scattered the light. 
In fact, it turns out that one doesn't have to be all that clever. If one merely 
illuminates this photographic film with a source of light of the same wavelength 
as the original light that produced the interference pattern, an image of the 
object will be created exactly where the object was in relation to the film, 
when you look through the film. If you move your head to one side, you will be 
able to "look around" the edges of the re-created object. If you cover up most 
of the piece of film, and hold it closer to your eyes and look through the 
uncovered part, you will still see the entire object! In this sense, the 
experience is just like looking through a window at a scene outdoors, except 
that the scene you are seeing isn't really there. The light coming to your eyes 
through the film is affected in just such a way as to make your eyes believe 
that it has been scattered off objects, which you then "see." This is a 
hologram. 
Normally, in order for the reference light and the light from the scattered 
object to be carefully controlled, holograms are made using laser light, which 
is coherent and well collimated. However, so-called "white light" holograms 
exist, which can be illuminated by ordinary light to produce the same effect. 
One can be trickier and arrange, just as one can using various lenses, for the 
image of the objects you see to appear to be between you and the film, and you 
will see before you the three-dimensional image of an object, which you can walk 
around and view from all sides. Or you can arrange for the light source to be in 
front of the film instead of behind itas in the holograms on credit cards. 
Presumably the former sort of hologram is used on the holodeck, and to re-create 
the image of a doctor in the sick bay, as in the Voyager series. What's more, in 
order to create such holograms, one would not need to use the original objects 
to make the holographic images. Digital computers are now sophisticated enough 
to do "ray tracing" that is, they can calculate the pattern of light scattered 
from any hypothetical object you want to draw on the screen, and illuminate it 
from any angle. In the same way, the computer could determine the configuration 
of the interference pattern that would be caused by merging the light from a 
direct beam with the scattered light from an object. This computer-generated 
interference pattern could be projected onto a transparent screen, and when this 
screen is illuminated from behind, a three-dimensional image is produced of an 
object that in fact never existed. If the computer is fast enough, it can 
project a continuously changing interference pattern on the screen, thereby 
producing a moving three-dimensional image. So the holographic aspect of the 
holodeck is not particularly far-fetched. 
However, holograms aren't all there is to the holodeck. As noted, they have no 
corporeal integrity. You can walk through oneor shoot through one, as was 
evidenced by the wonderful holographic representations created by Spock and Data 
to trick the Romulans in the episode "Unification." This incorporeality simply 
will not do for the objects one would like to interact withthat is, touchon 
the holodeck. Here techniques that are more esoteric are required, and the Star 
Trek writers have turned to the transporter, or at least to the replicators, 
which are less sophisticated versions of the transporter. Presumably, using 
transporter technology, matter is replicated and moved around on the holodeck to 
resemble exactly the beings in question, in careful coordination with computer 
programs that control the voices and movements of the re-created beings. 
Similarly, the replicators reproduce the inanimate objects in the scenetables, 
chairs, and so forth. This "holodeck matter" owes its form to the pattern held 
in the replicator buffer. When the transporter is turned off or the object is 
removed from the holodeck, the matter can then disassemble as easily as it would 
if the pattern buffer were turned off during the beaming process. Thus, 
creatures created from holodeck matter can be trapped on the holodeck, as the 
fictional detectives Cyrus Redblock and Felix Leach found to their dismay in the 
Next Generation episode "The Big Goodbye," and as Sherlock Holmes's nemesis 
Professor Moriarty surmised and then attempted to overcome in several other 
episodes. 
So here is how I envisage the holodeck: holograms would be effective around the 
walls, to give one the impression of being in a three-dimensional environment 
that extended to the horizon, and the transporter-based replicators would then 
create the moving "solid" objects within the scene. Since holography is 
realistic, while (as I have explained earlier) transporters are not, one would 
have to find some other way of molding and moving matter around in order to make 
a workable holodeck. Still, one out of two technologies in hand isn't bad. 
Where does all this leave the pure holograms, like the holographic doctor of the 
Voyager series? The answer is, Absolutely nowhere. With just the scattered light 
and no matter around, I'm afraid that these images would not be very effective 
at lifting, manipulating, or probing. However, a good bedside manner and 
compassionate words of advice, which are at the heart of good medical practice, 
can be dispensed by a hologram as easily as by the real thing. 
 
SECTION THREE - The Invisible Universe, or Things That Go Bump in the Night - In 
which we speak of things that may exist but are not yet seen extraterrestrial 
life, multiple dimensions, and an exotic zoo of other physics possibilities and 
impossibilities
An aerial view of the Fermi National Accelerator Laboratory (Fermilab) in 
Batavia, Illinois, housing the highest energy accelerator in the world, the 
Tevatron, and the world's largest production and storage facility of 
antiprotons. The ring housing the 4-mile in circumference accelerator is clearly 
discernable. The circle in the foreground outlines an accelerator upgrade, the 
Main Injector, under construction. (Fermilab Photo) 


  


John Peoples, director of Fermilab, shown with the antiproton source which he 
designed. The antiprotons produced by collisions of protons on a lithium target 
are stored in a circular beam using the array of magnets shown in the 
photograph. (Fermilab Photo) 
 





A portion of the accelerator tunnel, 4 miles long, located 20 feet below the 
ground, housing the proton-antiproton beams, and the array of superconducting 
magnets (lower ring) used to steer and accelerate them to energies approaching 
1012 electron volts. {Fermilab Photo) 

One of the two large detectors at Fermilab built to analyze the high-energy 
collisions of protons and antiprotons. The 5000-ton detector is moved in and out 
of the beam on large rollers. (Fermilab Photo) 

The Harvard radio-telescope located at Harvard, Massachusetts, used to obtain 
the data for the Megachannel Extra Terrestrial Array (META) experiment designed 
to search for the signals of extraterrestrial life in our galaxy. 

 


The META supercomputer array designed to scan millions of channels at a single 
time in the search for a signal of intelligent life elsewhere in the galaxy. 
 

 


The new Billionchannel Extra Terrestrial Array (BETA)supercomputer which will be 
part of the next generation search for extraterrestrial intelligence. 

 


The Andromeda Galaxy (M31). This is the nearest large spiral galaxy similar to 
our own, located about 6 million light years away. (Lick Observatory 
Photograph/Image) 

 


A photograph of our own galaxy obtained using radio and microwave detectors 
aboard the Cosmic Background Explorer (COBE) satellite. This is the first true 
photograph of the Milky Way showing its spiral structure, as edge on from the 
vantage point of the earth. (NASA/COBE) 

 


A high resolution photograph of the core of the galaxy M87, which is thought to 
house a black hole in excess of 2 billion solar masses. The small disk of 
ionized gas at the very center, almost perpendicular to the large radio jet seen 
to be emerging from the center is rotating at about 750 kilometers per second, 
which gives strong dynamical evidence for the existence of such a black hole. 
(Holland Ford and NASA) 
CHAPTER EIGHT - The Search for Spock
 
"It's difficult to work in a group when you are omnipotent." 
Q, upon joining the crew of the Enterprise, in "Dj Q" 
 
