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A Primer On Time Travel (from issue #19)
by Damon Shavers

The idea of time travel has always been a popular and intriguing notion in books, movies, and TV, but in reality, can one really travel backward and forward in time, according to the present known laws of physics?

Paradoxes, Relativity, Light Cones, and Worldlines
The possibility of time travel depends on which model of reality is correct. In one model, man's future is predetermined, so time travel into either the past or future must also be predetermined. In the second model, man's future is unknown; he can't travel into the future, since none exists, nor into the past, since he wouldn't exist. In the third model, man chooses his future from an infinite number of existing parallel universes; he can travel into the future since all possible futures exist and into the past, since even if he alters the past, there is always an alternate future.

Because of what's known as Causality Time Paradoxes, physicists have traditionally stated a chronology principle that rules out travel into the past. The most common and well-known argument against two-way time travel has become known as the Grandfather Paradox. A time traveler ventures to the past just in time to prevent the meeting of his or her grandparents. Therefore, the time traveler would not be born, and could not possibly travel to the past to prevent the meeting. Because of this paradox, common sense tells us that if working time machines could actually be constructed, there would be a serious problem with causality. Much of the recent work in this area of physics has been directed toward resolving the conflict between causality and time travel, or proving because of causality, time travel is impossible.

But one-way travel into the future raises none of these problems. Einstein's special theory of relativity predicts that, with sufficient acceleration, an astronaut could go on a journey and return to the earth decades into the future, while physically aging only a year or two. The reason is because as one approaches the speed of light (186,000 miles per second), time for the traveler slows.

And there are ways to travel back in time and not violate causality. To do so, you have to first understand the concept of time itself, as physicists understand it. In Einstein's special and general theories of relativity, three-dimensional space is combined with time to form four-dimensional space-time. Where space consists of spatial points, space-time consists of spatio-temporal points, or events, each of which represents a particular place at a particular time. A Minkowski diagram can show this: You put three-dimensional space on the x-axis, and time on the y. Now since light is a constant, it would appear in the Minkowski diagram as a straight, 45-degree line. That is, for every one unit of space, it moves one unit of time (or x=y). Since light moves in all directions through space-time, the 45-degree angles in a three-dimensional model looks like two conjoined inverted cones. All events in the "light cone" above the x-axis is in the future, while all those below the x-axis is in the past. The vertex point of the cones (where the cones meet on the x-axis) is the immediate "here-now." (See A)

In this diagram, one's life forms a kind of four-dimensional "worm" in space-time. The tip of the worm's tail corresponds to the event of your birth, and the front of its head to the event of your death. An object, seen at any one instant, is a three-dimensional cross section of this long, thin, intricately curved worm. The line along which the worm lies is called the "worldline."

But a worldline cannot be any stray squiggle. Since nothing can travel faster than light, the worldline of a physical object must remain inside the light cone originating from any event in its past. Time increases in one direction along a worldline.

Einstein's general theory of relativity states that gravity results from the curvature of space-time caused by massive bodies. Consider heavy objects lying on a couch. The objects cause imprints or dents in the couch. Then, if you dropped some crumbs on the couch, they would move in towards the dent. The same is for space-time. Matter makes space-time bend, which in turn tells other matter how to move. Einstein said that worldlines are also affected by gravity. That is, earth's worldline goes around the sun's, which also goes around the worldline of the center of our galaxy, and so on.

But what if space-time becomes so distorted that some worldlines form closed loops (also called closed timelike curves, or CTCs)? That is, if an object, traveling through its worldline in space-time, returns to the same space-time point it started from at the moment it left. Theoretically, this could happen if there was a body massive enough to bend two points in space-time on top of itself.

Wormholes, Cosmic Strings, Tipler Cylinders
In his 1915 theory of general relativity, Einstein showed that space-time is curved, and that curvature is large in the area of very massive objects. Gravity can warp and slow time, especially in regions of large masses. If an object is dense enough, the curvature in space-time becomes nearly infinite, opening a "tunnel" that connects distant regions of space-time (two space-time points lying on top of each other). This is what physicists (and Trekkies) call a wormhole.

