THE INTRIGUING notion that time might run backwards when the
Universe collapses has run into difficulties. Raymond Laflamme, of the
Los Alamos National Laboratory in New Mexico, has carried out a new
calculation which suggests that the Universe cannot start out uniform,
go through a cycle of expansion and collapse, and end up in a uniform
state. It could start out disordered, expand, and then collapse back into
disorder. But, since the COBE data show that our Universe was born in a
smooth and uniform state, this symmetric possibility cannot be applied
to the real Universe.

Physicists have long puzzled over the fact that two distinct "arrows
of time" both point in the same direction. In the everyday world, things
wear out -- cups fall from tables and break, but broken cups never re-
assemble themselves spontaneously. In the expanding Universe at
large, the future is the direction of time in which galaxies are further
apart.

Many years ago, Thomas Gold suggested that these two arrows might
be linked. That would mean that if and when the expansion of the
Universe were to reverse, then the everyday arrow of time would also
reverse, with broken cups re-assembling themselves.

More recently, these ideas have been extended into quantum physics.
There, the arrow of time is linked to the so-called "collapse of the
wave function", which happens, for example, when an electron wave
moving through a TV tube collapses into a point particle on the screen
of the TV. Some researchers have tried to make the quantum
description of reality symmetric in time, by including both the original
state of the system (the TV tube before the electron passes through)
and the final state (the TV tube after the electron has passed through)
in one mathematical description.

Murray Gell-Mann and James Hartle recently extended this idea to
the whole Universe. They argued that if, as many cosmologists believe
likely, the Universe was born in a Big Bang, will expand out for a finite
time and then recollapse into a Big Crunch, the time-neutral quantum
theory could describe time running backwards in the contracting half of
its life.

Unfortunately, Laflamme has now shown that this will not work. He
has proved that if there are only small inhomogeneities present in the
Big Bang, then they must get larger throughout the lifetime of the
Universe, in both the expanding and the contracting phases. "A low
entropy Universe at the Big Bang cannot come back to low entropy at
the Big Crunch" (Classical and Quantum Gravity, vol 10 p L79).
He has found time-asymmetric solutions to the equations -- but
only if both Big Bang and Big Crunch are highly disordered, with the
Universe more ordered in the middle of its life.

Observations of the cosmic microwave background radiation show
that the Universe emerged from the Big Bang in a very smooth and
uniform state. This rules out the time-symmetric solutions. The
implication is that even if the present expansion of the Universe does
reverse, time will not run backwards and broken cups will not start re-
assembling themselves.

It sounds like science fiction, but it is taken so seriously by
relativists that some of them have proposed that there must be a law
of nature to prevent time travel and thereby prevent paradoxes arising,
even though nobody has any idea how such a law would operate. The
classic paradox, of course, occurs when a person travels back in time
and does something to prevent their own birth -- killing their granny as
a baby, in the more gruesome example, or simply making sure their
parents never get together, as in Back to the Future. It goes against
commonsense, say the sceptics, so there must be a law against it. This
is more or less the same argument that was used to prove that space
travel is impossible.

So what do Einstein's equations tell us, if pushed to the limit? As
you might expect, the possibility of time travel involves those most
extreme objects, black holes. And since Einstein's theory is a theory of
space and time, it should be no surprise that black holes offer, in
principle, a way to travel through space, as well as through time.
A simple black hole won't do, though. If such a black hole formed
out of a lump of non-rotating material, it would simply sit in space,
swallowing up anything that came near it. At the heart of such a black
hole there is a point known as a singularity, where space and time
cease to exist, and matter is crushed to infinite density. Thirty years
ago, Roger Penrose (now of Oxford University) proved that anything
which falls into such a black hole must be drawn into the singularity by
its gravitational pull, and also crushed out of existence.

But, also in the 1960s, the New Zealand mathematician Roy Kerr
found that things are different if the black hole is rotating. A
singularity still forms, but in the form of a ring, like the mint with a
hole. In principle, it would be possible to dive into such a black hole
and through the ring, to emerge in another place and another time. This
"Kerr solution" was the first mathematical example of a time machine,
but at the time nobody took it seriously. At the time, hardly anybody
took the idea of black holes seriously, and interest in the Kerr solution
only really developed in the 1970s, after astronmers discovered what
seem to be real black holes, both in our own Milky Way Galaxy and in the
hearts of other galaxies.