"Restless aggression, territorial conquest, and genocidal annihilation ... 
whenever possible.... The colony is integrated as though it were in fact one 
organism ruled by a genome that constrains behavior as it also enables it.... 
The physical superorganism acts to adjust the demographic mix so as to optimize 
its energy economy.... The austere rules allow of no play, no art, no empathy." 
The Borg are among the most frightening, and intriguing, species of alien 
creature ever portrayed on the television screen. What makes them so 
fascinating, from my point of view, is that some organism like them seems 
plausible on the basis of natural selection. Indeed, although the paragraph 
quoted above provides an apt description of the Borg, it is not taken from a 
Star Trek episode. Rather it appears in a review of Bert Holldobler and Edward 
O. Wilson's Journey to the Ants, and it is a description not of the Borg but of 
our own terrestrial insect friends.1 Ants have been remarkably successful on an 
evolutionary scale, and it is not hard to see why. Is it impossible to imagine a 
cognizant society developing into a similar communal superorganism? Would 
intellectual refinements such as empathy be necessary to such a society? Or 
would they be a hindrance? 
Gene Roddenberry has said that the real purpose of the starship Enterprise was 
to serve as a vehicle not for space travel but for story-telling. Beyond all the 
technical wizardry, even a techie such as myself recognizes that what makes Star 
Trek tick is drama, the same grand themes that have driven storytelling since 
the Greek epicslove, hate, betrayal, jealousy, trust, joy, fear, wonder.... We 
all connect most closely with stories that illuminate those human emotions that 
govern our own lives. If warp drive were used merely to propel unmanned probes, 
if the transporters were developed merely to move soil samples, if medical 
scanners were utilized merely on plant life, Star Trek would never have made it 
past the first season. 
Indeed, the "continuing mission" of the starship Enterprise is not to further 
explore the laws of physics but "to explore strange new worlds, to seek out new 
life and new civilizations." What makes Star Trek so fascinatingand so 
long-lived, I suspectis that this allows the human drama to be extended far 
beyond the human realm. We get to imagine how alien species might develop to 
deal with the same problems and issues that confront humanity. We are exposed to 
new imaginary cultures, new threats. It provides some of the same fascination as 
visiting a foreign country for the first time does, or as one sometimes gets 
from reading history and discovering both what is completely different and what 
is exactly the same about the behavior of people living centuries apart. 
We must, of course, suspend disbelief for such entertainment. Remarkably, almost 
all alien species encountered by the Enterprise are humanlike, and they all 
speak English! (In their defense, the Star Trek writers invented, in the sixth 
season of The Next Generation, a rationale for this. The archeologist Richard 
Galen apparently discovers that a wide variety of these civilizations share 
genetic material, which was seeded in the primordial oceans of many different 
worlds by some very ancient civilization. This is a notion reminiscent of the 
Nobel laureate Francis Crick's [only partly] tongue-in-cheek theory of 
Panspermia.)2 This has not escaped the notice of any trekker, and it was perhaps 
most colorfully put to me by the theoretical physicist and Nobel laureate 
Sheldon Glashow, who said of the aliens, "They all look like people with 
elephantiasis!" Nevertheless, he is willing to ignore, as are most trekkers, 
these plot contrivances in order to appreciate the Star Trek writers' 
exploration of alien psychologies. Hollywood screenwriters are generally neither 
scientists nor engineers, and thus it is natural to expect that most of their 
creative energy would go into designing alien cultures rather than alien 
biology. 
And creative they have been. Besides the Borg and the omnipotent prankster Q, 
over two hundred specific life-forms populated the Star Trek universe at the 
point when I gave up counting. Our galaxy is apparently full of other 
intelligent civilizations, some more advanced and some less advanced. Somelike 
the Federation, the Klingons, the Romulans, and the Cardassianscontrol large 
empires, while others exist in isolation on single planets or in the emptiness 
of space. 
The discovery of extraterrestrial intelligence could be, as emphasized by the 
practitioners of the ongoing search, the greatest discovery in the history of 
the human race. Certainly it is hard to imagine a discovery that might change 
our view of ourselves and our place in the universe more than this. 
Nevertheless, after three decades of concerted searching, we have yet to find 
any definitive evidence for any form of life outside our own planet. One might 
find this surprising. Certainly, if there is life out there, it seems inevitable 
that we should find it, just as many of the civilizations that independently 
emerged on several continents here on Earth eventually ran into each other, 
sometimes traumatically. 
Nevertheless, when one thinks in some detail about the likelihood of discovering 
intelligent life elsewhere in the universe, the daunting nature of the search 
becomes clear. Consider, for example, that some other civilization in the galaxy 
was informed somehow of exactly where to look among the 400 billion or so stars 
in the Milky Way to find a planet that could support life. Say further that they 
were directed to look in the direction of our Sun. What is the probability even 
then that they would discover our existence? Life has existed on Earth for much 
of the 4.5 billion years since it formed. Yet only in the past half century or 
so have we been transmitting any signals of our existence. Furthermore, only in 
the past 25 years or so have we had radiotlescopes sufficiently powerful to 
serve as radio beacons for observation by other civilizations. Thus, in the 4.5 
billion years during which aliens might have been scanning the Earth from space, 
they could have discovered us only during the last half century. Assuming that 
an alien civilization chose to make its observations at some random time during 
the planet's history, the possibility of discovering our existence would be 
about 1 in 100 million. And I remind you, this applies only if they knew exactly 
where to look! 
There have been whole books written about the possibility of life existing 
elsewhere in the galaxy, and also about the possibility of detecting it. 
Estimates for the number of advanced civilizations range from millions on the 
high side to one on the low side (liberally interpreting our own civilization as 
advanced). It is not my purpose to review all the arguments in depth here. I 
would like, however, to describe some of the more interesting physical arguments 
related to the origin of the sorts of life the Enterprise was sent out to 
discover, and to discuss some of the strategies currently being employed here on 
Earth to search for it. 
The a priori argument that life should exist elsewhere in our galaxy seems to me 
to be compelling. As noted, there are roughly 400 billion stars in our galaxy. 
It would seem truly remarkable if our Sun were the only one around which 
intelligent life developed. One can propose what on the surface seems like a 
more sophisticated argument to estimate the probability that life like ourselves 
occurs elsewhere, starting with obvious questions such as: "What is the 
probability that most stars have planets?" or "What is the probability that this 
[particular] star will live long enough to sustain life on a planetary system?" 
and then moving on to planetary matters, such as "Is this planet big enough to 
hold an atmosphere?" or "What is the likelihood of its having undergone 
sufficient early volcanism to produce enough water on the surface?" or "What is 
the probability of its having a moon either massive enough or close enough to 
produce tides sufficient to make tidal pools where life might originate, but not 
daily tidal waves?" While I will discuss some of these issues, the problem with 
trying to determine realistic probabilities is, first, that many of the relevant 
parameters are undetermined and, second, that we do not know how all the 
parameters are correlated. It is difficult enough to determine accurately the 
probability of everyday events. When one sets out to estimate a sequence of very 
small probabilities, the operational significance of such an attempt often 
becomes marginal. 
One should also remember that even if one derives a well-defined probability, 
its interpretation can be pretty subtle. For example, the probability of any 
specific sequence of eventssuch as the fact that I am sitting in this specific 
type of chair typing at this specific computer (among all the millions of 
computers manufactured each year), in this specific place (among all the 
possible cities in the world), at this specific time of day (among the 86,400 
seconds in each day) is vanish-ingly small. The same can be said for any other 
set of circumstances in my life. Likewise, in the inanimate world, the 
probability that, say, a radioactive nucleus will decay at the exact moment it 
does is also vanishingly small. However, we do not calculate such probabilities. 
We ask, rather, how likely it is that the nucleus will decay in some nonzero 
time interval, or how much more probable a decay is at one time compared to 
another time. 
When one is attempting to estimate the probabilities of life in the galaxy, one 
has to be very careful not to overrestrict the sequence of events one considers. 
If one does, and people have, one is likely to conclude that the probability 
that life formed on Earth when it did is infinitesimally small, which is 
sometimes used as an argument for the existence of Divine intervention. However, 
as I have just indicated, the same vanishingly small probability could be 
assigned to the likelihood that the stoplight I can see out my window will turn 
red while I am waiting in my car there at precisely 11:57 A.M. on June 3, 1999. 
This does not mean, however, that such a thing won't happen. 
The important fact to recognize is that life did form in the galaxy at least 
once. I cannot overemphasize how important this is. Based on all our experience 
in science, nature rarely produces a phenomenon just once. We are a test case. 
The fact that we exist proves that the formation of life is possible. Once we 
know that life can originate here in the galaxy, the likelihood of it occurring 
elsewhere is vastly increased. (Of course, as some evolutionary biologists have 
argued, it need not develop an intelligence.) 
While our imaginations are no doubt far too feeble to consider all the 
combinations of conditions which might give rise to intelligent life, we can use 
our own existence to ask what properties of the universe were essential or 
important in our own evolution. 
We first begin with the universe as a whole. I have already mentioned one cosmic 
coincidence: that there was one extra proton produced in the early universe for 
every 10 billion or so protons and antiprotons. Without these extra little guys, 
matter would have annihilated with antimatter, and there would be no matter left 
in the universe today, intelligent or otherwise. 
The next obvious feature of the universe in which we live is that it is old, 
very old. It took intelligent life about 3.5 billion years to develop on Earth. 
Hence, our existence requires a universe that accommodated our arrival by 
lasting billions of years. The current best estimate for the age of our universe 
is between about 10 billion and 20 billion years, which is plenty long enough. 
It turns out, however, that it is not so easy a priori to design a universe that 
expands, as our universe does, without either recollapsing very quickly in a 
reverse of the big banga big crunchor expanding so fast that there would have 
been no time for matter to clump together into stars and galaxies. The initial 
conditions of the universe, or some dynamical physical process early in its 
history, would have to be very finely tuned to get things just right. 
This has become known as the "flatness" problem, and understanding it has become 
one of the central issues in cosmology today. Gravitational attraction due to 
the presence of matter tends to slow the expansion of the universe. As a result, 
two possibilities remain. Either there is enough matter in the universe to cause 
the expansion to halt and reverse (a "closed" universe), or there is not (an 
"open" universe). What is surprising about the present universe is that when we 
add up all the matter we estimate is out there, the amount we find is 
suspiciously close to the borderline between these two possibilitiesa "flat" 
universe, in which the observed expansion would slow but never quite stop in any 
finite amount of time. 
What makes this particularly surprising is that as the universe evolves, if it 
is not exactly flat then it deviates more and more from being flat as time goes 
on. Since the universe is probably at least 10 billion years old today, and 
observations suggest that the universe is close to being flat today, then at 
much earlier times it must have been immeasurably close to being flat. It is 
hard to imagine how this could happen at random without some physical process 
enforcing it. Some 15 years ago, a candidate physical process was invented. 
Known as "inflation," it is a ubiquitous process that can occur due to quantum 
mechanical effects in the early universe. 
Recall that empty space is not really empty but that quantum fluctuations in the 
vacuum can carry energy. It turns out that it is possible, as the nature of 
forces between elementary particles evolves with temperature in the early 
universe, for the energy stored as quantum fluctuations in empty space to be the 
dominant form of energy in the universe. This vacuum energy can repel 
gravitationally rather than attract. It is hypothesized that the universe went 
through a brief inflationary phase, during which it was dominated by such vacuum 
energy, resulting in a very rapid expansion. One can show that when this period 
ends and the vacuum energy is transferred into the energy of matter and 
radiation, the universe can easily end up being flat to very high precision. 
However, another, perhaps more severe, problem remains. In fact Einstein first 
introduced the problem when he tried to apply his new general theory of 
relativity to the universe. At that time, it was not yet known that the universe 
was expanding; rather, the universe was believed to be static and unchanging on 
large scales. So Einstein had to figure out some way to stop all this matter 
from collapsing due to its own gravitational attraction. He added a term to his 
equations called the cosmological constant, which essentially introduced a 
cosmic repulsion to balance the gravitational attraction of matter on large 
scales. Once it was recognized that the universe is not static, Einstein 
realized that there was no need for such a term, whose addition he called "the 
biggest blunder" he had ever made. 
Unfortunately, as in trying to put the toothpaste back into the tube, once the 
possibility of a cosmological constant is raised, there is no going back. If 
such a term is possible in Einstein's equations then we must explain why it is 
absent in the observed universe. In fact, the vacuum energy I described above 
produces exactly the effect that Einstein sought to produce with the 
cosmological constant. So the question becomes, How come such vacuum energy is 
not overwhelmingly dominant in the universe today?or, How come the universe 
isn't still inflating? 
We have no answer to this question. It is probably one of the most profound 
unanswered questions in physics. Every calculation we perform with the theories 
we now have suggests that the vacuum energy should be many orders of magnitude 
larger today than it is allowed to be on the basis of our observations. There 
are ideas, based on exotica like Euclidean wormholes, for how to make it vanish, 
but none of these ideas is firmly grounded. Perhaps even more surprising, recent 
observations on a variety of scales all suggest that the cosmological constant, 
while much smaller than we can explain, may nevertheless not be zero today, and 
may therefore have had a measurable effect on the evolution of the 
universemaking it older than it might otherwise have been, for example. This is 
a subject of great interest, and in fact is occupying much of my own present 
research efforts. 
Nevertheless, whatever the resolution of this problem, it is clear that the near 
flatness of the universe was one of the conditions necessary for the eventual 
origin of life on Earth and that the cosmological conditions favoring the 
formation of life on Earth hold elsewhere as well. 
At a fundamental microphysical level, there is also a whole slew of cosmic 
coincidences that allowed life to form on Earth. If any one of a number of 
fundamental physical quantities in nature was slightly different, then the 
conditions essential for the evolution of life on Earth would not have existed. 
For example, if the very small mass difference between a neutron and proton 
(about 1 part in 1000) were changed by only a factor of 2, the abundance of 
elements in the universe, some of which are essential to life on Earth, would be 
radically different from what we observe today. Along the same lines, if the 
energy level of one of the excited states of the nucleus of the carbon atom were 
slightly different, then the reactions that produce carbon in the interiors of 
stars would not occur and there would be no carbon the basis of organic 
moleculesin the universe today. 
Of course, it is hard to know how much emphasis to put on these coincidences. It 
is not surprising, since we have evolved in this universe, to find that the 
constants of nature happen to have the values that allowed us to evolve in the 
first place. One might imagine, for the purposes of argument, that our observed 
universe is part of a meta-universe that exists on a much larger scale than we 
can observe. In each of the universes making up this meta-universe, the 
constants of nature could be different. In those universes that have constants 
incompatible with the evolution of life, no one is around to measure anything. 
To paraphrase the argument of the Russian cosmologist Andrei Linde, who happens 
to subscribe to this form of what is known as the "anthropic principle," it is 
like an intelligent fish wondering why the universe in which it lives (the 
inside of a fish bowl) is made of water. The answer is simple: if it weren't 
made of water, the fish wouldn't be there to ask the question. 
Since most of these issues, while interesting, are not empirically resolvable at 
the present time, they are perhaps best left to philosophers, theologians, or 
perhaps science fiction writers. Let us then accept the fact that the universe 
has managed to evolve, both microscopically and macroscopically, in a way that 
is conducive to the evolution of life. We next turn to our own home, the Milky 
Way galaxy. 
When we consider which systems in our own galaxy may house intelligent life, the 
physics issues are much more clear-cut. Given that there exist stars in the 
Milky Way which, from all estimates, are at least 10 billion years old, while 
life on Earth is no older than about 3.5 billion years, we are prompted to ask 
how long life could have existed in our galaxy before it arose on Earth. 
When our galaxy began to condense out of the universal expansion some 10 billion 
to 20 billion years ago, its first generation stars were made up completely of 
hydrogen and helium, which were the only elements created with any significant 
abundance during the big bang. Nuclear fusion inside these stars continued to 
convert hydrogen to helium, and once this hydrogen fuel was exhausted, helium 
began to "burn" to form yet heavier elements. These fusion reactions will 
continue to power a star until its core is primarily iron. Iron cannot be made 
to fuse to form heavier elements, and thus the nuclear fuel of a star is 
exhausted. The rate at which a star burns its nuclear fuel depends on its mass. 
Our own Sun, after 5 billion years of burning hydrogen, is not even halfway 
through the first phase of its stellar evolution. Stars of 10 solar massesthat 
is, 10 times heavier than the Sunburn fuel at about 1000 times the rate the Sun 
does. Such stars will go through their hydrogen fuel in less than 100 million 
years, instead of in the Sun's 10-billion-year lifetime. 
What happens to one of these massive stars when it exhausts its nuclear fuel? 
