Time TravelA general discussion about time travel, paradoxes, and other such phenomenon as it pertains to the Back to the Future movies or other films.
This is an article from the latest issue of New Scientist:
Quote:
No going back.
By Ivan Semeniuk.
3,163 words
20 September 2003
New Scientist
Forget about that excellent adventure where you visit the ancient Greeks or give your great-grandfather the fright of his life. The idea of travelling through time is suddenly beginning to fall apart says Ivan Semeniuk
IT MIGHT be your greatest dream, but for many physicists, time travel is their worst nightmare. "I think most of us would like to get rid of time machines if we possibly could," says Amanda Peet of the University of Toronto. "They offend our fundamental sensibilities."
There's a very simple reason for this. Although the laws of nature seem to allow time machines to exist, they violate the principle of causality - the basic assumption that causes must precede their effects. The problem is, no one has come up with a definitive explanation for why time machines can't work. The best we have is Stephen Hawking's "chronology protection conjecture", which, in a nutshell, suggests that the universe has a built-in time cop. Whenever anyone is on the verge of constructing a working time machine the time cop intervenes, shutting the operation down before it has a chance to wreak havoc with the past. However, there are no time cops evident in the laws of physics, so at the moment the chronology protection conjecture is simply wishful thinking, a physicist crossing his fingers and hoping for the best.
But that may be about to change. A few independent groups of researchers are claiming to have finally glimpsed the long arm of chronology protection. In the past year, a variety of new approaches to the time travel conundrum have appeared. Although different from one another, these approaches have one thing in common: they invoke string theory, the leading candidate for a "theory of everything". With strings, it appears, the time travel loophole may finally be sewn shut.
Physicists wouldn't have to worry about time travel if it weren't for the most famous physicist of all. When Albert Einstein came up with his general theory of relativity in 1915 he unknowingly threw open the doors for wholesale chronology violation. "General relativity is completely infested with time machines," says Matt Visser, professor of applied mathematics at Victoria University of Wellington, New Zealand. "It certainly seems to permit all of these weird solutions in which time travel is theoretically possible."
Before general relativity came along, such solutions were unimaginable. In Newton's universe the direction of time is, by definition, absolute and irreversible. Even special relativity, Einstein's earlier tour de force, maintains the one-way flow of time.
But general relativity - which includes Einstein's breakthrough idea that gravity is the result of matter warping space and time - is a very different story. Unlike earlier theories it does not start with an assumed global framework for time, but merely provides the rules for how time is perceived in local circumstances.
"It turns out general relativity relates the distribution of matter 'here' to the curvature of space and the flow of time 'here', but it doesn't give you much long-distance information," Visser says.
Because of its "generalness", general relativity imposes no extra assumptions on the nature of space and time as a whole. For example, cosmologists have no way of knowing whether the universe is infinite simply by reading Einstein's equations. Additional information is needed to determine if space stretches out to infinity or curves back on itself. Similarly, just because time appears to flow one way in our part of the universe there is nothing explicit in general relativity that says it cannot behave differently elsewhere. In particular, some solutions of Einstein's equations lead to "closed time-like curves", unbroken pathways through space-time that allow travellers to loop back in time and bump into earlier versions of themselves. "Physicists tend to get upset about that," Visser says.
Perhaps that is why, in the jargon of relativistic physics, regions of space that contain closed time-like curves are called "sick". There are at least two good reasons to feel queasy about the possible existence of such regions. One is the famous grandfather paradox. In this scenario, you, the time traveller, follow a closed time-like curve into the past in order to murder a direct ancestor, thereby preventing the circumstances leading to your own birth. Science fiction is full of paradoxical scenarios like this, in which a visitor from the future changes history.
A second problem is the equally perplexing bootstrap paradox. Suppose someone tells you the funniest joke you've ever heard, and then you travel back in time one week and share the joke at cocktail party. Of course, the joke catches on and is told and retold, until it eventually comes back to you, one week in the future, thereby starting the loop all over again. The question is: where did the joke come from?
In one case, an effect eliminates its cause; in the other, it becomes its own cause. Yet the physical conditions that allow these situations to happen exist as solutions to Einstein's equations.
Closed time-like curves are not easily manufactured or exploited, of course. If time travel is possible it can only be achieved with technology on a scale far beyond 21st-century civilisation. But that's not the point: the point is that general relativity doesn't rule it out, it just tells us that time travel is difficult and expensive. So is Hawking's conjecture wrong? Is time travel just a technical challenge rather than a fundamental impossibility?
Concerned physicists, ever resourceful in their arguments, are interpreting relativity's permissive attitude to time travel as a sign that the theory must be incomplete. "In some sense, general relativity is an amazing theory in that it predicts its own demise," says Rob Myers of the Perimeter Institute in Ontario, Canada. "Einstein's theory is telling you it can only bring you so far and then you're going to need a better theory to understand how physics proceeds from there."