This led to a rash of popular publications claiming, to the annoyance
of many relativists, that time travel might be possible. In the 1980s,
though, Kip Thorne, of CalTech (one of the world's leading experts in the
general theory of relativity), and his colleagues set out to prove once
and for all that such nonsense wasn't really allowed by Einstein's
equations. They studied the situation from all sides, but were forced
to the unwelcome conclusion that there really was nothing in the
equations to prevent time travel, provided (and it is a big proviso) you
have the technology to manipulate black holes. As well as the Kerr
solution, there are other kinds of black hole time machine allowed,
including setups graphically described as "wormholes", in which a black
hole at one place and time is connected to a black hole in another place
and time (or the same place at a different time) through a "throat".
Thorne has described some of these possibilities in a recent book,
Black Holes and Time Warps (Picador), which is packed with
information but far from being an easy read. Now, Michio Kaku, a
professor of physics in New York, has come up with a more accessible
variation on the theme with his book Hyperspace (Oxford UP), which
(unlike Thorne's book) at least includes some discussion of the
contribution of researchers such as Robert Heinlein to the study of
time travel. The Big Bang, string theory, black holes and baby universes
all get a mention here; but it is the chapter on how to build a time
machine that makes the most fascinating reading.

"Most scientists, who have not seriously studied Einstein's equations,"
says Kaku, "dismiss time travel as poppycock". And he then
goes on to spell out why the few scientists who have seriously studied
Einstein's equations are less dismissive. Our favourite page is the one
filled by a diagram which shows the strange family tree of an
individual who manages to be both his/her own father and his/her own
mother, based on the Heinlein story "All you zombies --".

[It] consists of two chambers, each containing two parallel
metal plates. The intense electric fields created between
each pair of plates (larger than anything possible with
today's technology) rips the fabric of space-time, creating a
hole in space that links the two chambers.

Taking advantage of Einstein's special theory of relativity, which says
that time runs slow for a moving object, one of the chambers is then
taken on a long, fast journey and brought back:

Time would pass at different rates at the two ends of the
wormhole, [and] anyone falling into one end of the wormhole
would be instantly hurled into the past or the future [as
they emerge from the other end].

And all this, it is worth spelling out, has been published by serious
scientists in respectable journals such as Physical Review Letters (you
don't believe us? check out volume 61, page 1446). Although, as you
may have noticed, the technology required is awesome, involving taking
what amounts to a black hole on a trip through space at a sizeable
fraction of the speed of light. We never said it was going to be easy!
So how do you get around the paradoxes? The scientists have an
answer to that, too. It's obvious, when you think about it; all you have
to do is add in a judicious contribution from quantum theory to the time
travelling allowed by relativity theory. As long as you are an expert in
both theories, you can find a way to avoid the paradoxes.

It works like this. According to one interpretation of quantum
physics (there are several interpretations, and nobody knows which
one, if any, is "right"), every time a quantum object, such as an
electron, is faced with a choice, the world divides to allow it to take
every possibility on offer. In the simplest example, the electron may
be faced with a wall containing two holes, so that it must go through
one hole or the other. The Universe splits so that in one version of
reality -- one set of relative dimensions -- it goes through the hole on
the left, while in the other it goes through the hole on the right.
Pushed to its limits, this interpretation says that the Universe is
split into infinitely many copies of itself, variations on a basic theme,
in which all possible outcomes of all possible "experiments" must
happen somewhere in the "multiverse". So there is, for example, a
Universe in which the Labour Party has been in power for 15 years, and
is now under threat from a resurgent Tory Party led by vibrant young
John Major.

How does this resolve the paradoxes? Like this. Suppose someone
did go back in time to murder their granny when she was a little girl.
On this multiverse picture, they have slid back to a bifurcation point in
history. After killing granny, they move forward in time, but up a
different branch of the multiverse. In this branch of reality, they were
never born; but there is no paradox, because in he universe next door
granny is alive and well, so the murderer is born, and goes back in time
to commit the foul deed!