Within seconds of burning the last bit, the outer parts of the star are blown 
off in an explosion known as a supernova, one of the most brilliant fireworks 
displays in the universe. Supernovae briefly shine with the brightness of a 
billion stars. At the present time, they are occurring at the rate of about two 
or three every 100 years in the galaxy. Almost 1000 years ago, Chinese 
astronomers observed a new star visible in the daytime sky, which they called a 
"guest star." This supernova created what we now observe telescopically as the 
Crab Nebula. It is interesting that nowhere in Western Europe was this transient 
object recorded. Church dogma at the time declared the heavens to be eternal and 
unchanging, and it was much easier not to take notice than to be burned at the 
stake. Almost 500 years later, European astronomers had broken free enough of 
this dogma so that the Danish astronomer Tycho Brahe was able to record the next 
observable supernova in the galaxy. 
Many of the heavy elements created during the stellar processing, and others 
created during the explosion itself, are dispersed into the interstellar medium, 
and some of this "stardust" is incorporated in gas that collapses to form 
another star somewhere else. Over billions of years, later generations of 
starsso-called Population 1 stars, like our Sunform, and any number of these 
can be surrounded by a swirling disk of gas and dust, which would coalesce to 
form planets containing heavy elements like calcium, carbon, and iron. Out of 
this stuff we are made. Every atom in our bodies was created billions of years 
ago, in the fiery furnace of some long dead star. I find this one of the most 
fascinating and poetic facts about the universe: we are all literally star 
children. 
Now, it would not be much use if a planet like the Earth happened to form near a 
very massive star. As we have seen, such stars evolve and die within the course 
of 100 million years or so. Only stars of the mass of our Sun or less will last 
longer than 5 billion years in a stable phase of hydrogen burning. It is hard to 
imagine how life could form on a planet orbiting a star that changed in 
luminosity by huge amounts over the course of such evolution. Conversely, if a 
star smaller and dimmer than our Sun should have a planetary system, any planet 
warm enough to sustain life would probably be so close in as to be wracked by 
tidal forces. Thus, if we are going to look for life, it is a good bet to look 
at stars not too different from our own. As it happens, the Sun is a rather 
ordinary member of the galaxy. About 25 percent of all stars in the Milky 
Waysome 100 billion of themfall in the range required. Most of these are older 
even than the Sun and could therefore, in principle, have provided sites for 
life up to 4 billion to 5 billion years before the Sun did. 
On to the Earth. What is it about our fair green-blue planet that makes it 
special? In the first place, it is in the inner part of the solar system. This 
is important, because the outer planets have a much higher percentage of 
hydrogen and heliummuch closer to that of the Sun. Most of the heavy elements 
in the disk of gas and dust surrounding the Sun at its birth appear to have 
remained in the inner part of the system. Thus, one might expect potential sites 
for life to be located at distances smaller than, say, the distance of Mars from 
a 1-solar-mass star. 
Next, as Goldilocks might have said, the Earth is just rightnot too big or too 
small, too cold or too hot. Since the inner planets probably had no atmospheres 
when they formed, these had to be generated by gases produced by volcanoes. The 
water on the Earth's surface was also produced in this fashion. A smaller planet 
might well have radiated heat from its surface rapidly enough to prevent a large 
amount of volcanism. Presumably this is the case with Mercury and the Moon. Mars 
is a borderline case, while Earth and Venus have successfully developed an 
atmosphere. Recent measurements of radioactive gas isotopes in the terrestrial 
rocks suggest that after an initial period of bombardment, in which the Earth 
was created by the accretion of infailing material over a period of 100 million 
to 150 million years about 4.5 billion years ago, volcanism produced about 85 
percent of the atmosphere within a few million years. So, again, it is not 
surprising that organic life formed on Earth rather than on other planets in the 
solar system, and one might expect similar proclivities elsewhere in the 
galaxyon Class M planets, as they are called in the Star Trek universe. 
The next question is how quickly life, followed by intelligent life, might take 
to evolve, based on our experience with the Earth. The answer to the first part 
of the question is: Remarkably quickly. Fossil relics of blue-green algae about 
3.5 billion years old have been discovered, and various researchers have argued 
that life was already flourishing as long as 3.8 billion years ago. Within a few 
100 million years of the earliest possible time that life could have evolved on 
Earth, it did. This is very encouraging. 
Of course, from the time life first began on Earth until complex multicellular 
structures, and later intelligent life, evolved, almost 3 billion years may have 
elapsed. There is every reason to believe that this time was governed more by 
physics than biology. In the first place, the Earth's original atmosphere 
contained no oxygen. Carbon dioxide, nitrogen, and trace amounts of methane, 
ammonia, sulfur dioxide, and hydrochloric acid were all present, but not oxygen. 
Not only is oxygen essential for the advanced organic life-forms on Earth, it 
plays another important role. Only when there is sufficient oxygen in the 
atmosphere can ozone form. Ozone, as we are becoming more and more aware, is 
essential to life on Earth because it screens out ultraviolet radiation, which 
is harmful to most life-forms. It is therefore not surprising that the rapid 
explosion of life on Earth began only after oxygen was abundant. 
Recent measurements indicate that oxygen began building up in the atmosphere 
about 2 billion years ago, and reached current levels within 600 million years 
after that. While oxygen had been produced earlier, by photosynthesis in the 
blue-green algae of the primordial oceans, it could not at first build up in the 
atmosphere. Oxygen reacts with so many substances, such as iron, that whatever 
was photosyn-thetically produced combined with other elements before it could 
reach the atmosphere. Eventually, enough materials in the ocean were oxidized so 
that free oxygen could accumulate in the atmosphere. (This process never took 
place on Venus because the temperature was too high there for oceans to form, 
and thus the life-forming and life-saving blue-green algae never arose there.) 
So, after conditions were really ripe for complex life-forms, it took about a 
billion years for them to evolve. Of course, it is not clear at all that this is 
a characteristic timescale. Accidents such as evolutionary wrong turns, climate 
changes, and cataclysmic events that caused extinctions affected both the 
biological timescale and the end results. 
Nevertheless, these results indicate that intelligent life can evolve in a 
rather short interval on the cosmic timescalea billion years or so. The extent 
of this timeframe has to do with purely physical factors, such as heat 
production and chemical reaction rates. Our terrestrial experience suggests that 
even if we limit our expectations of intelligent life to the organic and 
aerobicsurely a very conservative assumption, and one that the Star Trek 
writers were willing to abandon (the silicon-based Horta is one of my 
favorites)planets surrounding several-billion-year-old stars of about 1 solar 
mass are good candidates. 
Granting that the formation of organic life is a robust and relatively rapid 
process, what evidence do we have that its fundamental ingredientsnamely, 
organic molecules, and other planetsexist elsewhere in the universe? Here, 
again, recent results lead to substantial optimism. Organic molecules have been 
observed in asteroids, comets, meteorites, and interstellar space. Some of these 
are complex molecules, including amino acids, the building blocks of life. 
Microwave measurements of interstellar gas and dust grains have led to the 
identification of dozens of organic compounds, some of which are presumed to be 
complex hydrocarbons. There is little doubt that organic matter is probably 
spread throughout the galaxy. 
Finally, what about planets? In spite of the fact that to date only one direct 
observation of a planetary system other than our own has been made, it has long 
been believed that most stars have planets around them. Certainly a fair 
fraction of observed stars have another stellar companion, in so-called binary 
systems. Moreover, many young stars are observed to have circumstellar disks of 
dust and gas, which are presumably the progenitors of planets. Various numerical 
models for predicting the distribution of planetary masses and orbits in such 
disks suggest (and I emphasize here the word "suggest") that they will produce 
on average at least one Earthlike planet at an Earth-like distance from its 
star. Most recently, another planetary system was finally directly detected, 
1400 light-years from Earth. Somewhat surprisingly, the system observed is one 
of the least hospitable places one might imagine for planets: three planets all 
orbiting a pulsarthe collapsed core of a supernovaat a distance closer than 
Venus is to our Sun. These planets could easily have formed after rather than 
before the supernova, but either way, this discovery indicates that planetary 
formation is probably not rare. 
I do not want to lose the forest for the trees here. It is almost miraculous 
that the normal laws of physics and chemistry, combined with an expanding 
universe more than some 10 billion years old, lead to the evolution of conscious 
minds that can study the universe out of which they were born. Nevertheless, 
while the circumstances that led to life on Earth are special, they appear to be 
by no means peculiar to Earth. The arguments above suggest that there could 
easily be over a billion possible sites for organic life in our galaxy. And 
since our galaxy is merely one out of 100 billion galaxies in the observable 
universe, I find it hard to believe that we are alone. Moreover, as I noted 
earlier, most Population 1 stars were formed earlier than our Sun wasup to 5 
billion years earlier. Given the time frame discussed above, it is likely that 
intelligent life evolved on many sites billions of years before our Sun was even 
born. In fact, it might be expected that most intelligent life in the galaxy 
existed before ours. Thus, depending upon how long intelligent civilizations 
persist, the galaxy could be full of civilizations that have been around 
literally billions of years longer than we have. On the other hand, given our 
own history, such civilizations may well have faced the perils of war and 
famine, and many may not have made it past a few thousand years; in this case, 
most of the intelligent life in the universe would be long gone. As one 
researcher cogently put the issue over 20 years ago, "The question of whether 
there is intelligent life out there depends, in the last analysis, upon how 
intelligent that life is."3 
So, how will we ever know? Will we first send out starships to explore strange 
new worlds and go where no one has gone before? Or will we instead be discovered 
by our galactic neighbors, who have tuned in to the various Star Trek series as 
these signals move at the speed of light throughout the galaxy? I think neither 
will be the case, and I am in good company. 
In the first place, we have clearly seen how daunting interstellar space travel 
would be. Energy expenditures beyond our current wildest dreams would be 
neededwarp drive or no warp drive. Recall that to power a rocket by propulsion 
using matter-antimatter engines at something like 3/4 the speed of light for a 
10-year round-trip voyage to just the nearest star would require an energy 
release that could fulfill the entire current power needs in the United States 
for more than 100,000 years! This is dwarfed by the power that would be required 
to actually warp space. Moreover, to have a fair chance of finding life, one 
would probably want to be able to sample at least several thousand stars. I'm 
afraid that even at the speed of light this couldn't be done anytime in the next 
millennium. 
That's the bad news. The good news, I suppose, is that by the same token we 
probably don't have to worry too much about being abducted by aliens. They, too, 
have probably figured out the energy budget and will have discovered that it is 
easier to learn about us from afar. 
So, do we then devote our energies to broadcasting our existence? It would 
certainly be much cheaper. We could send to the nearest star system a 10-word 
message, which could be received by radio antennae of reasonable size, for much 
less than a dollar's worth of electricity. Howeverand here again I borrow an 
argument from the Nobel laureate Edward Purcellif we broadcast rather than 
listen, we will miss most of the intelligent life-forms. Obviously, those 
civilizations far ahead of us can do a much better job of transmitting powerful 
signals than we can. And since we have been in the radio-transmission business 
for only 80 years or so, there are very few societies less advanced than we are 
that could still have the technology to receive our signals. So, as my mother 
used to say, we should listen before we speak. Although as I write this, I 
suddenly hope that all those more advanced societies aren't thinking exactly the 
same thing. 
But what do we listen to? If we have no idea which channel to turn to in 
advance, the situation seems hopeless. Here we can be guided by Star Trek. In 
the Next Generation episode "Galaxy's Child," the Enterprise stumbles upon an 
alien life-form that lives in empty space, feeding on energy. Particularly tasty 
is radiation with a very specific frequency1420 million cycles per second, 
having a wavelength of 21 cm. 
In the spirit of Pythagoras, if there were a Music of the Spheres, surely this 
would be its opening tone. Fourteen hundred and twenty megahertz is the natural 
frequency of precession of the spin of an electron as it encircles the atomic 
nucleus of hydrogen, the dominant material in the universe. It is, by a factor 
of at least 1000, the most prominent radio frequency in the galaxy. Moreover, it 
falls precisely in the window of frequencies that, like visible light, can be 
transmitted and received through an atmosphere capable of supporting organic 
life. And there is very little background noise at this frequency. 
Radioastronomers have used this frequency to map out the location of hydrogen in 
the galaxywhich is, of course, synonymous with the location of matterand have 
thus determined the galactic shape. Any species intelligent enough to know about 
radio waves and about the universe will know about this frequency. It is the 
universal homing beacon. Thirty-six years ago, the astrophysicists Giuseppe 
Cocconi and Philip Morrison proposed that this is the natural frequency to 
transmit at or listen to, and no one has argued with this conclusion since. 
Hollywood not only guessed the right frequency to listen to but helped put up 
the money to do the listening. While small-scale listening projects have been 
carried out for more than 30 years, the first large-scale comprehensive program 
came on line in the autumn of 1985, when Steven Spielberg threw a big copper 
switch that formally initiated Project META, which stands for Megachannel Extra 
Terrestrial Array. The brainchild of electronics wizard Paul Horowitz at Harvard 
University, META is located at the Harvard/Smithsonian 26-meter radiotlescope 
in Harvard, Massachusetts, and funded privately by the Planetary Society, 
including a $100,000 contribution from Mr. ET himself. META uses an array of 128 
parallel processors to scan simultaneously 8,388,608 frequency channels in the 
range of 1420 megahertz and its so-called second harmonic, 2840 megahertz. More 
than 5 years of data have been taken, and META has covered the sky three times 
looking for an extraterrestrial signal. 
Of course, you have to be clever when listening. First, you have to recognize 
that even if a signal is sent out at 1420 megahertz, it may not be received at 
this frequency. This is because of the infamous Doppler effecta train whistle 
sounds higher when it is approaching and lower when it is receding. The same is 
true for all radiation emitted by a moving source. Since most of the stars in 
the galaxy are moving at velocities of several hundreds of kilometers per second 
relative to us, you cannot ignore the Doppler shift. (The Star Trek writers 
haven't ignored it; they added "Doppler compensators" to the transporter to 
account for the relative motion of the starship and the transporter target.) 
Reasoning that the transmitters of any signal would have recognized this fact, 
the META people have looked at the 1420 megahertz signal as it might appear if 
shifted from one of three reference frames: (a) one moving along with our local 
set of stars, (b) one moving along with the center of the galaxy, and (c) one 
moving along with the frame defined by the cosmic microwave background radiation 
left over from the big bang. Note that this makes it easy to distinguish such 
signals from terrestrial signals, because terrestrial signals are all emitted in 
a frame fixed on the Earth's surface, which is not the same as any of these 
frames. Thus terrestrial signals have a characteristic "chirp" when present in 
the META data. 
What would an extraterrestrial signal involve? Cocconi and Mor-rison suggested 
that we might look for the first few prime numbers: 1,3,5,7,11,13.... In fact, 
this is precisely the series that Picard taps out in the episode "Allegiance," 
when he is trying to let his captors know that they are dealing with an 
intelligent species. Pulses from, say, a surface storm on a star are hardly 
likely to produce such a series. The META people have searched for an even 
simpler signal: a uniform constant tone at a fixed frequency. Such a "carrier" 
wave is easy to search for. 
Horowitz and his collaborator, the Cornell astronomer Carl Sagan, have reported 
on an analysis of the 5 years of META data. Thirty-seven candidate events, out 
of 100,000 billion signals detected, were isolated. However, none of these 
"signals" has ever repeated. Horowitz and Sagan prefer to interpret the data as 
providing no definitive signal thus far. As a result, they have been able to put 
limits on the number of highly advanced civilizations within various distances 
of our Sun which have been trying to communicate with us. 
Nevertheless, in spite of the incredible complexity of the search effort, only a 
small range of frequencies has actually been explored, and the power 
requirements for a signal capable of being detected by the META telescope are 
rather largecivilizations would have to use broadcast powers in excess of the 
total power received on Earth from the Sun (about 1017 watts) in their 
transmitters to produce a detectable signal. Thus, there is yet no cause for 
pessimism. It is a difficult task just to listen. The META group is now building 
a bigger, better (or BETA) detector, which should improve the search strength by 
roughly a factor of 1000. 
The search goes on. The fact that we have not yet heard anything should not 
dissuade us. It is something like what my friend Sidney Coleman, a physics 
professor at Harvard, once told me about buying a house: You shouldn't get 
discouraged if you look at a hundred and don't find anything. You only have to 
like one.... A single definitive signal, as improbable as it is that we will 
ever hear one, would change the way we think about the universe, and would 
herald the beginning of a new era in the evolution of the human race. 
And for those of you who are disheartened at the idea that our first contact 
with extraterrestrial civilizations will not be made by visiting them in our 
starships, remember the Cytherians, a very advanced civilization encountered by 
the Enterprise who made outside contact with other civilizations not by 
traveling through space themselves but by bringing space travelers to them. In 
some sense, that is exactly what we are doing as we listen to the signals from 
the stars. 
CHAPTER NINE - The Menagerie of Possibilities
"That is the exploration that awaits you! Not mapping stars and studying nebula, 
but charting the unknown possibilities of existence." 
Q to Picard, in "All Good Things...." 
 
