To see video demonstrations of key concepts from the book, please visit this website: http://www.press.uchicago.edu/sites/timewarp/ Sci-fi makes it look so easy. Receive a distress call from Alpha Centauri? No problem: punch the warp drive and you're there in minutes. Facing a catastrophe that can't be averted? Just pop back in the timestream and stop it before it starts. But for those of us not lucky enough to live in a science-fictional universe, are these ideas merely flights of fancy—or could it really be possible to travel through time or take shortcuts between stars? Cutting-edge physics may not be able to answer those questions yet, but it does offer up some tantalizing possibilities. In Time Travel and Warp Drives, Allen Everett and Thomas A. Roman take readers on a clear, concise tour of our current understanding of the nature of time and space—and whether or not we might be able to bend them to our will. Using no math beyond high school algebra, the authors lay out an approachable explanation of Einstein's special relativity, then move through the fundamental differences between traveling forward and backward in time and the surprising theoretical connection between going back in time and traveling faster than the speed of light. They survey a variety of possible time machines and warp drives, including wormholes and warp bubbles, and, in a dizzyingly creative chapter, imagine the paradoxes that could plague a world where time travel was possible—killing your own grandfather is only one of them! Written with a light touch and an irrepressible love of the fun of sci-fi scenarios—but firmly rooted in the most up-to-date science, Time Travel and Warp Drives will be a delightful discovery for any science buff or armchair chrononaut.
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About the Author
Allen Everett is professor emeritus of physics at Tufts University. Thomas Roman is a professor in the Mathematical Sciences Department at Central Connecticut State University. Both have taught undergraduate courses in time-travel physics.
Read an Excerpt
Time Travel and Warp DrivesA Scientific Guide to Shortcuts through Time and Space
By Allen Everett Thomas Roman
The University of Chicago PressCopyright © 2012 The University of Chicago
All right reserved.
As humans, we have always been beckoned by faraway times and places. Ever since man realized what the stars were, we have wondered whether we would ever be able to travel to them. Such thoughts have provided fertile ground over the years for science fiction writers seeking interesting plotlines. But the vast distances separating astronomical objects forced authors to invent various imaginary devices that would allow their characters to travel at speeds greater than the speed of light. (The speed of light in empty space, generally denoted as c by physicists, is 186,000 miles/second.) To give you an idea of the enormous distances between the stars, let's start with a few facts. The nearest star, Proxima Centauri (in the Alpha Centauri star system) is about 4 light-years away. A light-year is the distance that light travels in a year, about 6 trillion miles. So the nearest star is about 24 trillion miles away. It would take a beam of light traveling 186,000 miles per second, or a radio message, which would travel at the same speed, 4 years to get there.
On an even greater scale, the distance across our Milky Way galaxy is approximately 100,000 light-years. Our nearby neighbor galaxy, Andromeda, is about 2,000,000 light-years away. With present technology, it would take some tens of thousands of years just to send a probe, traveling at a speed far less than c, to the nearest star. It's not surprising then that science fiction writers have long imagined some sort of "shortcut" between the stars involving travel faster than the speed of light. Otherwise it is difficult to see how one could have the kinds of "federations" or "galactic empires" that are so prominent in science fiction. Without shortcuts, the universe is a very big place.
And what about time, that most mysterious feature of the universe? Why is the past different from the future? Why can we remember the past and not the future? Is it possible that the past and future are "places" that can be visited, just like other regions of space? If so, how could we do it?
This book examines the possibility of time travel and of space travel at speeds exceeding the speed of light, in light of physics research conducted during the last twenty years or so. The ideas of faster-than-light travel and time travel have long existed in popular imagination. What you may not know is that some physicists study these concepts very seriously—not just as a "what might someday be possible" question, but also as a "what can we learn from such studies about basic physics" question.