Lisa Dyson, a graduate student in theoretical physics at the Massachusetts Institute of Technology, agrees. "We know that relativity is not the whole story," she says. "General relativity is a theory of gravity, but there are other forces that govern the world: the strong, weak and electromagnetic forces. Once we understand how all the forces are unified, we may find that time travel is inconsistent with this unified theory."
Today, forces other than gravity are understood through quantum mechanics. For decades physicists have been striving to unite quantum mechanics with relativity to produce a theory of "quantum gravity". And the best candidate so far is string theory.
String theory is a sprawling, multidimensional way of describing the universe. Because causality is such a fundamental part of that description, many physicists expect that string theory will, in some way, explicitly rule out time travel. "String theory shows promise as the theory that unifies gravity with the other fundamental forces of nature," Dyson says. "If our usual notion of chronology is built into our universe, then chronology should be protected in string theory."
In some specific cases, this expectation is now being borne out. One particularly useful development came recently, when a group led by physicist Jerome Gauntlett, then at Queen Mary University of London, was working on a simpler approximation to string theory known as five-dimensional supergravity. Although it is a close relative of full-blown string theory, the group discovered that many solutions to supergravity allow for time travel in the same way that general relativity does. "What surprised me," Gauntlett says, "was that such solutions turn out to be rather common."
Petr Horava, a theorist at the University of California at Berkeley, was teaching a graduate course in string theory when Gauntlett's paper appeared online. He decided to devote a lecture to dealing with the issues it raised, and then assigned chronology protection as a problem for his students to solve. The idea was to use the tools of string theory to eliminate some or all of the time travel scenarios that showed up in five-dimensional supergravity.
Horava and a group of students went to work on one particular example. In 1949 the mathematician Kurt Goedel found a solution to Einstein's equations in which a universe was neither expanding nor contracting, but rapidly rotating. One of the consequences of living in this kind of universe is that it is possible, by moving in the right way, to arrive back at the starting point of your journey before you leave. In fact every point in Goedel's rotating universe lies on a closed time-like curve.
Gauntlett's work indicates that similar closed time-like curves permeate the five-dimensional supergravity version of Goedel's universe. Horava's group decided to examine those closed time-like curves with the help of the holographic principle. In its simplest version, this states that all the information present in a given volume of space can be represented as existing on a surface, or "holographic screen", that surrounds that space. According to the holographic principle, what we know as reality is actually a projection from a two-dimensional hologram.
Horava thought that the holographic principle might have something to say about the information problems presented by time travel. So he and his students applied a prescription, worked out by Raphael Bousso, also at Berkeley, for finding where the holographic screen is located for any solution of general relativity.
Shield your eyes
To their surprise, they identified the problem with time travel in Goedel's universe. They found that every possible observer in Goedel's universe has an associated holographic screen that either slices through any closed time-like curve or hides it from the observer. Not only are those curves rendered invisible, they cannot be probed by any experiment. In a sense, Horava suggests, the holographic screen separates reality from illusion, with closed time-like curves falling squarely on the illusion side. "If the screen shields violations of causality from the observer," Horava says, "Then no observer inside the universe has access to violations of causality."
Horava cautions that the result is limited. For a start, holography is a new tool and poorly understood as yet, so it is not necessarily useful in more complex situations. And the result for Goedel's universe applies only to observers that are not accelerating through space. But their finding does point the way to dealing with a particular kind of time machine using a string theory approach.
Of course there are other time machines to deal with. Among the other solutions listed in Gauntlett's analysis is a five-dimensional spinning black hole known as a BMPV black hole (after physicists Jason Breckenridge, Myers, Peet and Cumrun Vafa). BMPV black holes can become time machines, but only when they are spinning fast enough. They are also the supergravity counterparts of Kerr-Newman black holes, well known as time machines in general relativity. Dyson, who sat in on Horava's class, began to wonder how difficult it would it be to build such an object and spin it up to the right speed. Using only paper and pencil she set about a task that would have made the gods tremble - constructing a whirling five-dimensional black hole from scratch.
How do you do that? It's not so hard, Dyson insists; it's similar to constructing an ordinary black hole. You start with empty space, then bring in matter from all directions until there is a sufficient amount in a small enough region, and the black hole will form. In the same way, she says, a BMPV black hole is made of constituents brought in from an infinite distance, like a contracting shell. But instead of ordinary matter, the necessary constituents turn out to be gravitational waves and D-branes. D-branes are creatures of string theory most easily understood as multidimensional membranes or "hypersurfaces" that inhabit a 10-dimensional space-time. In the mathematically simpler world of the BMPV black hole, D-branes appear as particles and the gravitational waves as ripples in the gravitational field (they can also be considered as the result of particles called gravitons).