In the course of more than 13 TV-years of the various Star Trek series, the 
writers have had the opportunity to tap into some of the most exciting ideas 
from all fields of physics. Sometimes they get it right; sometimes they blow it. 
Sometimes they just use the words that physicists use, and sometimes they 
incorporate the ideas associated with them. The topics they have dealt with read 
like a review of modern physics: special relativity, general relativity, 
cosmology, particle physics, time travel, space warping, and quantum 
fluctuations, to name just a few. 
In this penultimate chapter, I thought it might be useful to make a brief 
presentation of some of the more interesting ideas from modern physics which the 
Star Trek writers have borrowedin particular, concepts I haven't concentrated 
on elsewhere in the book. Because of the diversity of the ideas, I give them 
here in glossary form, with no particular ordering or theme. In the last 
chapter, I will follow a similar formatthis time to sample the most blatant 
physics blunders in the series, as chosen by myself, selected fellow-physicists, 
and various trekkers. In both chapters, I have restricted my lists to the top 
ten examples; there are a lot more to choose from. 
 
THE SCALE OF THE GALAXY AND THE UNIVERSE: Our galaxy is the stage on which the 
Star Trek drama is enacted. Throughout the series, galactic distance scales of 
various sorts play a crucial role in the action. Units from AUs (for 
Astronomical Unit: 1 AU is 93 million miles, the distance from the Earth to the 
Sun), which were used to describe the size of the V'ger cloud in the first Star 
Trek movie, to light-years are bandied about. In addition, various features of 
our galaxy are proposed, including a "Great Barrier" at the center (Star Trek V: 
The Final Frontier) and, in the original series, a "galactic barrier" at the 
edge (cf. "Where No Man Has Gone Before," "By Any Other Name," and "Is There in 
Truth No Beauty?"). It seems appropriate, therefore, in order to describe the 
playing field where Star Trek's action takes place, to offer our own present 
picture of the galaxy and its neighbors, and of distance scales in the universe. 

Because of the large number of digits required, one rarely expresses 
astronomical distances in conventional units such as miles or kilometers. 
Instead, astronomers have created several fiducial lengths that seem more 
appropriate. One such unit is the AU, the distance between the Earth and the 
Sun. This is the characteristic distance scale of the solar system, with Pluto, 
the ultima Thule, being nearly 40 AU from the Sun. In Star Trek: The Motion 
Picture, the V'ger cloud is described as 82 AU in diameter, which is remarkably 
bigbigger, in fact, than the size of our solar system! 
For comparison with interstellar distances, it is useful to express the 
Earth-Sun distance in terms of the time it takes light (or the time it would 
take the Enterprise at warp 1) to travel from the Sun to the Earthabout 8 
minutes. (This should be the time it would take light to travel to most Class M 
planets from their suns.) Thus, we can say that an AU is 8 light-minutes. By 
comparison, the distance to the nearest star, Alpha Centauria binary star 
system where the inventor of warp drive, Zefrem Cochrane, apparently livedis 
about 4 light-years! This is a characteristic distance between stars in our 
region of the galaxy. It would take rockets, at their present rate of speed, 
more than 10,000 years to travel from here to Alpha Centauri. At warp 9, which 
is about 1500 times the speed of light, it would take about 6 hours to traverse 
1 light-year. 
The distance of the Sun from the center of the galaxy is approximately 25,000 
light-years. At warp 9, it would take almost 15 years to traverse this distance, 
so it is unlikely that Sybok, having commandeered the Enterprise, would have 
been able to take her to the galactic center, as he did in Star Trek V: The 
Final Frontier, unless the Enterprise was essentially already there. 
The Milky Way is a spiral galaxy, with a large central disk of stars. It is 
approximately 100,000 light-years across and a few thousand light-years deep. 
The Voyager, tossed 70,000 light-years away from Earth in the first episode of 
that series, would thus indeed be on the other side of the galaxy. At warp 9, 
the ship would take about 50 years to return to the neighborhood of our Sun from 
that distance. 
At the center of our galaxy is a large galactic bulgea dense conglomeration of 
starsseveral thousand light-years across. It is thought to harbor a black hole 
of about a million solar masses. Black holes ranging from 100,000 to more than a 
billion solar masses are likely at the center of many other galaxies. 
A roughly spherical halo of very old stars surrounds the galaxy. The 
conglomerations of thousands of stars called globular clusters found here are 
thought to be among the oldest objects in our galaxy, perhaps as old as 18 
billion years according to our current methods of datingmore ancient even than 
the "black cluster" in the episode "Hero Worship," which was said to be 9 
billion years old. An even larger spherical halo, consisting of "dark matter" 
(about which more later), is thought to encompass the galaxy. This halo is 
invisible to all types of telescopes; its existence is inferred from the motion 
of stars and gas in the galaxy, and it may well contain 10 times as much mass as 
the observable galaxy. 
The Milky Way is an average-size spiral galaxy, containing a few hundred billion 
stars. There are approximately 100 billion galaxies in the observable universe, 
each containing more or less that many stars! Of the galaxies we see, roughly 70 
percent are spiral; the rest are somewhat spherical in shape and are known as 
elliptical galaxies. The largest of them are giant ellipticals more than 10 
times as massive as the Milky Way. 
Most galaxies are clustered in groups. In our local group, the nearest galaxies 
to the Milky Way are small satellite galaxies orbiting our own. These objects, 
observable in the Southern Hemisphere, are called the Large and Small Magellanic 
Clouds. It is about 6 million light-years to the nearest large galaxy, the 
Andromeda galaxyhome to the Kelvans, who attempt to take over the Enterprise 
and return to their home galaxy in the original-series episode "By Any Other 
Name." At warp 9, the voyage would take approximately 4000 years! 
Because of the time it takes light to travel, as we observe farther and farther 
out, we are also observing farther and farther back in time. The farthest we can 
now observe with electromagnetic sensors is back to a time when the universe was 
about 300,000 years old. Before then, matter existed as a hot ionized gas opaque 
to electromagnetic radiation. When we look out in all directions, we see the 
radiation emitted when matter and radiation finally "decoupled." This is known 
as the cosmic microwave background. Observing it, most recently with the COBE 
satellite launched by NASA in 1989, we get a picture of what the universe looked 
like when it was only about 300,000 years old. 
Finally, the universe itself is expanding uniformly. As a result, distant 
galaxies are observed to be receding from usand the farther away they are, the 
faster they are receding, at a rate directly proportional to their distance from 
us. This rate of expansion, characterized by a quantity called the Hubble 
constant, is such that galaxies located 10 million light-years from us are 
moving away at an average rate of about 150 to 300 kilometers per second. 
Working backward, we find that all the observed galaxies in the universe would 
converge about 10 billion to 20 billion years ago, at the time of the big bang. 
 
DARK MATTER: As I mentioned above, our galaxy is apparently immersed in a vast 
sea of invisible material.1 By studying the motion of the stars, of hydrogen gas 
clouds, and even of the Large and Small Magellanic Clouds around the galactic 
center, and using Newton's laws relating the velocity of orbiting objects to the 
mass pulling them, it has been determined that there is a roughly spherical halo 
of dark material stretching out to distances perhaps 10 times as far from the 
center of the galaxy as we are. This material accounts for at least 90 percent 
of the mass of the Milky Way. Moreover, as we observe the motion of other 
galaxies, including the ellipticals, and also the motion of groups of galaxies, 
we find that there is more matter associated with these systems than we can 
account for on the basis of the observable material. The entire observable 
universe therefore seems to be dominated by dark matter. It is currently 
believed that between 90 and 99 percent of the mass of the universe is made of 
this material. 
The notion of dark matter has crept into both the Next Generation and the 
Voyager series, and in an amusing way. For example, in the Voyager episode 
"Cathexis," the ship enters a "dark matter nebula," which, as you might imagine, 
is like a dark cloud, so that you cannot see into it. The Enterprise had already 
encountered similar objects, including the "black cluster" mentioned earlier. 
However, the salient fact about dark matter is not that it shields light in any 
way but that it does not shinethat is, emit radiationand does not even absorb 
significant amounts of radiation. If it did either, it would be detectable by 
telescopes. If you were inside a dark matter cloud, as we probably are, you 
would not even see it. 
The question of the nature, origin, and distribution of dark matter is probably 
one of the most exciting unresolved issues in cosmology today. Since this 
unknown material dominates the mass density of the universe, its distribution 
must have determined how and when the observable matter gravitationally 
collapsed to create the galactic clusters, galaxies, stars, and planets that 
make the universe so interesting to us. Our very existence is directly dependent 
on this material. Moreover, the amount of dark matter in the universe will 
determine the universe's eventual fate: whether it ends in a bang (by 
recollapsing) or an endless whimper (by continuing to expand even as the stars 
eventually burn out) will depend on how much matterof whatever sortit 
contains, since gravitational attraction is what slows the expansion. 
Even more interesting are the strong arguments that the dark matter may be made 
of particles completely different from the protons and neutrons that make up 
normal matter. Independent limits on the amount of normal matter in the 
universe, based on calculations of nuclear reaction rates in the early universe 
and the subsequent formation of light elements, suggest that there may not be 
enough protons and neutrons to account for the dark matter around galaxies and 
clusters. Moreover, it seems that in order for the small fluctuations in the 
initial distribution of matter to have collapsed in the hot plasma of the early 
universe to form the galaxies and clusters we observe today, some new type of 
elementary particleof a kind that does not interact with electromagnetic 
radiationhad to be involved. If the dark matter is indeed made of some new type 
of elementary particle, then: 
(a) the dark matter is not just "out there," it is in this room as you are 
reading this book, passing imperceptibly through your body. These exotic 
elementary particles would not clump into astronomical objects; they would form 
a diffuse "gas" streaming throughout the galaxy. Since they interact at best 
only very weakly with matter, they would be able to sail through objects as big 
as the Earth. Indeed, examples of such particles already exist in nature 
notably, neutrinos (particles that should be familiar to trekkers, and which I 
will later discuss). 
(b) the dark matter might be detected directly here on Earth, using 
sophisticated elementary-particle-detection techniques. Various detectors 
designed with a sensitivity to various dark matter candidates are currently 
being constructed. 
(c) the detections of such particles might revolutionize elementary particle 
physics. It is quite likely that these objects are remnants of production 
processes in the very early universe, well before it was 1 second old, and would 
thus be related to physics at energy scales comparable to or even beyond those 
we can directly probe using modern accelerators. 
Of course, as exciting as this possibility is, we are not yet certain that the 
dark matter may not be made of less exotic stuff. There are many ways of putting 
protons and neutrons together so that they do not shine. For example, if we 
populated the galaxy with snowballs, or boulders, these would be difficult to 
detect. Perhaps the most plausible possibility for this scenario is that there 
are many objects in the galaxy which are almost large enough to be stars but are 
too small for nuclear reactions to start occurring in their cores. Such objects 
are known as brown dwarfs, and Data and his colleagues aboard the Enterprise 
have discussed them (for instance, in "Manhunt"). In fact, there are interesting 
experiments going on right now to find out whether or not brown dwarfsknown in 
this context as MACHOs (for Massive Astrophysical Compact Halo Objects)make up 
a significant component of the dark matter halo around the Milky Way galaxy. 
While these objects are not directly observable, if one of them were to pass in 
front of a star the star's light would be affected by the MACHO's gravity in 
such a way as to make the star appear brighter. This "gravitational lensing" 
phenomenon was first predicted by Einstein back in the 1930s, and we now have 
the technology to detect it. Several experiments are observing literally 
millions of stars in our galaxy each night, to see if this lensing phenomenon 
takes place. The sensitivity is sufficient to detect a dark matter halo of 
MACHOS, if they do indeed make up most of the dark matter surrounding our 
galaxy. Preliminary data have set upper limits that tend to suggest that the 
dark matter halo is not composed of MACHOs, but the question is still open. 
 
