Proof of time travel non-existence?
robertaxel
the current knowledge of physics, science is not any closer to ruling
out time travel than it is deeming it a possibility....
Robert A.
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
away, 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
10a^'^X221235 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
Lisa Dyson, "Chronology Protection in String Theory" (
www.arxiv.org/hep-th/0302052)
Matt Visser, "The quantum physics of chronology protection" (
www.arxiv.org/gr-qc/0204022)
Time Travel in Einstein's Universe by Richard Gott (Weidenfeld &
Nicolson, 2001).
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