Once again, it sounds like science fiction, and once again science
fiction writers have indeed been here before. But this idea of parallel
universes and alternative histories as a solution to the time travel
paradoxes is also now being taken seriously by some (admittedly, not
many) researchers, including David Deutsch, in Oxford. Their research
deals with both time, and relative dimensions in space. You could make
a nice acronym for that -- TARDIS, perhaps?

Exactly one hundred years ago, in 1895, H. G. Wells classic story The
Time Machine was first published in book form. As befits the subject
matter, that was the minus tenth anniversary of the first publication,
in 1905, of Albert Einstein's special theory of relativity. It was
Einstein, as every schoolchild knows, who first described time as "the
fourth dimension" -- and every schoolchild is wrong. It was actually
Wells who wrote, in The Time Machine, that "there is no difference
between Time and any of the three dimensions of Space, except that our
consciousness moves along it".

Since the time of Wells and Einstein, there has been a continuing
literary fascination with time travel, and especially with the
paradoxes that seem to confront any genuine time traveller (something
that Wells neglected to investigate). The classic example is the so-
called "granny paradox", where a time traveller inadvertantly causes
the death of his granny when she was a small girl, so that the
traveller's mother, and therefore the traveller himself, were never
born. In which case, he did not go back in time to kill granny . . . and so on.

A less gruesome example was entertainingly provided by the science
fiction writer Robert Heinlein in his story "By his bootstraps" (available
in several Heinlein anthologies). The protagonist in the story stumbles
on a time travel device brought back to the present by a visitor from
the far future. He steals it and sets up home in a deserted stretch of
time, constantly worrying about being found by the old man he stole the
time machine from -- until one day, many years later, he realises that
he is now the old man, and carefully arranges for his younger self to
"find" and "steal" the time machine. Such a narcissistic view of time
travel is taken to its logical extreme in David Gerrold's "The Man Who
Folded Himself" (Random House, 1973).

Few of the writers of Dr Who have had the imagination actually to
use his time machine in this kind of way. It would, after all, make for
rather dull viewing if every time the Doctor had been confronted by a
disaster he popped into the TARDIS, went back in time and warned his
earlier self to steer clear of the looming trouble. But the implications
were thoroughly explored for a wide audience in the Back to the Future
trilogy, ramming home the point that time travel runs completely
counter to common sense. Obviously, time travel must be impossible.
Only, common sense is about as reliable a guide to science as the
well known "fact" that Einstein came up with the idea of time as the
fourth dimension is to history. Sticking with Einstein's own theories,
it is hardly common sense that objects get both heavier and shorter the
faster they move, or that moving clocks run slow. Yet all of these
predictions of relativity theory have been born out many times in
experiments, to an impressive number of decimal places. And when you
look closely at the general theory of relativity, the best theory of time
and space we have, it turns out that there is nothing in it to forbid time
travel. The theory implies that time travel may be very difficult, to be
sure; but not impossible.

Perhaps inevitably, it was through science fiction that serious
scientists finally convinced themselves that time travel could be made
to work, by a sufficiently advanced civilization. It happened like this.
Carl Sagan, a well known astronomer, had written a novel in which he
used the device of travel through a black hole to allow his characters
to travel from a point near the Earth to a point near the star Vega.
Although he was aware that he was bending the accepted rules of
physics, this was, after all, a novel. Nevertheless, as a scientist
himself Sagan wanted the science in his story to be as accurate as
possible, so he asked Kip Thorne, an established expert in gravitational
theory, to check it out and advise on how it might be tweaked up. After
looking closely at the non-commonsensical equations, Thorne realised
that such a wormhole through spacetime actually could exist as a
stable entity within the framework of Einstein's theory.