NEUTRON STARS: These objects are, as you will recall, all that is left of the 
collapsed cores of massive stars that have undergone a supernova. Although they 
typically contain a mass somewhat in excess of the mass of our Sun, they are so 
compressed that they are about the size of Manhattan! Once again, the Star Trek 
writers have outdone themselves in the nomenclature department. The Enterprise 
has several times encountered material expelled from a neutron stara material 
that the writers have dubbed "neutronium." Since neutron stars are composed 
almost entirely of neutrons held so tightly together that the star is basically 
one huge atomic nucleus, the name is a good one. The Doomsday machine in the 
episode of the same name was apparently made of pure neutronium, which is why it 
was impervious to Federation weapons. However, in order for this material to be 
stable it has to be under the incredibly high pressure created by the 
gravitational attraction of a stellar mass of material only 15 kilometers in 
radius. In the real world, such material exists only as part of a neutron star. 
The Enterprise has had several close calls near neutron stars. In the episode 
"Evolution," when the Nanites began eating the ship's computers, the crew was in 
the act of studying a neutron star that was apparently about to erupt as it 
accreted material. In the episode "The Masterpiece Society," the Enterprise must 
deflect a stellar core fragment hurtling toward Moab IV. 
There are no doubt millions of neutron stars in the galaxy. Most of these are 
born with incredibly large magnetic fields inside them. If they are spinning 
rapidly, they make wonderful radio beacons. Radiation is emitted from each of 
their poles, and if the magnetic field is tilted with respect to the spin axis, 
a rotating beacon is created. On Earth, we detect these periodic bursts of radio 
waves, and call their sources pulsars. Rotating out in space, they make the best 
clocks in the universe. The pulsar signals can keep time to better than one 
microsecond per year. Moreover, some pulsars produce more than 1000 pulses per 
second. This means that an object that is essentially a huge atomic nucleus with 
the mass of the Sun and 10 to 20 kilometers across is rotating over 1000 times 
each second. Think about that. The rotation speed at the neutron star surface is 
therefore almost half the speed of light! Pulsars are one illustration of the 
fact that nature produces objects more remarkable than any the Star Trek writers 
are likely to invent. 
 
OTHER DIMENSIONS: As James T. Kirk slowly drifts in and out of this universe in 
"The Tholian Web," we find that the cause is a "spatial interphase" briefly 
connecting different dimensional planes, which make up otherwise "parallel 
universes." Twice before in the series, Kirk encountered parallel universesone 
made of antimatter, in "The Alternative Factor," and the other accessed via the 
transporter, in "Mirror, Mirror." In The Next Generation, we have the 
Q-continuum, Dr. Paul Manheim's nonlinear time "window into other dimensions," 
and of course subspace itself, containing an infinite number of dimensions, 
which aliens, like the ones who kidnapped Lieutenant Riker in "Schisms," can 
hide in. 
The notion that somehow the four dimensions of space and time we live in are not 
all there is has had great tenacity in the popular consciousness. Recently a 
Harvard psychiatrist wrote a successful book (and apparently got in trouble with 
the Medical School) in which he reported on his analysis of a variety of 
patients, all of whom claimed they had been abducted by aliens. In an interview, 
when asked where the aliens came from and how they got here, he is reported to 
have suggested, "From another dimension." 
This love affair with higher dimensions no doubt has at its origin the special 
theory of relativity. Once three-dimensional space was tied with time to make 
four-dimensional spacetime by Hermann Minkowski, it was natural to suppose that 
the process might continue. Moreover, once general relativity demonstrated that 
what we perceive as the force of gravity can be associated with the curvature of 
spacetime, it was not outrageous to speculate that perhaps other forces might be 
associated with curvature in yet other dimensions. 
Among the first to speculate on this idea were the Polish physicist Theodor 
Kaluza in 1919 and, independently, the Swedish physicist Oskar Klein in 1926. 
They proposed that electromagnetism could be unified with gravity in a 
five-dimensional universe. Perhaps the electromagnetic force is related to some 
"curvature" in a fifth dimension, just as the gravitational force is due to 
curvature in four-dimensional spacetime. 
This is a very pretty idea, but it has problems. In fact, in any scenario in 
which one envisages extra dimensions in the universe, one has to explain why we 
don't experience these dimensions as we do space and time. The proposed answer 
to this question is very important, because it crops up again and again when 
physicists consider the possibility of higher dimensions in the universe. 



Consider a cylinder and an intelligent bug. As long as the circumference of the 
cylinder is large compared to the size of the bug, then the bug can move along 
both dimensions and will sense that it is crawling on a two-dimensional surface. 

However, if the circumference of the cylinder becomes very small, then as far as 
the bug is concerned it is crawling on a one-dimensional objectnamely, a line 
or a stringand can move only up or down: 

Now think how such a bug might actually find out that there is another 
dimension, corresponding to the circumference of the cylinder. With a 
microscope, it might be able to make out the "string's" width. However, the 
wavelength of radiation needed to resolve sizes this small would have to be on 
order of the diameter of the cylinder or smaller, because, as I noted in chapter 
5, waves scatter off only those objects that are at least comparable to their 
wavelength. Since the energy of radiation increases as its wavelength decreases, 
it would require a certain minimum energy of radiation to resolve this "extra 
dimension." 
If somehow a fifth dimension were "curled up" in a tight circle, then unless we 
focused a lot of energy at a small point, we would not be able to send waves 
traveling through it to probe its existence, and the world would continue to 
look to us to be effectively four-dimensional. After all, we know that space is 
three-dimensional because we can probe it with waves traveling in all three 
dimensions. 
If the only waves that can be sent into the fifth dimension have much more 
energy than we can produce even in high-energy accelerators, then we cannot 
experience this extra dimension. 
In spite of its intrinsic interest, the Kaluza-Klein theory cannot be a complete 
theory. First, it does not explain why the fifth dimension would be curled up 
into a tiny circle. Second, we now know of the existence of two other 
fundamental forces in nature beyond electro-magnetism and gravitythe strong 
nuclear force and the weak nuclear force. Why stop at a fifth dimension? Why not 
include enough extra dimensions to accommodate all the fundamental forces? 
In fact, modern particle physics has raised just such a possibility. The modern 
effort, centered around what is called superstring theory, focused initially on 
extending the general theory of relativity so that a consistent theory of 
quantum gravity could be constructed. In the end, however, the goal of a unified 
theory of all interactions has resurfaced. 
I have already noted the challenges faced in developing a theory wherein general 
relativity is made consistent with quantum mechanics. The key difficulty in this 
effort is trying to understand how quantum fluctuations in spacetime can be 
handled. In elementary particle theory, quantum excitations in fieldsthe 
electric field, for exampleare manifested as elementary particles, or quanta. 
If one tries to understand quantum excitations in the gravitational fieldwhich, 
in general relativity, correspond to quantum excitations of spacetime the 
mathematics leads to nonsensical predictions. 
The advance of string theory was to suppose that at microscopic levels, typical 
of the very small scales (that is, 10-33 cm) where quantum gravitational effects 
might be important, what we think of as pointlike elementary particles actually 
could be resolved as vibrating strings. The mass of each particle would 
correspond in some sense to the energy of vibration of these strings. 
The reason for making this otherwise rather outlandish proposal is that it was 
discovered as early as the 1970s that such a theory requires the existence of 
particles having the properties that quantum excitations in spacetimeknown as 
gravitonsshould have. General relativity is thus in some sense imbedded in the 
theory in a way that may be consistent with quantum mechanics. 
However, a quantum theory of strings cannot be made mathematically consistent in 
4 dimensions, or 5, or even 6. It turns out that such theories can exist 
consistently only in 10 dimensions, or perhaps only 26! Indeed, Lieutenant 
Reginald Barclay, while he momentarily possessed an IQ of 1200 after having been 
zapped by a Cytherian probe, had quite a debate with Albert Einstein on the 
holodeck about which of these two possibilities was more palatable in order to 
incorporate quantum mechanics in general relativity. 
This plethora of dimensions may seem an embarrassment, but it was quickly 
recognized that like many embarrassments it also presented an opportunity. 
Perhaps all the fundamental forces in nature could be incorporated in a theory 
of 10 or more dimensions, in which all the dimensions but the four we know curl 
up with diameters on the order of the Planck scale (10-33 cm)as Lieutenant 
Barclay surmised they mustand are thus unmeasurable today. 
Alas, this great hope has remained no more than that. We have, at the present 
time, absolutely no idea whether the tentative proposals of string theory can 
produce a unified Theory of Everything. Also, just as with the Kaluza-Klein 
theory, no one has any clear notion of why the other dimensions, if they exist, 
would curl up, leaving four-dimensional spacetime on large scales. 
So, the moral of this saga is that Yes, Virginia, there may be extra dimensions 
in the universe. In fact, there is now some reason to expect them. However, 
these extra dimensions are not the sort that might house aliens who could then 
abduct psychiatric patients (or Commander Riker, for that matter). They are not 
"parallel universes." 
They also cannot be mixed up with the four dimensions of spacetime in a way that 
would allow objects to drift from one place to another in space by passing 
through another dimension, as "subspace" seems to allow in the Star Trek 
universe. 
Nevertheless, we cannot rule out the possibility that there might exist 
microscopic or even macroscopic "bridges" to otherwise disconnected (or 
parallel) universes. Indeed, in general relativity, regions of very high 
curvatureinside a black hole, or in a wormholecan be thought of as connecting 
otherwise disconnected and potentially very large regions of spacetime. I know 
of no reason to expect such phenomena outside black holes and wormholes, based 
on our present picture of the universe, but since we cannot rule them out, I 
suppose that Federation starships are free to keep finding them. 
ANYONS: In the Next Generation episode "The Next Phase," a transporter mix-up 
with a new Romulan cloaking device that puts matter "out of phase" with other 
matter causes Geordi LaForge and Ro Laren to vanish. They are presumed dead, and 
remain invisible and incommunicado until Data modifies an "anyon emitter" for 
another purpose and miraculously "dphass" them. 
If the Star Trek writers had never heard of anyons, and I am willing to bet that 
they hadn't, their penchant for pulling apt names out of the air is truly eerie. 
Anyons are theoretical constructs proposed and named by my friend Frank Wilczek, 
a physicist at the Institute for Advanced Study in Princeton, and his 
collaborators. Incidentally, he also invented another particlea dark matter 
candidate he called the axion, after a laundry detergent. "Axionic chips" also 
crop up in Star Trek, as part of an advanced machine's neural network. But I 
digress. 
In the three-dimensional space in which we live, elementary particles are 
designated as fermions and bosons, depending on their spin. We associate with 
each variety of elementary particle a quantum number, which gives the value of 
its spin. This number can be an integer (0,1, 2,... ) or a half integer (1/2, 
3/2, 5/2,...). Particles with integer spin are called bosons, and particles with 
half integer spin are called fermions. The quantum mechanical behavior of 
fermions and bosons is different: When two identical fermions are interchanged, 
the quantum mechanical wavefunction describing their properties is multiplied by 
minus 1, whereas in an interchange of bosons nothing happens to the 
wavefunction. Therefore, two fermions can never be in the same place, because if 
they were, interchanging them would leave the configuration identical but the 
wavefunction would have to be multiplied by minus 1, and the only thing that can 
be multiplied by minus 1 and remain the same is 0. Thus, the wavefunction must 
vanish. This is the origin of the famous Pauli exclusion principleoriginally 
applied to electronswhich states that two identical fermions cannot occupy the 
same quantum mechanical state. 
In any case, it turns out that if one allows panicles to move in only two 
dimensionsas the two-dimensional beings encountered by the Enterprise (see next 
item) are forced to do; or, more relevantly, as happens in the real world when 
atomic configurations in a crystal are arranged so that electrons, say, travel 
only on a two-dimensional plane the standard quantum mechanical rules that 
apply in three-dimensional space are changed. Spin is no longer quantized, and 
particles can carry any value for this quantity. Hence, instead of fermi-ons or 
bos-ons, one can have any-ons. This was the origin of the name, and the idea 
that Wilczek and others have explored. 
Back to the Star Trek writers: What I find amusing is that the number by which 
the wavefunction of particles is multiplied when the particles are interchanged 
is called a "phase." Fermion wavefunctions are multiplied by a phase of minus 1, 
while bosons are multiplied by a phase of 1 and hence remain the same. Anyons 
are multiplied by a combination of 1 and an imaginary number (imaginary numbers 
are the square roots of negative numbers), and hence in a real sense are "out of 
phase" with normal particles. So it seems fitting that an "anyon emitter" would 
change the phase of something, doesn't it? 
COSMIC STRINGS: In the Next Generation episode "The Loss," the crew of the 
Enterprise encounters two-dimensional beings who have lost their way. These 
beings live on a "cosmic-strings fragment." In the episode, this is described as 
an infinitesimally thin filament in space, with a very strong gravitational pull 
and vibrating with a characteristic set of "subspace" frequencies. 
In fact, cosmic strings are objects proposed to have been created during a phase 
transition in the early universe. One of the world's experts on these 
theoretical objects recently joined the faculty at Case Western Reserve, so I 
hear a lot about cosmic strings these days. Their properties would be similar in 
some respects to the object encountered by the Enterprise. 
During a phase transition in materialsas when water boils, say, or freezesthe 
configuration of the material's constituent particles changes. When water 
freezes, it forms a crystalline structure. As crystals aligned in various 
directions grow, they can meet to form random lines, which create the patterns 
that look so pretty on a window in the winter. During a phase transition in the 
early universe, the configuration of matter, radiation, and empty space (which, 
I remind you, can carry energy) changes, too. Sometimes during these 
transitions, various regions of the universe relax into different 
configurations. As these configurations grow, they too can eventually 
meetsometimes at a point, and sometimes along a line, marking a boundary 
between the regions. Energy becomes trapped in this boundary line, and it forms 
what we call a cosmic string. 
We have no idea whether cosmic strings actually were created in the early 
universe, but if they were and lasted up to the present time they could produce 
some fascinating effects. They would be infinitesimally thinthinner than a 
protonyet the mass density they carry would be enormous, up to a million 
million tons per centimeter. They might form the seeds around which matter 
collapses to form galaxies, for example. They would also "vibrate," producing 
not subspace harmonics but gravitational waves. Indeed, we may well detect the 
gravitational wave signature of a cosmic string before we ever directly observe 
the string itself. 
So much for the similarities with the Star Trek string. Now for the differences. 
Because of the way they are formed, cosmic strings cannot exist in fragments. 
They have to exist either in closed loops or as a single long string that winds 
its way through the universe. Moreover, in spite of their large mass density, 
cosmic strings exert no gravitational force on faraway objects. Only if a cosmic 
string moves past an object will the object experience a sudden gravitational 
force. These are subtle points, however; on the whole, the Star Trek writers 
have done pretty well by cosmic strings. 
 