Science fiction television and movie series, such as Star Trek, contain many fictional examples of faster-than-light travel. Captains Kirk or Picard give the helmsman of the starship Enterprise an order like, "All ahead warp factor 2." We're never told quite what that means, but we're clearly meant to understand that it means some speed greater than the speed of light (c). Some fans have speculated that it refers to a speed of 22c, or four times the speed of light. These speeds are supposed to be achieved by making use of the Enterprise's "warp drive." This term was never explained and seems to be merely a nice example of the good "technobabble" usually necessary in a piece of science fiction to make things sound "scientific." But by chance—or good insight—Star Trek's "warp drive" turns out to be an apt description of one conceivable mechanism for traveling at faster-than-light speed, as we shall discuss later in some detail. For this reason, we will use the term "warp drive" from now on to mean a capacity for faster-than-light travel.
By analogy with the term "supersonic" for speeds exceeding the speed of sound in air, speeds greater than the speed of light are often referred to in physics as "superluminal speeds." However, superluminal travel seems to involve a violation of the known laws of physics, in this case, Einstein's special theory of relativity. Special relativity has built into it the existence of a "light barrier." The terminology is intended to be reminiscent of the sound barrier encountered by aircraft when their speed reaches that of sound and which some, at one time, thought might prevent supersonic flight. But whereas it proved possible to overcome the sound barrier without violating any physical laws, special relativity seems to imply that superluminal travel, that is, an actual warp drive, is absolutely forbidden, no matter how powerful some future spaceship's engines might be.
Time travel also abounds in science fiction. For example, the characters in a story may find themselves traveling back to our time period and becoming involved with a NASA space launch on Earth, perhaps after passing through a "time gate." Often in science fiction, the occurrence of backward time travel seems to have nothing to do with the existence of a warp drive for spaceships; the two phenomena of superluminal travel and time travel appear quite unrelated. In fact, we shall see that there is a direct connection between the two.
Science fiction writers often provide imaginative answers to questions beginning with the word "what."—"What technological developments might occur in the future?"—but in general, science fiction does not provide answers to the question of "how". It usually provides no practical guidance as to just how some particular technological advance might be achieved. Scientists and engineers by contrast work to answer "how," attempting to extend our knowledge of the laws of nature and to apply this knowledge creatively in new situations.
The fact that science, in due course, frequently has provided answers as to how some imagined technological advance can actually be achieved may tend to lead to an expectation that this will always occur. But this is not necessarily true. Well-established laws of physics often take the form of asserting that certain physical phenomena are absolutely forbidden. For example, as far as we know, no matter what occurs, the total amount of energy of all kinds in the universe does not change. That is, in the language of physics, energy is said to be "conserved," as you were probably told in your high school and university science courses.
Although works of science fiction usually cannot address the "how" questions, they often serve science through their explorations of "what." By envisioning conceivable phenomena outside of our everyday experience, they may offer science possible avenues of experimentation. Some of the chapters of this book contain suggested science fiction readings or films that relate to the subject matter of the chapter and can prove helpful in visualizing various scenarios which might occur if, for example, time travel became possible.
A writer of science fiction is at liberty to imagine a world in which humans have learned to create energy in unlimited quantities by means of some imaginary device. However, a physicist will say that, according to well-established physical laws, this will not be possible, no matter how clever future scientists and engineers may be. In other words, sometimes the answer to the question "How can such and such a thing be done?" is "In all probability, it can't." We must be prepared for the possibility that we will encounter such situations.
Unless we specify otherwise, the term "time travel" will normally mean time travel into the past, which is where the most interesting problems arise. As a convenient shorthand we will refer to a device that would allow this as a "time machine" and to a process of developing a capacity for backward time travel as "building a time machine." This implies the possibility that you could go back in time and meet a younger version of yourself. In physics jargon, such a circular path in space and time is referred to as a "closed timelike curve." It is closed because you can return to your starting point in both space and time. It is called "timelike" because the time changes from point to point along the curve. The statement that a closed timelike curve exists is just a fancy way of saying that you have a time machine.