In 1988, a physicist at Caltech named Kip Thorne and several other scientists suggested that you could use a wormhole to travel into the past. You simply construct a wormhole tunnel 600 million miles in circumference, massing over two hundred million times that of the sun (just gather around a 1000 stars like the sun, put them together, and squeeze them within the critical Schwartzchild radius). You then "move" the one mouth of the wormhole through space at nearly the speed of light, leaving the other end stationary. You somehow quickly enter the moving end. This moving end "ages" less, but it connects back to the earlier time on the fixed end. So when you emerge from that fixed end, you'll emerge in your own past. Unfortunately, openings of wormholes can only be kept open by matter that has negative density, that is, exotic matter that weighs less than nothing.

Another way of creating a time machine is by using what's called cosmic strings. Recently, Richard Gott III of Princeton University has discovered that one can make a time machine by taking two infinitely long cosmic strings (hypothetical thin strands of energy millions of light years long that may or may not actually exist) and moving them past each other at a very high speed, manipulating it so that it would contract rapidly under its own tension (due to the Lorentz Transformations). The incredible energy density of the string curves space-time, and if one enters two sides of a loop as they pass each other at almost the speed of light, one enters the past. But to go back into the past just one year, one would need a loop containing about one half the mass energy of an entire galaxy, not to mention the fact that the contracting cosmic string would create the formation of a rotating black hole, sealing off all time travel regions. (But one could sort of fix this problem and create an opening in the black hole by inserting a wormhole into the black hole, across its event horizon [the area on the outskirts of a black hole where light is not fast enough to escape the gravitation], since the wormhole is composed of exotic matter. Still following us?)

But the easiest and most plausible time machine that can be constructed is what's known as a Tipler Cylinder. The materials may be practically "exotic" and the energy requirements enormous, but according to Dr. Frank Tipler of Tulane University in 1974, the construction of a time machine is theoretically feasible. He determined that if you somehow rotate an infinitely long massive cylinder fast enough, it would also "tip" a series of light cones into a CTC. (See B) The speed at the outer surface of the cylinder, though, would have to be greater than half the speed of light. But if something were to rotate this fast, part of it would likely collapse into a singularity - an infinitely small point of space-time, usually caused by a star collapsing under its own gravity, that has infinite mass and where the laws of physics break down. And Tipler stresses, "The stability of massive rotational bodies is questionable. The energy associated with a strong angular momentum would have to be about equal to the rest-mass energy, energy so great that the accompanying centrifugal force may tear the rotating body apart."

But do time machines already exist? Assuming that the general theory of relativity is correct, then natural CTC's or natural time machines exist. And if they do exist, then to prevent causality paradoxes would require the existence of parallel universes.

Parallel Universes
Most science fiction writers, and later, physicists, use the concept of parallel universes to avoid the paradoxes of time travel.

The Many Worlds interpretation of quantum mechanics, first proposed by Hugh Everett III in 1957, states that physical reality consists of a collection of universes called a multiverse. At each quantum event, the universe splits into a multitude of new universes, each having a different outcome for that event. Basically, the Many Worlds theory is the idea that every outcome at the quantum level really does happen. This theory is the direct result of the famous Schrodinger cat thought experiment.

In 1935, the German theorist Erwin Schrodinger illustrated a paradox to show why he thought the standard model of quantum theory was ridiculous. He suggested that a live cat and a capsule of poison gas be placed inside a box. The capsule would be broken, and the lethal poison released by a trigger mechanism controlled by the decay of a radioactive atom. The experiment would be conducted during a specified time in which there would be a precisely 50-50 chance that the atom would decay, either killing the cat or leaving the cat alive. Quantum mechanics deals with the statistics of probability, not constants or fate. So under quantum probability, the radioactive atom that could trigger the release of the poison is considered to have a wave function that is made up of equal parts of a decayed state and an undecayed state. Only when an observer sees (or measures) the state of the atom, and the survival or death of the cat become definite, is there a situation the physicist calls a "collapsing wave function."

But until someone looks into the box, both possibilities of the cat's life remains likely, in a "superimposition of states." The cat is both dead and alive at the same time. As soon as someone opens the box and checks the condition of the cat, the superposition of states collapses and either possibility becomes real. So when the universe is faced with "choices" at a basic level, it decides between them at random, according to the laws of probability. It also says that the choice is not made until the quantum event is observed. Some physicists, distraught by Shrodinger's thought experiment, came up with a "solution" - at every situation that creates a probability wave on the quantum level, the universe splits into all the universes for each outcome, but we can only experience one of them.