QUANTUM MEASUREMENTS: There was a wonderful episode in the final season of The 
Next Generation, called "Parallels," in which Worf begins to jump between 
different "quantum realities." The episode touches, albeit incorrectly, on one 
of the most fascinating aspects of quantum mechanicsquantum measurement theory. 

Since we live on a scale at which quantum mechanical phenomena are not directly 
observed, our entire intuitive physical picture of the universe is classical in 
character. When we discuss quantum mechanics, we generally use a classical 
language, so as to try and explain the quantum mechanical world in terms we 
understand. This approach, which is usually referred to as "the interpretation 
of quantum mechanics" and so fascinates some philosophers of science, is 
benighted; what we really should be discussing is "the interpretation of 
classical mechanics"that is, how can the classical word we seewhich is only an 
approximation of the underlying reality, which in turn is quantum mechanical in 
naturebe understood in terms of the proper quantum mechanical variables? 
If we insist on interpreting quantum mechanical phenomena in terms of classical 
concepts, we will inevitably encounter phenomena that seem paradoxical, or 
impossible. This is as it should be. Classical mechanics cannot account properly 
for quantum mechanical phenomena, and so there is no reason that classical 
descriptions should make sense. 
Having issued this caveat, I will describe the relevant issues in classical 
mechanics terms, because these are the only tools of language I have. While I 
have the proper mathematical terms to describe quantum mechanics, like all other 
physicists I have recourse only to a classical mental picture, because all my 
direct experience is classical. 
As I alluded to in chapter 5, one of the most remarkable features of quantum 
mechanics is that objects observed to have some property cannot be said to have 
had that property the instant before the observation. The observation process 
can change the character of the physical system under consideration. The quantum 
mechanical wavefunc-tion of a system describes completely the configuration of 
this system at any one time, and this wavefunction evolves according to 
deterministic laws of physics. However, what makes things seem so screwy is that 
this wavefunction can encompass two or more mutually exclusive configurations at 
the same time. 
For example, if a particle is spinning clockwise, we say that its spin is "up." 
If it is spinning counterclockwise, we say that its spin is "down." Now, the 
quantum mechanical wavefunction of this particle can incorporate a sum with 
equal probabilities: spin up and spin down. If you measure the direction of the 
spin, you will measure either spin up or spin down. Once you have made the 
measurement, the wavefunction of the particle will from then on include only the 
component you measured the particle to have; if you measured spin up, you will 
go on measuring this same value for this panicle. 
This picture presents problems. How, you may ask, can the particle have had both 
spin up and spin down before the measurement? The correct answer is that it had 
neither. The configuration of its spin was indeterminate before the measurement. 

The fact that the quantum mechanical wavefunction that describes objects does 
not correspond to unique values for observables is especially disturbing when 
one begins to think of living objects. There is a famous paradox called 
"Schrdinger's cat." (Erwin Schrdinger was one of the young Turks in their 
twenties who, early in this century, helped uncover the laws of quantum 
mechanics. The equation describing the time evolution of the quantum mechanical 
wavefunction is known as Schrdinger's equation.) Imagine a box, inside of which 
is a cat. Inside the box, aimed at the cat, is a gun, which is hooked up to a 
radioactive source. The radioactive source has a certain quantum mechanical 
probability of decaying at any given time. When the source decays, the gun will 
fire and kill the cat. Is the wavefunction describing the cat, before I open the 
box, a linear superposition of a live cat and a dead cat? This seems absurd. 
Similarly, our consciousness is always unique, never indeterminate. Is the act 
of consciousness a measurement? If so, then it could be said that at any instant 
there is a nonzero quantum mechanical probability for a number of different 
outcomes to occur, and our act of consciousness determines which outcome we 
experience. Reality then has an infinite number of branches. At every instant 
our consciousness determines which branch we inhabit, but an infinite number of 
other possibilities exist a priori. 
This "many worlds" interpretation of quantum mechanicswhich says that in some 
other branch of the quantum mechanical wavefunction Stephen Hawking is writing 
this book and I am writing the forewordis apparently the basis for poor Worf's 
misery. Indeed, Data says as much during the episode. When Worf's ship traverses 
a "quantum fissure in spacetime," while simultaneously emitting a "subspace 
pulse," the barriers between quantum realities "break down," and Worf begins to 
jump from one branch of the wavefunction to another at random times, 
experiencing numerous alternative quantum realities. This can never happen, of 
course, because once a measurement has been made, the system, including the 
measuring apparatus (Worf, in this case), has changed. Once Worf has an 
experience, there is no going back ... or perhaps I should say sideways. The 
experience itself is enough to fix reality. The very nature of quantum mechanics 
demands this. 
There is one other feature of quantum mechanics touched upon in the same 
episode. The Enterprise crew are able to verify that Worf is from another 
"quantum reality" at one point by arguing that his "quantum signature at the 
atomic level" differs from anything in their world. According to Data, this 
signature is unique and cannot change due to any physical process. This is 
technobabble, of course; however, it does relate to something interesting about 
quantum mechanics. The entire set of all possible states of a system is called a 
Hubert space, after David Hubert, the famous German mathematician who, among 
other things, came very close to developing general relativity before Einstein. 
It sometimes happens that the Hubert space breaks up into separate sectors, 
called "superselection sectors." In this case, no local physical process can 
move a system from one sector to another. Each sector is labeled by some 
quantityfor instance, the total electric charge of the system. If one wished to 
be poetic, one could say that this quantity provided a unique "quantum 
signature" for this sector, since all local quantum operations preserve the same 
sector, and the behavior of the operations and the observables they are 
associated with is determined by this quantity. 
However, the different branches of the quantum mechanical wave-function of a 
system must be in a single superselection sector, because any one of them is 
physically accessible in principle. So, unfortunately for Worf, even if he did 
violate the basic tenets of quantum mechanics by jumping from one branch to 
another, no external observable would be likely to exist to validate his story. 
The whole point of the many-worlds interpretation of quantum mechanics (or any 
other interpretation of quantum mechanics, for that matter) is that you can 
never experience more than one world at a time. And thankfully there are other 
laws of physics that would prevent the appearance of millions of Enterprises 
from different realities, as happens at the end of the episode. Simple 
conservation of energy a purely classical conceptis enough to forbid it. 
 
SOLITONS: In the Next Generation episode "New Ground," the Enterprise assists in 
an experiment developed by Dr. Ja'Dor, of the planet Bilana III. Here a "soliton 
wave," a nondispersing wavefront of subspace distortion, is used to propel a 
test ship into warp speed without the need for warp drive. The system requires a 
planet at the far end of the voyage, which will deliver a scattering field to 
dissipate the wave. The experiment nearly results in a disaster, which is of 
course averted at the last instant. 
Solitons are not an invention of the Star Trek writers. The term is short for 
"solitary waves" and in fact refers to a phenomenon originally observed in water 
waves by a Scottish engineer, John Scott Russell, in 1834. While conducting an 
unpaid study of the design of canal barges for the Union Canal Society of 
Edinburgh, he noticed something peculiar. In his own words: 
 
I was observing the motion of a boat which was rapidly drawn along a narrow 
channel by a pair of horses, when the boat suddenly stoppedNot so the mass of 
water in the channel which it had put in motion; it accumulated round the prow 
of the vessel in a state of violent agitation, then suddenly leaving it behind, 
rolled forward with great velocity, assuming the form of a large solitary 
elevation, a rounded smooth and well defined heap of water, which continued its 
course along the channel apparently without change of form or diminution of 
speed, I followed it on horseback and overtook it still rolling on at a rate of 
some eight or nine miles an hour, preserving its original figure some thirty 
feet long and a foot to a foot and a half in height. Its height gradually 
diminished and after a chase of one or two miles I lost it in the windings of 
the channel. Such in the months of August 1834 was my first chance interview 
with that singular and beautiful phenomenon which I have called the Wave of 
Translation.2 
 
Scott Russell later coined the words "solitary wave" to describe this marvel, 
and the term has persisted, even as solitons have cropped up in many different 
subfields of physics. More generally, solitons are nondissipative, classically 
extended, but finite-size objects that can propagate from point to point. In 
fact, for this reason the disasters that drive the plot in "New Ground" could 
not happen. First of all, the soliton would not "emit a great deal of radio 
interference." If it did, it would be dissipating its energy. For the same 
reason, it would not continue to gain energy or change frequency. 
Normal waves are extended objects that tend to dissipate their energy as they 
travel. However, classical forcesresulting from some interaction throughout 
space, called a "field"generally keep soli-tons intact, so that they can 
propagate without losing energy to the environment. Because they are 
self-contained energetic solutions of the equations describing motion, they 
behave, in principle, just like fundamental objectslike elementary particles. 
In fact, in certain mathematical models of the strong interaction holding quarks 
together, the proton could be viewed as a soliton, in which case we are all made 
of solitons! New fields have been proposed in elementary-particle physics which 
may coalesce into "soliton stars"objects that are the size of stars but involve 
a single coherent field. Such objects have yet to be observed, but they may well 
exist. 
 
QUASARS: In the episode "The Pegasus"wherein we learn about the Treaty of 
Algon, which forbade the Federation to use cloaking deviceswe find Picard's 
Enterprise exploring the Mecoria Quasar. Earlier, in the original-series episode 
"The Galileo Seven," we learned that the original Enterprise had standing orders 
to investigate these objects whenever they might be encountered. But neither 
ship would in fact likely ever encounter a quasar while touring the outskirts of 
our galaxy. This is because quasars, the most energetic objects yet known in the 
universe (they radiate energies comparable to those of entire galaxies, yet they 
are so small that they are unresolvable by telescopes), are thought to be 
enormous black holes at the center of some galaxies, and to be literally 
swallowing up the central mass of their hosts. This is the only mechanism yet 
proposed that can explain the observed energies and size scales of quasars. As 
matter falls into a black hole, it radiates a great deal of energy (as it loses 
its potential gravitational energy). If million- or billion-solar-mass black 
holes exist at the centers of some galaxies, they can swallow whole star 
systems, which in turn will radiate the necessary energy to make up the quasar 
signal. For this reason, quasars are often part of what we call "active galactic 
nuclei." Also for this reason, you would not want to encounter one of these 
objects up close. The encounter would be fatal. 
 