Sagan gratefully accepted Thorne's modification to his fictional
"star gate", and the wormhole duly featured in the novel, Contact,
published in 1985. But this was still only presented as a shortcut
through space. Neither Sagan nor Thorne realised at first that what
they had described would also work as a shortcut through time. Thorne
seems never to have given any thought to the time travel possibilities
opened up by wormholes until, in December 1986, he went with his
student, Mike Morris, to a symposium in Chicago, where one of the other
participants casually pointed out to Morris that a wormhole could also
be used to travel backwards in time. Thorne tells the story of what
happened then in his own book Black Holes and Time Warps (Picador).
The key point is that space and time are treated on an essentially
equal footing by Einstein's equations -- just as Wells anticipated. So a
wormhole that takes a shortcut through spacetime can just as well link
two different times as two different places. Indeed, any naturally
occurring wormhole would most probably link two different times.
As word spread, other physicists who were interested in the exotic
implications of pushing Einstein's equations to extremes were
encouraged to go public with their own ideas once Thorne was seen to
endorse the investigation of time travel, and the work led to the
growth of a cottage industry of time travel investigations at the end of
the 1980s and in to the 1990s. The bottom line of all this work is that
while it is hard to see how any civilization could build a wormhole
time machine from scratch, it is much easier to envisage that a
naturally occurring wormhole might be adapted to suit the time
travelling needs of a sufficiently advanced civilization. "Sufficiently
advanced", that is, to be able to travel through space by conventional
means, locate black holes, and manipulate them with as much ease as
we manipulate the fabric of the Earth itself in projects like the
Channel Tunnel.

Even then, there's one snag. It seems you can't use a time machine
to go back in time to before the time machine was built. You can go
anywhere in the future, and come back to where you started, but no
further. Which rather neatly explains why no time travellers from our
future have yet visited us -- because the time machine still hasn't been
invented!

So where does that leave the paradoxes, and common sense? There
is a way out of all the difficulties, but you may not like it. It involves
the other great theory of physics in the twentieth century, quantum
mechanics, and another favourite idea from science fiction, parallel
worlds. These are the "alternative histories", in which, for example,
the South won the American Civil War (as in Ward Moore's classic novel
Bring the Jubilee), which are envisaged as in some sense lying
"alongside" our version of reality.

According to one interpretation of quantum theory (and it has to be
said that there are other interpretations), each of these parallel worlds
is just as real as our own, and there is an alternative history for every
possible outcome of every decision ever made. Alternative histories
branch out from decision points, bifurcating endlessly like the branches
and twigs of an infinite tree. Bizarre though it sounds, this idea is
taken seriously by a handful of scientists (including David Deutsch, of
the University of Oxford). And it certainly fixes all the time travel
paradoxes.

On this picture, if you go back in time and prevent your own birth it
doesn't matter, because by that decision you create a new branch of
reality, in which you were never born. When you go forward in time,
you move up the new branch and find that you never did exist, in that
reality; but since you were still born and built your time machine in the
reality next door, there is no paradox.

Hard to believe? Certainly. Counter to common sense? Of course.
But the bottom line is that all of this bizarre behaviour is at the very
least permitted by the laws of physics, and in some cases is required
by those laws. I wonder what Wells would have made of it all.

This is the latest twist in a story that began in the late 1980s,
when Kip Thorne and colleagues at the California Institute of
Technology suggested that although there might be considerable
practical difficulties in constructing a time machine, there is nothing
in the laws of physics as understood at present to forbid this. Other
researchers tried to find flaws in the arguments of the CalTech team,
and pointed in particular to problems in satisfying a requirement known
as the "weak energy condition", which says that any real observer
should always measure energy distributions that are positive.
This rules out some kinds of theoretical time machines, which
involve travelling through black holes held open by negative energy
stuff.

There are also problems with time machines that involve so-called
singularities, points where space and time are crushed out of existence
and the laws of physics break down. But Ori has found mathematical
descriptions, within the framework of the general theory of relativity,
of spacetimes which loop back upon themselves in time, but in which no
singularity appears early enough to interfere with the time travel, and
the weak energy condition is satisfied (Physical Review Letters, vol 71
p 2517).

"At present," he says, "one should not completely rule out the
possibility of constructing a time machine from materials with
positive energy densities."

This approach has a long (if not entirely respectable) history, but
the implications have never been spelled out as clearly as Price does in
an article to be published in the journal Mind. It is one of the
curiosities of Maxwell's equations, for example, that they allow two
sets of solutions for the effect of a moving electric charge, one
describing an electromagnetic wave moving out from the particle into
the future at the speed of light (a retarded wave) and the other
describing waves from the future converging on the particle at the
speed of light (advanced waves). The advanced wave solutions have
been largely ignored since Maxwell developed his equations in the 19th
century, but a few researchers, including Richard Feynman and Fred
Hoyle, have considered the implications of taking such waves to be
physically real.