It would seem that time travel into the past should also be impossible outside the world of science fiction simply on the basis of ordinary common sense because of the paradoxes to which it seems to lead. These are typified by what is often called the "grandfather paradox." According to this scenario, were it possible to travel into the past, a time traveler could in principle murder his own grandfather before the birth of his mother. In this case he would never be born, in which case he would never travel back in time to murder his grandfather, in which case he would be born and murder his grandfather, and so on and so on forever. In summary, the entrance of the grandson into the time machine prevents his entrance into the machine. Such paradoxical situations that involve logical contradictions are called "inconsistent causal loops." The laws of physics should allow one to predict that, in a given situation, a certain event either does or does not occur. Hence, they must be such that inconsistent causal loops are not allowed.
For some time, warp drives and time machines were generally believed to be confined to the realm of science fiction because of the special relativistic light barrier and the paradoxes involved with backward time travel. Over the past several decades, the possibility that superluminal travel and backward time travel might actually be possible, at least in principle, has become a subject of serious discussion among physicists. Much of this change is due to an article entitled "Wormholes, Time Machines, and the Weak Energy Condition," by three physicists at the California Institute of Technology: M. S. Morris, K. S. Thorne, and U. Yurtsever. Their article was published in 1988 in the prestigious journal Physical Review Letters. (You will learn something of the meaning of that strange-sounding phrase "weak energy condition" later.) The senior author, K. S. Thorne (who is the Feynman Professor of Theoretical Physics at Caltech), is one of the world's foremost experts on the general theory of relativity, which is Einstein's theory of gravity. The discovery of the latter theory followed that of special relativity by about a decade. General relativity offers potential loopholes that might allow a sufficiently advanced civilization to find a way around the light barrier.
As far as time travel into the future is concerned, it is well understood in physics—and has been for a good part of a century—that it is not only possible but also, indeed, rather commonplace. Here, by "time travel into the future," we implicitly mean at a rate greater than the normal pace of everyday life. Forward time travel is, in fact, directly relevant to observable physics, since it is seen to occur for subatomic particles at high energy accelerators, such as that at Fermi National Laboratory, or the new Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) in Geneva, where such particles attain speeds very close to the speed of light. (Sending larger masses, such as people or spaceships, a significant distance into the future, while possible in principle, requires amounts of energy which are at present prohibitively large.)
We begin the exploration of forward time travel with a brief discussion of the meaning of time itself in physics. We will then have to do some thinking about just what the phrase "time travel" means. For example, what would we expect to observe if we traveled in time, and what would non-time travelers around us see? Like a number of things in this book, answering these questions requires stretching the imagination to envision phenomena that you have never actually encountered or probably even thought carefully about.
After that, you will learn the fundamentals of Einstein's special theory of relativity. The discovery of special relativity is one of the great intellectual achievements in the history of physics, and yet the theory involves only rather simple ideas and no mathematics beyond high school algebra. Again, however, to understand what is going on you have to be prepared to stretch your thinking beyond what you observe in your everyday life. Special relativity describes the behavior of objects when their speed approaches the speed of light. As we will see, special relativity leaves no doubt that forward time travel is possible. We will discuss one of the most remarkable predictions of special relativity, namely, that a clock appears to run slower when it is moving relative to a stationary observer, an effect called "time dilation." This effect becomes significant when the speed of the clock approaches c. Time dilation is closely related to what is called the "twin paradox." This is essentially the same phenomenon that is responsible for the "forward time travel" seen to occur for elementary particles at Fermilab and the LHC.
At first glance, faster-than-light travel might seem to be a natural extension of ordinary travel at sub-light speeds, just requiring the development of much more powerful engines. Space travel in many science fiction stories of the 1930s and '40s involved no violations of fundamental laws of physics. The speculation of science fiction began to be realized in practice about a quarter of a century later, when Neil Armstrong took his "one small step" onto the surface of the moon. However, superluminal travel seems to involve a violation of the known laws of physics, in this case, the special theory of relativity, with its light barrier.