NEUTRINOS: Neutrinos are my favorite particles in nature, which is why I saved 
them for last. I have spent a fair fraction of my own research on these 
critters, because we know so little about them yet they promise to teach us much 
about the fundamental structure of matter and the nature of the universe. 
Many times, in various Star Trek episodes, neutrinos are used or measured on 
starships. For example, elevated neutrino readings are usually read as objects 
traverse the Bajoran wormhole. We also learn in the episode "The Enemy" that 
Geordi LaForge's visor can detect neutrinos, when a neutrino beacon is sent to 
locate him so that he can be rescued from an inhospitable planet. A "neutrino 
field" is encountered in the episode "Power Play," and momentarily interferes 
with the attempt to transport some noncorporeal criminal life-forms aboard the 
Enterprise. 
Neutrinos were first predicted to exist as the result of a puzzle related to the 
decay of neutrons. While neutrons are stable inside atomic nuclei, free neutrons 
are observed to decay, in an average time of about 10 minutes, into protons and 
electrons. The electric charge works out fine, because a neutron is electrically 
neutral, while a proton has a positive charge and an electron an equal and 
opposite negative charge. The mass of a proton plus an electron is almost as 
much as the mass of a neutron, so there is not much free energy left to produce 
other massive particles in the decay, in any case. 
However, sometimes the proton and electron are observed to travel off in the 
same direction during the decay. This is impossible, because each emitted 
particle carries momentum. If the original neutron was at rest, it had zero 
momentum, so something else would have to be emitted in the decay to carry off 
momentum in the opposite direction. 
Such a hypothetical particle was proposed by Wolfgang Pauli in the 1930s, and 
was named a "neutrino" (for "little neutron") by Enrico Fermi. He chose this 
name because Pauli's particle had to be electrically neutral, in order not to 
spoil the charge conservation in the decay, and had to have, at most, a very 
small mass, in order to be produced with the energy available after the proton 
and electron were emitted. 
Because neutrinos are electrically neutral, and because they do not feel the 
strong force (which binds quarks and helps hold the nucleus together), they 
interact only very weakly with normal matter. Yet because neutrinos are produced 
in nuclear reactions, like those that power the Sun, they are everywhere. Six 
hundred billion neutrinos per second pierce every square centimeter of your body 
every second of every day, coming from the Sunan inexorable onslaught that has 
even inspired a poem by John Updike. You don't notice this neutrino siege, 
because the neutrinos pass right through your body without a trace. On average, 
these solar neutrinos could go through 10,000 light-years of material before 
interacting with any of it. 
If this is the case, then how can we be sure that neutrinos exist other than in 
theory, you may ask? Well, the wonderful thing about quantum mechanics is that 
it yields probabilities. That is why I wrote "on average" in the above 
paragraph. While most neutrinos will travel 10,000 light-years through matter 
without interacting with anything, if one has enough neutrinos and a big enough 
target, one can get lucky. 
This principle was first put to use in 1956 by Frederick Reines and Clyde Cowan, 
who put a several-ton target near a nuclear reactor and indeed observed a few 
events. This empirical discovery of the neutrino (actually, the antineutrino) 
occurred more than 20 years after it was posited, and well after most physicists 
had accepted its existence. 
Nowadays we use much larger detectors. The first observation of solar neutrinos 
was made in the 1960s, by Ray Davis and collaborators, using 100,000 gallons of 
cleaning fluid in a tank underground at the Homestake Gold Mine in South Dakota. 
Each day, on average, one neutrino from the Sun would interact with an atom of 
chlorine and turn it into an atom of argon. It is a tribute to these 
experimenters that they could detect nuclear alchemy at such a small rate. It 
turns out that the rate that their detector and all subsequent solar-neutrino 
detectors measured is different from the predicted rate. This "solar neutrino 
puzzle," as it is called, could signal the need for new fundamental physics 
associated with neutrinos. 
The biggest neutrino detector in the world is being built in the Kamiokande mine 
in Japan. Containing over 30,000 tons of water, it will be the successor to a 
5000-ton detector, which was one of two neutrino detectors to see a handful of 
neutrinos from a 1987 supernova in the Large Magellanic Cloud, more than 150,000 
light-years away! 
Which brings me back to where I began. Neutrinos are one of the new tools 
physicists are using to open windows on the universe. By exploiting every 
possible kind of elementary-particle detection along with our conventional 
electromagnetic detectors, we may well uncover the secrets of the galaxy long 
before we are able to venture out and explore it. Of course, if it were possible 
to invent a neutrino detector the size of Geordi's visor, that would be a great 
help! 
CHAPTER TEN - Impossibilities: The Undiscoverable Country
 
Geordi: "Suddenly it's like the laws of physics went right out the window." 
Q: "And why shouldn't they? They're so inconvenient!"
In "True Q" 
 
"Bones, I want the impossible checked out too."
Kirk to McCoy, in "The Naked Time" 


"What you're describing is ... nonexistence!"
Kirk to Spock, in "The Alternative factor" 
 
Any sensible trekker-physicist recognizes that Star Trek must be taken with a 
rather large grain of salt. Nevertheless, there are times when for one reason or 
another the Star Trek writers cross the boundaries from the merely vague or 
implausible to the utterly impossible. While finding even obscure technical 
flaws with each episode is a universal trekker pastime, it is not the subtle 
errors that physicists and physics students seem to relish catching. It is the 
really big ones that are most talked about over lunch and at coffee breaks 
during professional meetings. 
To be fair, sometimes a sweet piece of physics in the serieseven a minor 
momentcan trigger a morning-after discussion at coffee time. Indeed, I remember 
vividly the day when a former graduate student of mine at YaleMartin White, who 
is now at the University of Chicago came into my office fresh from seeing Star 
Trek VI: The Undiscovered Country. I had thought we were going to talk about 
gravitational waves from the very early universe. But instead Martin started 
raving about one particular scene from the moviea scene that lasted all of 
about 15 seconds. Two helmeted assassins board Chancellor Gorkon's vesselwhich 
has been disabled by photon torpedoes fired from the Enterprise and is thus in 
zero gravity conditionsand shoot everyone in sight, including Gorkon. What 
impressed Martin and, to my surprise, a number of other physics students and 
faculty I discussed the movie with, was that the drops of blood flying about the 
ship were spherical. On Earth, all drops of liquid are tear-shaped, because of 
the relentless pull of gravity. In a region devoid of gravity, like Gorkon's 
ship, even tears would be spherical. Physicists know this but seldom have the 
opportunity to see it. So by getting this simple fact perfectly right, the Star 
Trek special effects people made a lot of physics types happy. It doesn't take 
that much.... 
But the mistakes also keep us going. In fact, what may be the most memorable 
Star Trek mistake mentioned by a physicist doesn't involve physics at all. It 
was reported to me by the particle physicist (and science writer) Steven 
Weinberg, who won the Nobel Prize for helping develop what is now called the 
Standard Model of elementary particle interactions. As I knew that he keeps the 
TV on while doing intricate calculations, I wrote to him and asked for his Star 
Trek memories. Weinberg replied that "the main mistake made on Star Trek is to 
split an infinitive every damn time: To boldly go ... !" 
More often than not, though, it is the physics errors that get the attention of 
physicists. I think this is because these mistakes validate the perception of 
many physicists that physics is far removed from popular culturenot to mention 
the superior feeling it gives us to joke about the English majors who write the 
show. It is impossible to imagine that a major motion picture would somehow have 
Napoleon speaking German instead of French, or date the signing of the 
Declaration of Independence in the nineteenth century. And so when a physics 
mistake of comparable magnitude manages to creep into what is after all supposed 
to be a scientifically oriented series, physicists like to pounce. I was 
surprised to find out how many of my distinguished colleaguesfrom Kip Thorne to 
Weinberg to Sheldon Glashow, not to mention Stephen Hawking, perhaps the most 
famous physicist trekker of allhave watched the Star Trek series. Here is a 
list of my favorite blunders, gleaned from discussions with these and other 
physicists and e-mail from techni-trekkers. I have made an effort here to focus 
mostly (but not exclusively) on blunders of "down-to-Earth physics." Thus, for 
example, I don't address such popular complaints as "Why does the starlight 
spread out whenever warp speed is engaged?" and the like. Similarly, I ignore 
here the technobabblethe indiscriminant use of scientific and pseudoscientific 
terminology used during each episode to give the flavor of futuristic 
technology. Finally, I have tried for the most part to choose examples I haven't 
discussed before. 
 
"IN SPACE, NO ONE CAN HEAR YOU SCREAM": The promo for Alien got it right, but 
Star Trek usually doesn't. Sound waves DO NOT travel in empty space! Yet when a 
space station orbiting the planet Tanuga IV blows up, from our vantage point 
aboard the Enterprise we hear it as well as see it. What's worse, we hear it at 
the same time as we see it. Even if sound waves could travel in space, which 
they can't, the speed of a pressure wave such as sound is generally orders of 
magnitude smaller than the speed of light. You don't have to go farther than a 
local football game to discover that you see things before you hear them. 
A famous experiment in high school physics involves putting an electric buzzer 
in a bell jar, a glass container from which the air can be removed by a pump. 
When the air is removed, the sound of the buzzer disappears. As early as the 
seventeenth century, it was recognized that sound needed some medium to travel 
in. In a vacuum, such as exists inside the bell jar, there is nothing to carry 
the sound waves, so you don't hear the buzzer inside. To be more specific, sound 
is a pressure wave, or disturbance, which moves as regions where the pressure is 
higher or lower than the average pressure propagate through a medium. Take away 
the medium, and there is no pressure to have a disturbance in. Incidentally, the 
bell jar example was at the origin of a mystery I discussed earlier, which was 
very important in the history of physics. For while you cannot hear the buzzer, 
you can still see it! Hence, if light is supposed to be some sort of wave, what 
medium does it travel in which isn't removed when you remove the air? This was 
one of the prime justifications for the postulation of the aether. 
I had never taken much notice of the sound or lack of it in space in the series. 
However, after Steven Weinberg and several others mentioned that they remembered 
sound associated with Star Trek explosions, I checked the episode I had just 
watched"A Matter of Perspective," the one in which the Tanuga IV space station 
explodes. 
Sure enough, kaboom! The same thing happened in the next episode I watched (when 
a shuttle which was carrying stolen trilithium crystals away from the Enterprise 
blew up with a loud bang near the planet Arkaria). I next went to the most 
recent Star Trek movie, Generations. There, even a bottle of champagne makes 
noise when it explodes in space. 
In fact, a physics colleague, Mark Srednicki of U.C. Santa Barbara, brought to 
my attention a much greater gaffe in one episode, in which sound waves are used 
as a weapon against an orbiting ship. As if that weren't bad enough, the sound 
waves are said to reach "18 to the 12th power decibels." What makes this 
particularly grate on the ear of a physicist is that the decibel scale is a 
logarithmic scale, like the Richter scale. This means that the number of 
decibels already represents a power of 10, and they are normalized so that 20 
decibels is 10 times louder than 10 decibels, and 30 decibels is 10 times louder 
again. Thus, 18 to the 12th power decibels would be 10(18)^12, or 1 followed by 
11,568,313,814,300 zeroes times louder than a jet plane! 
 
FASTER THAN A SPEEDING PHASER: While faster-than-light warp travel is something 
we must live with in Star Trek, such a possibility relies on all the subtleties 
of general relativity and exotic new forms of matter, as I have described. But 
for normal objects doing everyday kinds of things, light speed is and always 
will be the ultimate barrier. Sometimes this simple fact is forgotten. In a wild 
episode called "Wink of an Eye," Kirk is tricked by the Scalosians into drinking 
a potion that speeds up his actions by a huge factor to the Scalosian level, so 
that he can become a mate for their queen, Deela. The Scalosians live a 
hyperaccelerated existence and cannot be sensed by the Enterprise's crew. Before 
bedding the queen, Kirk first tries to shoot her with his phaser. However, since 
she can move in the wink of an eye by normal human standards, she moves out of 
the way before the beam can hit her. Now, what is wrong with this picture? The 
answer is, Everything! 
What has been noticed by some trekkers is that the accelerated existence 
required for Deela to move significantly in the time it would take a phaser beam 
to move at the speed of light across the room would make the rest of the episode 
impossible. Light speed is 300 million meters per second. Deela is about a meter 
or so away from Kirk when he fires, implying a light travel time of about 1/300 
millionth of a second. For this time to appear to take a second or so for her, 
the Scalosian clock must be faster by a factor of 300 million. However, if this 
is so, 300 million Scalosian seconds take 1 second in normal Enterprise time. 
Unfortunately, 300 million seconds is about 10 years. 
OK, let's forgive the Star Trek writers this lapse. Nevertheless, there is a 
much bigger problem, which is impossible to solve and which several physicists I 
know have leapt upon. Phasers are, we are told, directed energy weapons, so that 
the phaser beam travels at the speed of light. Sorry, but there is no way out of 
this. If phasers are pure energy and not particle beams, as the Star Trek 
technical manual states, the beams must move at the speed of light. No matter 
how fast one moves, even if one is sped up by a factor of 300 million, one can 
never move out of the way of an oncoming phaser beam. Why? Because in order to 
know it is coming, you have to first see the gun being fired. But the light that 
allows you to see this travels at the same speed as the beam. Put simply, it is 
impossible to know it is going to hit you until it hits you! As long as phaser 
beams are energy beams, there is no escape. A similar problem involving the 
attempt to beat a phaser beam is found in the Voyager episode "The Phage." 
Sometimes, however, it is the Star Trek critics who make the mistakes. I was 
told that I should take note of an error in Generations in which a star shining 
down on a planet is made to disappear and at the same instant the planet 
darkens. This of course is impossible, because it takes light a finite time to 
travel from the star to the planet. Thus, when I turn off the light from a star, 
the planet will not know it for some time. However, in Generations, the whole 
process is seen from the surface of the planet. When viewed from the planet, the 
minute the star is seen to implode, the planet's surface should indeed get dark. 
This is because both the information that the star has imploded and the lack of 
light will arrive at the planet at the same time. Both will be delayed, but they 
will be coincident! 
Though the writers got this right, they blew it by collapsing the delay to an 
unreasonably short time. We are told that the probe that will destroy the star 
will take only 11 seconds to reach it after launch from the planet's surface. 
The probe is traveling at sublight speeds as we can ascertain because it takes 
much less than twice that time after the probe is launched for those on the 
planet to see the star begin to implode, which indicates that the light must 
have taken fewer than 11 seconds to make the return journey. The Earth, by 
comparison, is 8 light-minutes from our Sun, as I have noted. If the Sun 
exploded now, it would take 8 minutes for us to know about it. I find it hard to 
believe that the Class M planet in Generations could exist at a distance of 10 
light-seconds from a hydrogen-burning star like our Sun. This distance is about 
5 times the size of the Sunfar too close for comfort. 
 