When Dyson's calculations brought these constituents together to make a theoretical BMPV black hole, she discovered an interesting phenomenon. At the point in the assembly process when the black hole is on the verge of becoming a time machine, the building blocks no longer behave as planned. Instead of everything converging at the same point, the system forms a shell of gravitons with the D-branes inside. No amount of mathematical manipulation can get the gravitons to come any closer. The end result of this is that the BMPV black hole's spin never gets fast enough to make an accessible closed time-like curve.
Forbidden territory
Dyson's result suggests that the way the D-branes and gravitons affect each other - and the space they occupy - creates an obstacle to time travel around BMPV black holes. "It's as though you're trying to build that last little bit of your time machine and there's a force that stays your hand," Myers says.
As with Horava's group, Dyson's result only applies to a specific situation: it cannot be taken as a universal proof of Hawking's conjecture. On the other hand, it does show that the tools of string theory can intervene to prevent the existence of some of the kinds of time machines that general relativity allows. "Whether or not string theory uses the same mechanism to prohibit other kinds of time travel is something that is currently being investigated," Dyson says.
But because string theory itself remains incomplete, new tools to attack problems like chronology protection continue to emerge. So is this the beginning of the end for time travel? Theorists are still cautious about formally announcing its demise. "I think a lot of string theorists would be happy if we could find a concrete mechanism that just disallows all closed time-like curves," Myers says. "On the other hand, perhaps in other situations closed time-like curves do exist and we have to come to grips with all the paradoxes and problems
that brings."
Peet is similarly non-committal. "So far we've been pretty lucky but I think there are some nagging doubts among people who work on this," she says. "Maybe there are examples of chronology violation that string theory can't cure. We hope that's not true."
Science fiction writers, of course, hope otherwise. Even Peet, a devoted Star Trek fan, does admit a fleeting regret at the prospect of time travel's demise. "If someone made a spaceship that was capable of time travel I'd be one of the first to go on a tourist mission," she says. "When I realised it might not be possible, I was kind of sad," she adds. "But I got over it."
Seven kinds of time machines
Einstein's general theory of relativity not only allows time machines to exist, it is "completely infested with them," says physicist Matt Visser of Victoria University of Wellington, New Zealand. Visser has compiled a short list of the time travel opportunities that have turned up since Einstein showed us how to warp space-time. Each threatens the logic of cause and effect that lies at the foundation of physics. Together, they are a rogue's gallery that makes physicists long for a solution to the problem of time travel.
Goedel's universe
Goedel's classic solution to Einstein's equations describes a universe that spins rapidly to resist contraction under gravity. One of the side-effects of living in such a universe is that light travels in looping paths instead of straight lines. A traveller can outrun light by taking a shorter path and, after a long enough journey, return to the starting point before leaving.
Van Stockum space-times
This group contains a family of time machine scenarios related by their use of a dense and rapidly rotating cylinder or, alternatively, a rotating cosmic string - a long strand of high-density matter left over from the early universe. The rotation distorts space-time in such a way that a traveller looping around the cylinder or string can follow a closed time-like curve back into the past. How far back depends on the number of loops.
Kerr black holes
The simplest kind of black hole has a singularity of infinite density at its centre. Kerr black holes are rotating, which stretches the singularity into a ring. By passing through the ring in just the right way, one can travel back in time. The trouble is, there is no escape from the black hole. A five-dimensional equivalent, the BMPV black hole, permits closed time-like curves outside the black hole's boundaries if it is rotating fast enough.
Gott's time machine
Richard Gott of Princeton University has suggested taking two parallel cosmic strings and sending them flying past each other at high speed. Travellers passing around the two strings while they are sufficiently close together can encounter themselves at the start of their own journey.
Space-time foam
Physicists predict that at the smallest possible scale (about 10^-35 metres) the smooth regularity of Einstein's space-time breaks down into a bubbling morass of topological irregularities. At this micro-scale, travelling forwards and backwards in time would be like bobbing up and down with the waves on a stormy sea.
Morris-Thorne wormholes
In the early 1990s Michael Morris of the University of Minnesota and Kip Thorne of the California Institute of Technology postulated that a wormhole - a tunnel through space-time - can be turned into a time machine by whirling one end of the wormhole around at high speeds and then bringing the two ends close together again. By passing through the wormhole and returning back to the entrance via normal space, a traveller can retrace the past. A drawback to this method is that exotic matter (with negative energy) is needed to hold the wormhole open.
Alcubierre warp drive
By warping space it is possible to achieve an effect similar to the wormhole scenario. Physicist Miguel Alcubierre of the University of Wales first hit upon this type of time machine in 1994 while investigating the plausibility of a Star Trek-style warp drive. Instead of a tunnel, space is folded and a slot-like passage created to allow faster than light travel between two points. A side effect is that the warp drive doubles as a time machine.
Ivan Semeniuk is a writer and producer with Discovery Channel, Canada
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