When one thinks about it, in reality, travel to a parallel world is not really time travel at all. So if the many quantum universes do exist, they are all parallel to each other, and there is no way to get from one to another except by going backward in time and then "up" another branch. For example, in the Back To The Future movies, when Marty McFly goes back in time, he makes a change that alters the future (his original present). His new present is now a new branch, while his original present (without him) continues on in a parallel universe. In other words, his worldline was really going down one branch of time and forward up another branch, so that he continues his life in a different quantum universe, never to return to his original universe again.

How does parallel universe resolve paradoxes? Consider the Grandfather Paradox once again. Suppose you travel back in time and accidentally kill or cause the death of your grandfather before he reaches puberty. You can't get born because your mother or father can't get born, right?

The answer to this is that in this parallel world sequence where you kill your younger grandfather, quantum wave streams result in a universe where you are not born. However, the original universe where your grandfather lived to a ripe old age and sired your mom/dad still exists, thus allowing you to be born. So Everett's version of the Many World theory of quantum mechanics allows history-changing events.

This means that there are many interlacing world histories, so that if anyone went back in time and killed their grandfather when he was a kid, it would just cause space-time to branch off into a new parallel universe that is different from the one that we know. A new generation of parallel universes is created each time a time traveler reenters the time stream.

Other pasts are waiting to be discovered. There are parallel pasts - infinite numbers of them. The past that is altered by the present is just one of many. Since, according to relativity theory, there is no such thing as absolute time, then what is present for someone could be the past or the future for another.

We aren't yet equipped with the necessary technology to herd neutron stars and build Tipler cylinders. But parallel universes and time travel do fit together along with our new understanding of time.

Illustrations by Adam Liebling
Also read: "Time & the Special Theory of Relativity" by Adam Liebling

FURTHER REFERENCE

Einstein: A Life. Denis Brown. John Wiley & Sons, Inc., 1996.

Einstein: The Life & Times. Ronald W. Clark. The World Publishing Group, 1971.

Paradox Lost. Paul Davies in NEW SCIENTIST, Vol. 157, No.21226, page 26; March 21, 1998.

Quantum Mechanics Near Closed Time Like Lines. David Deutsch in Physical Review D, Vol. 44, No. 10, pages 3197-3217; November 15, 1991.

Quantum Physics of Time Travel. David Deutsch and Michael Lockwood in Scientific American. Volume 270, number 3 Pages 68-74 March 1994.

Causal Loops. Michael Dummett in The Nature of Time. Edited by R. Flood and M. Lockwood. Basil Blackwell, 1986.

Relativity. Albert Einstein. Routledge Classics, 2001.

Six Not-So-Easy Pieces. Richard P. Feynman. Perseus Books, 1997.

Quantum Field Theory Constrains Transversable Wormhole Geometries. L.H. Ford and T.A. Roman in Physical Review D, Vol. 53, No. 10 pages 5496 - 5507, May 15, 1996.

Time Travel In Einstein's Universe: The Physical Possibilities of Travel Through Time. J. Richard Gott. Houghton Mifflin Company, 2001.

A Brief History of Time. Stephen Hawking. Bantam, 1988.

The Paradoxes of Time Travel. David Lewis in American Philosophical Quarterly, Vol. 13, No. 2, pages 145-152; April 1976. Reprinted in The Philosophy of Time. Edited by Robin Le Poidevin and Murtay MacBeath. Oxford University Press, 1993.

Time Machines: Time Travel In Physics, Metaphysics, And Science Fiction. Second Edition. Paul J. Nahin. AIP Press, Springer-Verlag, 1999.

Must Time Machine Construction Violate the Weak Energy Condition? Amos Ori in Physical Review Letters, Vol. 71, No. 16, pages 2517-2520; October 18, 1993.

Time: A Traveler's Guide. Clifford A. Pickover. Oxford University Press, 1998.

The Fourth Dimension: A Guided Tour of the Higher Universes. Rudy Rucker. Houghton Mifflin Company, 1984.

The ABC of Relativity. Bertrand Russell. Penguin, 1959.

Black Holes and Time Warps: Einstein's Outrageous Legacy. Kip S. Thorne. W.W. Norton, 1994.

Do the Laws of Physics Permit Closed Time Like Curves? Kip S. Thorne in Annals of the New York Academy of Sciences, Vol. 631, pages 182-193; August 1991.

Parallel Universes: The Search For Other Worlds. Fred Alan Wolf. Simon & Schuster, 1988.

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