operate. In order to survive, human beings have to consume food, which is an ordered form of energy, and
convert it into heat, which is a disordered form of energy. Thus intelligent life could not exist in the contracting
phase of the universe. This is the explanation of why we observe that the thermodynamic and cosmological
arrows of time point in the same direction. It is not that the expansion of the universe causes disorder to
increase. Rather, it is that the no boundary condition causes disorder to increase and the conditions to be
suitable for intelligent life only in the expanding phase.
To summarize, the laws of science do not distinguish between the forward and backward directions of time.
However, there are at least three arrows of time that do distinguish the past from the future. They are the
thermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the direction
of time in which we remember the past and not the future; and the cosmological arrow, the direction of time in
which the universe expands rather than contracts. I have shown that the psychological arrow is essentially the
same as the thermodynamic arrow, so that the two would always point in the same direction. The no boundary
proposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because the
universe must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow to
agree with the cosmological arrow is that intelligent beings can exist only in the expanding phase. The
contracting phase will be unsuitable because it has no strong thermodynamic arrow of time.
The progress of the human race in understanding the universe has established a small corner of order in an
increasingly disordered universe. If you remember every word in this book, your memory will have recorded
about two million pieces of information: the order in your brain will have increased by about two million units.
However, while you have been reading the book, you will have converted at least a thousand calories of
ordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air around
you by convection and sweat. This will increase the disorder of the universe by about twenty million million
million million units – or about ten million million million times the increase in order in your brain – and that’s if
you remember everything in this book. In the next chapter but one I will try to increase the order in our neck of
the woods a little further by explaining how people are trying to fit together the partial theories I have described
to form a complete unified theory that would cover everything in the universe.
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PREVIOUS NEXT
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CHAPTER 10
WORMHOLES AND TIME TRAVEL
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The last chapter discussed why we see time go forward: why disorder increases and why we remember the
past but not the future. Time was treated as if it were a straight railway line on which one could only go one way
or the other.
But what if the railway line had loops and branches so that a train could keep going forward but come back to a
station it had already passed? In other words, might it be possible for someone to travel into the future or the
past?
H. G. Wells in The Time Machine explored these possibilities as have countless other writers of science fiction.
Yet many of the ideas of science fiction, like submarines and travel to the moon, have become matters of
science fact. So what are the prospects for time travel?
The first indication that the laws of physics might really allow people to travel in time came in 1949 when Kurt
Godel discovered a new space-time allowed by general relativity. Godel was a mathematician who was famous
for proving that it is impossible to prove all true statements, even if you limit yourself to trying to prove all the
true statements in a subject as apparently cut and dried as arithmetic. Like the uncertainty principle, Godel’s
incompleteness theorem may be a fundamental limitation on our ability to understand and predict the universe,
but so far at least it hasn’t seemed to be an obstacle in our search for a complete unified theory.
Godel got to know about general relativity when he and Einstein spent their later years at the Institute for
Advanced Study in Princeton. His space-time had the curious property that the whole universe was rotating.
One might ask: “Rotating with respect to what?” The answer is that distant matter would be rotating with
respect to directions that little tops or gyroscopes point in.
This had the side effect that it would be possible for someone to go off in a rocket ship and return to earth
before he set out. This property really upset Einstein, who had thought that general relativity wouldn’t allow time
travel. However, given Einstein’s record of ill-founded opposition to gravitational collapse and the uncertainty
principle, maybe this was an encouraging sign. The solution Godel found doesn’t correspond to the universe
we live in because we can show that the universe is not rotating. It also had a non-zero value of the
cosmological constant that Einstein introduced when he thought the universe was unchanging. After Hubble
discovered the expansion of the universe, there was no need for a cosmological constant and it is now
generally believed to be zero. However, other more reasonable space-times that are allowed by general
relativity and which permit travel into the past have since been found. One is in the interior of a rotating black
hole. Another is a space-time that contains two cosmic strings moving past each other at high speed. As their
name suggests, cosmic strings are objects that are like string in that they have length but a tiny cross section.
Actually, they are more like rubber bands because they are under enormous tension, something like a million
million million million tons. A cosmic string attached to the earth could accelerate it from 0 to 60 mph in 1/30th
of a second. Cosmic strings may sound like pure science fiction but there are reasons to believe they could
have formed in the early universe as a result of symmetry-breaking of the kind discussed in Chapter 5.
Because they would be under enormous tension and could start in any configuration, they might accelerate to
very high speeds when they straighten out.
The Godel solution and the cosmic string space-time start out so distorted that travel into the past was always
possible. God might have created such a warped universe but we have no reason to believe he did.
Observations of the microwave background and of the abundances of the light elements indicate that the early
universe did not have the kind of curvature required to allow time travel. The same conclusion follows on
theoretical grounds if the no boundary proposal is correct. So the question is: if the universe starts out without
the kind of curvature required for time travel, can we subsequently warp local regions of space-time sufficiently
to allow it?
A closely related problem that is also of concern to writers of science fiction is rapid interstellar or intergalactic
travel. According to relativity, nothing can travel faster than light. If we therefore sent a spaceship to our nearest
neighboring star, Alpha Centauri, which is about four light-years away, it would take at least eight years before
we could expect the travelers to return and tell us what they had found. If the expedition were to the center of
our galaxy, it would be at least a hundred thousand years before it came back. The theory of relativity does
allow one consolation. This is the so-called twins paradox mentioned in Chapter 2.