In the absence of a time machine, everyday observations tell us that the laws of physics are such that effects always follow causes in time. Thus the effect cannot turn around and prevent the cause, and no causal loop can occur. This is no longer true in the presence of a time machine, since then a time traveler can observe the effect and then travel back in time to block the cause. Therefore it would appear that the existence of time machines—that is, backward time travel—is forbidden just by common sense. Moreover, we will see that in special relativity, backward time travel becomes closely connected to superluminal travel, so that the same "common sense" objections can be raised to the possibility of a warp drive, in addition to the light barrier problem.
Einstein's theory of gravity, general relativity, introduces a new ingredient into the mix. It combines space and time into a common structure called "spacetime." Space and time can be dynamical—spacetime has a structure that can curve and warp. Einstein showed that the warping of the geometry of space and time due to matter and energy is responsible for what we perceive as gravity. We will introduce you to some of the ideas of general relativity and its implications. One consequence that we will discuss is the black hole, which is believed to be the ultimate fate of the most massive stars. When such a star dies, it implodes on itself to the point where light emitted from the star is pulled right back in, rendering the object invisible. We will point out that sitting next to (or orbiting) a black hole also affords a possible means of forward time travel that is different from the time dilation of moving clocks discussed earlier.
As we will find, the laws of general relativity at least suggest that it is possible to curve, or warp, space in such a way as to produce a shortcut through space, and perhaps even time, which is known to general relativists as a "wormhole." Wormholes are one of the staple features of several science fiction series: Star Trek Deep Space Nine, Farscape, Stargate SG1, and Sliders. Several years after the article by Morris, Thorne, and Yurtsever, a possibility for actually constructing a warp drive was presented in a 1994 article by Miguel Alcubierre, then at the University of Cardiff in the United Kingdom, which was published in the journal Classical and Quantum Gravity. By making use of general relativity, Alcubierre exhibited a way in which empty spacetime could be curved, or warped, in such a way as to contain a "bubble" moving at an arbitrarily high speed as seen from outside the bubble. One might call such a thing a "warp bubble." If one could find a way of enclosing a spaceship in such a bubble, the spaceship would move at superluminal speed, for example, as seen from a planet outside the bubble, thus achieving an actual realization of a "warp drive." Another kind of warp drive was suggested by Serguei Krasnikov at the Central Astronomical Observatory in St. Petersberg, Russia in 1997. This "Krasnikov tube" is effectively a tube of distorted spacetime that connects the earth to, say, a distant star. From what we have said before about the connection between superluminal travel and backward time travel, one would expect that wormholes and warp bubbles could be used to construct time machines. This is indeed the case, as we will also show.
Excerpted from Time Travel and Warp Drives by Allen Everett Thomas Roman Copyright © 2012 by The University of Chicago. Excerpted by permission of The University of Chicago Press. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of ContentsPreface
2. Time, Clocks, and Reference Frames
3. Lorentz Transformations and Special Relativity
4. The Light Cone
5. Forward Time Travel and the Twin “Paradox”
6. “Forward, into the Past”
7. The Arrow of Time
8. General Relativity: Curved Space and Warped Time
9. Wormholes and Warp Bubbles: Beating the Light Barrier and Possible Time Machines
10. Banana Peels and Parallel Worlds
11. “Don’t Be So Negative”: Exotic Matter
12. “To Boldly Go . . .”?
13. Cylinders and Strings
Appendix 1. Derivation of the Galilean Velocity Transformation
Appendix 2. Derivation of the Lorentz Transformations
Appendix 3. Proof of the Invariance of the Spacetime Interval
Appendix 4. Argument to Show the Orientation of the x',t' Axes Relative to the x,t Axes
Appendix 5. Time Dilation via Light Clocks
Appendix 6. Hawking’s Theorem
Appendix 7. Light Pipe in the Mallett Time Machine