IF THE PLOT ISN'T CRACKED, MAYBE THE EVENT HORIZON IS: While I said I wouldn't 
dwell on technobabble, I can't help mentioning that the Voyager series wins in 
that department hands down. Every piece of jargon known to modern physics is 
thrown in as the Voyager tries to head home, traveling in time with the 
regularity of a commuter train. However, physics terms usually mean something, 
so that when you use them as a plot device you are bound to screw up every now 
and then. I mentioned in chapter 3 that the "crack" in the event horizon that 
saves the day for the Voyager (in the feckless "Phage" episode) sounds 
particularly ludicrous to physicists. A "crack" in an event horizon is like 
removing one end of a circle, or like being a little bit pregnant. It doesn't 
mean anything. The event horizon around a black hole is not a physical entity, 
but rather a location inside of which all trajectories remain inside the hole. 
It is a property of curved space that the trajectory of anything, including 
light, will bend back toward the hole once you are inside a certain radius. 
Either the event horizon exists, in which case a black hole exists, or it 
doesn't. There is no middle ground big enough to slip a needle through, much 
less the Voyager. 
 
HOW SOLID A GUY IS THE DOCTOR?: I must admit that the technological twist I like 
the most in the Voyager series is the holographic doctor. There is a wonderful 
scene in which a patient asks the doctor how he can be solid if he is only a 
hologram. This is a good question. The doctor answers by turning off a "magnetic 
confinement beam" to show that without it he is as noncorporeal as a mirage. He 
then orders the beam turned back on, so that he can slap the poor patient 
around. It's a great moment, but unfortunately it's also an impossible one. As I 
described in chapter 6, magnetic confinement works wonders for charged 
particles, which experience a force in a constant magnetic field that causes 
them to move in circular orbits. However, light is not charged. It experiences 
no force in a magnetic field. Since a hologram is no more than a light image, 
neither is the doctor. 
 
WHICH IS MORE SENSITIVE, YOUR HANDS OR YOUR BUTT? OR, TO INTERPHASE, OR NOT TO 
INTERPHASE: Star Trek has on occasion committed what I call the infamous Ghost 
error. I refer to a recent movie by this name in which the main character, a 
ghost, walks through walls and cannot lift objects because his hand passes 
through them. However, miraculously, whenever he sits on a chair or a couch, his 
butt manages to stay put. Similarly, the ground seems pretty firm beneath his 
feet. In the last chapter, I described how Geordi LaForge and Ro Laren were 
rendered "out of phase" with normal matter by a Romulan "interphase generator." 
They discovered to their surprise that they were invisible and could walk 
through people and walls leading Ro, at least, to believe that she was dead 
(perhaps she saw a replay of Ghost at some old movie house in her youth). Yet 
Geordi and Ro could stand on the floor and sit on chairs with impunity. Matter 
is matter, and chairs and floors are no different from walls, and as far as I 
know feet and butts are no more or less solid than hands. 
Incidentally, there is another fatal flaw associated with this particular 
episode which also destroys the consistency of a number of other Star Trek 
dramas. In physics, two things that both interact with something else will 
always be able to interact with each other. This leads us full circle back to 
Newton's First Law. If I exert a force on you, you exert an equal and opposite 
force on me. Thus, if Geordi and Ro could observe the Enterprise from their new 
"phase," they could interact with light, an electromagnetic wave. By Newton's 
Law if nothing else, they in turn should have been visible. Glass is invisible 
precisely because it does not absorb visible light. In order to seethat is, to 
sense lightyou have to absorb it. By absorbing light, you must disturb it. If 
you disturb light, you must be visible to someone else. The same goes for the 
invisible interphase insects that invaded the Enterprise by clinging to the 
bodies of the crew, in the Next Generation episode "Phantasms." The force that 
allows them to rest on normal matter without going through it is nothing other 
than electro-magnetismthe electrostatic repulsion between the charged particles 
making up the atoms in one body with the atoms in another body. Once you 
interact electromagnetically, you are part of our world. There is no such thing 
as a free lunch. 
 
SWEEPING OUT THE BABY WITH THE BATHWATER: In the Next Generation episode 
"Starship Mine," the Enterprise docks at the Remmler Array to have a "baryon 
sweep." It seems that these particles build up on starship superstructures as a 
result of long-term travel at warp speed, and must be removed. During the sweep, 
the crew must evacuate, because the removal beam is lethal to living tissue. 
Well, it certainly would be! The only stable baryons are (1) protons and (2) 
neutrons in atomic nuclei. Since these particles make up everything we see, 
ridding the Enterprise of them wouldn't leave much of it for future episodes. 
 
HOW COLD IS COLD?: The favorite Star Trek gaffe of my colleague and fellow Star 
Trek aficionado Chuck Rosenblatt involves an object's being frozen to a 
temperature of -295 Celsius. This is a very exciting discovery, because on the 
Celsius scale, absolute zero is -273. Absolute zero, as its name implies, is 
the lowest temperature anything can potentially attain, because it is defined as 
the temperature at which all molecular and atomic motions, vibrations, and 
rotations cease. Though it is impossible to achieve this theoretical zero 
temperature, atomic systems have been cooled to within a millionth of a degree 
above it (and as of this writing have just been cooled to 2 billionths of a 
degree above absolute zero). Since temperature is associated with molecular and 
atomic motion, you can never get less than no motion at all; hence, even 400 
years from now, absolute zero will still be absolute. 
 
I HAVE SEEN THE LIGHT!: I am embarrassed to say that this obvious error, which I 
should have caught myself, was in fact pointed out to me by a first-year physics 
student, Ryan Smith, when I was lecturing to his class and mentioned that I was 
writing this book. Whenever the Enterprise shoots a phaser beam, we see it. But 
of course this is impossible unless the phaser itself emits light in all 
directions. Light is not visible unless it reflects off something. If you have 
ever been to a lecture given with the help of a laser pointergenerally, these 
are helium-neon red lasersyou may recall that you see only the spot where the 
beam hits the screen, and not anything in between. The only way to make the 
whole beam visible is to make the room dusty, by clapping chalkboard erasers 
together, or something like that. (You should try this sometime; the light show 
is really quite spectacular.) Laser light shows are created by bouncing the 
laser light off either smoke or water. Thus, unless empty space is particularly 
dusty, we shouldn't see the phaser beam except where it hits. 
 
ASTRONOMERS GET PICKY: Perhaps it is not surprising to find that the physics 
errors various people find in the series are often closely related to their own 
areas of interest. As I polled people for examples, I invariably got responses 
that bore a correlation to the specific occupations of those who volunteered the 
information. I received several responses by e-mail from astronomer-trekkers who 
reacted to several subtle Star Trek errors. One astronomy student turned a 
valiant effort by the Star Trek writers to use a piece of real astronomy into an 
error. The energy-eating life-form in "Galaxy's Child" is an infant space 
creature, who mistakes the Enterprise for its mother and begins draining its 
energy. Just in the nick of time LaForge comes up with a way to get the baby to 
let go. The baby is attracted to the radiation the Enterprise is emitting, at a 
21cm wavelength. By changing the frequency of the emission, the crew "spoils the 
milk," and the baby lets go. What makes this episode interesting, and at the 
same time incorrect, is that the writers picked up on a fact I mentioned in 
chapter 8 namely, the 21-cm radiation is a universal frequency emitted by 
hydrogen, which astronomers use to map out interstellar gas. However, the 
writers interpreted this to mean that everything radiates at 21 cm, including 
the Enterprise. In fact, the atomic transition in hydrogen responsible for this 
radiation is extremely rare, so that a particular atom in interstellar space 
might produce such radiation on average only once every 400 years. However, 
because the universe is filled with hydrogen, the 21-cm signal is strong enough 
to detect on Earth. So, in this case, I would give the writers A for effort and 
reduce this grade to B+ for the misinterpretationbut I am known as an easy 
grader. 
A NASA scientist pointed out an error I had missed and which you might expect 
someone working for NASA to recognize. It is generally standard starship 
procedure to move into geosynchronous orbit around planetsthat is, the orbital 
period of the ship is the same as that of the planet. Thus the ship should 
remain above the same place on the planet's surface, just as geosynchronous 
weather satellites do on Earth. Nevertheless, when the Enterprise is shown 
orbiting a planet it is usually moving against the background of the planet's 
surface. And indeed, if it is not in a geosynchronous orbit, then you run into 
considerable beaming-up problems. 
 
THOSE DARNED NEUTRINOS: I suppose I can't help but bring up neutrinos again. And 
since I have skipped lightly over Deep Space Nine in this book perhaps it is 
fair to finish with a blooper from this seriesone I was told about by David 
Brahm, another physicist trekker. It seems that Quark has gotten hold of a 
machine that alters the laws of probability in its vicinity. One can imagine how 
useful this would be at his gambling tables, providing the kind of unfair 
advantage that a Ferengi couldn't resist. This ruse is discovered, however, by 
Dax, who happens to analyze the neutrino flux through the space station. To her 
surprise, she finds that all the neutrinos are coming through left-handedthat 
is, all spinning in one direction relative to their motion. Something must be 
wrong! The neutrinos that spin in the opposite direction seem to be missing! 
Unfortunately, of all the phenomena the Star Trek writers could have chosen to 
uncover Quark's shenanigans, they managed to pick one that is actually true. As 
far as we know, neutrinos are only left-handed! They are the only known 
particles in nature that apparently can exist in only one spin state. If Dax's 
analysis had yielded this information, she would have every reason to believe 
that all was as it should be. 
What makes this example so poignant, as far as I am concerned, is exactly what 
makes the physics of Star Trek so interesting: sometimes truth is indeed 
stranger than fiction. 
EPILOGUE 
Well, that's it for blunders and for physics. If I missed your favorite error or 
your favorite piece of physics, I suppose you can send your suggestion to my 
publisher. If there are enough, like Star Trek we can plan a sequel. I already 
have a name: The Physics of Star Trek II: The Wrath of Krauss. 
The point of finishing this book with a chapter on physics blunders is not to 
castigate the Star Trek writers unduly. It is rather to illustrate that there 
are many ways of enjoying the series. As long as Star Trek continues to remain 
on the air, I am sure that ever-new physics faux pas will give trekkers of all 
ilks, from high school students to university professors, something to look 
forward to talking about the morning after. And it offers a challenge to the 
writers and producers to try to keep up with the expanding world of physics. 
So I will instead close this book where I begannot with the mistakes but with 
the possibilities. Our culture has been as surely shaped by the miracles of 
modern physicsand here I include Galileo and Newton among the modernsas it has 
by any other human intellectual endeavor. And while it is an unfortunate modern 
misconception that science is somehow divorced from culture, it is, in fact, a 
vital part of what makes up our civilization. Our explorations of the universe 
represent some of the most remarkable discoveries of the human intellect, and it 
is a pity that they are not shared among as broad an audience as enjoys the 
inspirations of great literature, or painting, or music. 
By emphasizing the potential role of science in the development of the human 
species, Star Trek whimsically displays the powerful connection between science 
and culture. While I have argued at times that the science of the twenty-third 
century may bear very little resemblance to anything the imaginations of the 
Star Trek writers have come up with, nevertheless I expect that this science may 
be even more remarkable. In any case I am convinced that the physics of today 
and tomorrow will as surely determine the character of our future as the physics 
of Newton and Galileo colors our present existence. I suppose I am a scientist 
in part because of my faith in the potential of our species to continue to 
uncover hidden wonders in the universe. And this is after all the spirit 
animating the Star Trek series. Perhaps Gene Roddenberry should have the last 
word. As he said on the twenty-fifth anniversary of the Star Trek series, one 
year before his death: "The human race is a remarkable creature, one with great 
potential, and I hope that Star Trek has helped to show us what we can be if we 
believe in ourselves and our abilities." 
NOTES 
Chapter 1: Newton Antes 
1. Michael Okuda, Denise Okuda, and Debbie Mirak, The Star Trek Encyclopedia 
(New York: Pocket Books, 1994). 
2. Rick Sternbach and Michael Okuda, Star Trek: The Next GenerationTechnical 
Manual (New York: Pocket Books, 1991). 
Chapter 2: Einstein Raises 
1. Quoted in Paul Schilpp, ed., Albert Einstein: Philosopher-Scientist (New 
York: Tudor, 1957). 
2. Rick Sternbach and Michael Okuda, Star Trek: The Next GenerationTechnical 
Manual (New York: Pocket Books, 1991). 
3. Ibid. 
Chapter 3: Hawking Shows His Hand 
1. Michael Okuda, Denise Okuda, and Debbie Mirak, The Star Trek Encyclopedia 
(New York: Pocket Books, 1994). 
Chapter 8: The Search for Spock 
1. Review by Philip Morrison, in Scientific American, November 1994, of 
Hlldobler and Wilson, Journey to the Ants: A Story of Scientific Explorations 
(Cambridge, MA: Harvard University Press, 1994). 
2. Francis Crick, Life Itself (New York: Simon & Schuster, 1981). 
3. Bernard M. Oliver, "The Search for Extraterrestrial Life," Engineering and 
Science, December 1974. 
Chapter 9: The Menagerie of Possibilities 
1. For a cogent review of this subject, I suggest my own book The Fifth Essence: 
The Search for Dark Matter in the Universe (New York: Basic Books, 1989). 
2. John Scott Russell, Report of the 14th Meeting of the British Association for 
the Advancement of Science (London: John Murray, 1844). 