Because there is no unique standard of time, but rather observers each have their own time as measured by
clocks that they carry with them, it is possible for the journey to seem to be much shorter for the space travelers
than for those who remain on earth. But there would not be much joy in returning from a space voyage a few
years older to find that everyone you had left behind was dead and gone thousands of years ago. So in order to
have any human interest in their stories, science fiction writers had to suppose that we would one day discover
how to travel faster than light. What most of thee authors don’t seem to have realized is that if you can travel
faster than light, the theory of relativity implies you can also travel back in the, as the following limerick says:
There was a young lady of Wight
Who traveled much faster than light.
She departed one day,
In a relative way,
And arrived on the previous night
The point is that the theory of relativity says hat there is no unique measure of time that all observers will agree
on Rather, each observer has his or her own measure of time. If it is possible for a rocket traveling below the
speed of light to get from event A (say, the final of the 100-meter race of the Olympic Games in 202) to event B
(say, the opening of the 100,004th meeting of the Congress of Alpha Centauri), then all observers will agree
that event A happened before event B according to their times. Suppose, however, that the spaceship would
have to travel faster than light to carry the news of the race to the Congress. Then observers moving at
different speeds can disagree about whether event A occurred before B or vice versa. According to the time of
an observer who is at rest with respect to the earth, it may be that the Congress opened after the race. Thus
this observer would think that a spaceship could get from A to B in time if only it could ignore the speed-of-light
speed limit. However, to an observer at Alpha Centauri moving away from the earth at nearly the speed of light,
it would appear that event B, the opening of the Congress, would occur before event A, the 100-meter race.
The theory of relativity says that the laws of physics appear the same to observers moving at different speeds.
This has been well tested by experiment and is likely to remain a feature even if we find a more advanced
theory to replace relativity Thus the moving observer would say that if faster-than-light travel is possible, it
should be possible to get from event B, the opening of the Congress, to event A, the 100-meter race. If one
went slightly faster, one could even get back before the race and place a bet on it in the sure knowledge that
one would win.
There is a problem with breaking the speed-of-light barrier. The theory of relativity says that the rocket power
needed to accelerate a spaceship gets greater and greater the nearer it gets to the speed of light. We have
experimental evidence for this, not with spaceships but with elementary particles in particle accelerators like
those at Fermilab or CERN (European Centre for Nuclear Research). We can accelerate particles to 99.99
percent of the speed of light, but however much power we feed in, we can’t get them beyond the speed-of-light
barrier. Similarly with spaceships: no matter how much rocket power they have, they can’t accelerate beyond
the speed of light.
That might seem to rule out both rapid space travel and travel back in time. However, there is a possible way
out. It might be that one could warp space-time so that there was a shortcut between A and B One way of doing
this would be to create a wormhole between A and B. As its name suggests, a wormhole is a thin tube of
space-time which can connect two nearly flat regions far apart.
There need be no relation between the distance through the wormhole and the separation of its ends in the
nearly Hat background. Thus one could imagine that one could create or find a wormhole that world lead from
the vicinity of the Solar System to Alpha Centauri. The distance through the wormhole might be only a few
million miles even though earth and Alpha Centauri are twenty million million miles apart in ordinary space. This
would allow news of the 100-meter race to reach the opening of the Congress. But then an observer moving
toward 6e earth should also be able to find another wormhole that would enable him to get from the opening of
the Congress on Alpha Centauri back to earth before the start of the race. So wormholes, like any other
possible form of travel faster than light, would allow one to travel into the past.
The idea of wormholes between different regions of space-time was not an invention of science fiction writers
but came from a very respectable source.
In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed what
they called “bridges,” but which are now known as wormholes. The Einstein-Rosen bridges didn’t last long
enough for a spaceship to get through: the ship would run into a singularity as the wormhole pinched off.
However, it has been suggested that it might be possible for an advanced civilization to keep a wormhole open.
To do this, or to warp space-time in any other way so as to permit time travel, one can show that one needs a
region of space-time with negative curvature, like the surface of a saddle. Ordi-nary matter, which has a
positive energy density, gives space-time a positive curvature, like the surface of a sphere. So what one needs,
in order to warp space-time in a way that will allow travel into the past, is matter with negative energy density.
Energy is a bit like money: if you have a positive balance, you can distribute it in various ways, but according to
the classical laws that were believed at the beginning of the century, you weren’t allowed to be overdrawn. So
these classical laws would have ruled out any possibility of time travel. However, as has been described in
earlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle. The
quantum laws are more liberal and allow you to be overdrawn on one or two accounts provided the total
balance is positive. In other words, quantum theory allows the energy density to be negative in some places,
provided that this is made up for by positive energy densities in other places, so that the total energy re-mains
positive. An example of how quantum theory can allow negative energy densities is provided by what is called
the Casimir effect. As we saw in Chapter 7, even what we think of as “empty” space is filled with pairs of virtual
particles and antiparticles that appear together, move apart, and come back together and annihilate each other.