More recently, the idea has been investigated in a quantum context
by the American researcher John Cramer. He envisages a quantum
entity such as an electron that is about to be involved in an interaction
(from the everyday point of view) sending out an "offer" wave into the
future. The particle that the electron is about to interact with picks up
the offer wave, and sends a response echoing backwards in time to the
electron. The advanced and retarded waves combine to create a
"handshake" between the two particles which, in a sense atemporally,
determines the outcome of the interaction at the instant the electron
starts to make the offer.

As Price discusses, this kind of approach solves the classic quantum
puzzles, such as the electron faced with two holes in a screen,
"deciding" which hole to go through. Experiments show that, even
though an individual electron can only go through one hole, its behaviour
is affected by whether or not the second hole is open or closed. The
offer wave goes out through both holes, but the echo comes back only
through one hole, the one the electron then goes through. So the
handshake process does take account of the presence of both holes,
even though the electron only goes through one of them.

Many physicists find such ideas abhorrent, because they run counter
to "common sense". They would, for example, encourage speculations
like those of Henry Stapp (see Science, XX August), that our own minds
can influence things that have already happened. The power of Price's
approach, though, is that it offers a framework for understanding how
the world can include both forward and backward causation at a
fundamental level, but appear to have a unique direction of time from a
human perspective.

His argument is complex, but in words it boils down to an argument
that the reason why the things we do in the present do not seem to have
altered the past is that the past has already taken account of what we
are doing! If we decide to do something different, the past already
knows -- so "to say that if we suppose the present to be different,
while the past remains the same, it will follow that the past is
different . . . is untrue, of course, but simply on logical grounds. No
physical asymmetry is required to explain it".

TIME TRAVEL has become, if not respectable, then certainly fashionable
in some quarters of the physics world over the past decade or so. Much
of the blame can be laid at the door of the astronomer Carl Sagan, who
was writing a science fiction novel in the summer of 1985, and asked
the relativist Kip Thorne, of CalTech, to come up with some plausible
sounding scientific mumbo-jumbo to "explain" the literary device of a
wormhole through space which could enable his characters to travel
between the stars. Encouraged to look at the equations of the general
theory of relativity in a new light, Thorne and his colleagues first
found that there is nothing in those equations to prevent the existence
of such wormholes, and then realised that any tunnel through space is
also, potentially, a tunnel through time. The laws of physics do not
forbid time travel.

This realisation had two consequences. When Sagan's novel,
Contact, appeared in 1986 it contained a passage that read like pure Sf
hokum, but which was (although few readers realised it at the time) a
serious science factual description of a spacetime wormhole. And as
Thorne and his colleagues began to publish scientific papers about time
machines and time travel, the spreading ripples have stimulated a
cottage industry of similar studies.

Curiously, this anecdote does not feature in Paul Nahin's otherwise
remarkably comprehensive account of the fact and fiction of time
travel. Nahin is a professor of electrical engineering at the University
of New Hampshire, and the author of several published science fiction
stories, some dealing with the puzzles and paradoxes of time travel.
He tells us how he discovered, and "devoured" science fiction stories at
the age of ten, and this book is clearly a labour of love. The approach is
scholarly, with 36 pages of footnotes, nine technical (but not overly
mathematical) appendices, and a no-holds-barred bibliography. Nahin's
style is distinctly more sober than the material he deals with, but what
he lacks in sparkle he certainly makes up for in comprehensiveness.

The approach, in line with the author's background, is from the
fiction and towards the fact. Old favourites, such as H. G. Wells and
Frank Tipler, make their expected appearances, as do less familiar time
travel fictions from the nineteenth century (comfortably predating
Albert Einstein's theories) and more obscure scientists and philosophers.
And, of course, the familiar time travel paradoxes get a thorough airing.

When astronomer Carl Sagan decided to write a science fiction novel,
he needed a fictional device that would allow his characters to travel
great distances across the Universe. He knew, of course, that it is
impossible to travel faster than light; and he also knew that there was
a common convention in science fiction that allowed writers to use the
gimmick of a shortcut through "hyperspace" as a means around this
problem. But, being a scientist, Sagan wanted something that would
seem to be more substantial than a conventional gimmick for his story.
Was there any way to dress up the mumbo-jumbo of Sf hyperspace in a
cloak of respectable sounding science? Sagan didn't know. He isn't an
expert on black holes and general relativity -- his background specialty
is planetary studies. But he knew just the person to turn to for some
advice on how to make the obviously impossible idea of hyperspace
connections through spacetime sound a bit more scientifically
plausible in his book "Contact".

The man Sagan turned to for advice, in the summer of 1985, was Kip
Thorne, at CalTech. Thorne was sufficiently intrigued to set two of his
PhD students, Michael Morris and Ulvi Yurtsever, the task of working
out some details of the physical behaviour of what the relativists know
as "wormholes". At that time, in the mid-1980s, relativists had long
been aware that the equations of the general theory provided for the
possibility of such hyperspace connections. Indeed, Einstein himself,
working at Princeton with Nathan Rosen in the 1930s, had discovered
that the equations of relativity -- Karl Schwarzschild's solution to
Einstein's equations -- actually represent a black hole as a bridge
between two regions of flat spacetime -- an "Einstein-Rosen bridge".
A black hole always has two "ends", a property ignored by everyone
except a few mathematicians until the mid-1980s. Before Sagan set
the ball rolling again, it had seemed that such hyperspace connections
had no physical significance and could never, even in principle, be used
as shortcuts to travel from one part of the Universe to another.
Morris and Yurtsever found that this widely held belief was wrong.
By starting out from the mathematical end of the problem, they
constructed a spacetime geometry that matched Sagan's requirement of
a wormhole that could be physically traversed by human beings. Then
they investigated the physics, to see if there was any way in which the
known laws of physics could conspire to produce the required geometry.
To their own surprise, and the delight of Sagan, they found that there is.

To be sure, the physical requirements seem rather contrived and
implausible. But that isn't the point. What matters is that it seems
that there is nothing in the laws of physics that forbids travel through
wormholes. The science fiction writers were right -- hyperspace
connections do, at least in theory, provide a means to travel to far
distant regions of the Universe without spending thousands of years
pottering along through ordinary space at less than the speed of light.
The conclusions reached by the CalTech team duly appeared as the
scientifically accurate window dressing in Sagan's novel when it was
published in 1986, although few readers can have appreciated that most
of the "mumbo-jumbo" was soundly based on the latest discoveries
made by mathematical relativists. Since then, the discovery of
equations that describe physically permissible, traversable wormholes
has led to a booming cottage industry of mathematicians investigating
these strange phenomena. It all starts with the Einstein-Rosen bridge.

The Einstein connection

It's one of the intriguing curiosities of the history of science that
spacetime wormholes were actually investigated by mathematical
relativists in great detail long before anybody took the notion of black
holes seriously. As early as 1916, less than a year after Einstein had
formulated his equations of the general theory, the Austrian Ludwig
Flamm had realised that Schwarzschild's solution to Einstein's
equations actually describes a wormhole connecting two regions of flat
spacetime -- two universes, or two parts of the same universe.
Speculation about the nature of wormholes continued intermittently for
decades. What the pioneering relativists did establish, very early on,
was that Schwarzschild wormholes provide no means of communicating
from one universe to the other.

The problem is that in order to traverse an Einstein-Rosen bridge
from one universe to the other, a traveller would have to move faster
than light at some stage of the journey. And there is another problem
with this kind of wormhole -- it is unstable. If you imagine the "dent"
in spacetime made by a large mass such as the Sun, squeezed into a
volume only slightly bigger than its corresponding Schwarzschild
sphere, you would get an "embedding diagram", like Figure 1. The
surprise about the Schwarzschild geometry is that when you shrink the
mass down to within its Schwarzschild radius, you don't just get a
bottomless pit, as in Figure 2; instead, the bottom of the embedding
diagram opens out to make the connection with another region of flat
spacetime (Figure 3). But this beautiful, open throat, offering the
tantalising prospect of travel between universes, exists for only a tiny
fraction of a second before it snaps shut. The wormhole itself does not
even exist for long enough for light to cross from one universe to the
other. In effect, gravity slams shut the door between universes.
This is especially disappointing, because if you ignore the rapid
evolution of the wormhole and only look at the geometry corresponding
to the instant when the throat is wide open, it seems as if such
wormholes might even connect, not separate universes but separate
regions of our own Universe. Space may be flat near each mouth of the
wormhole, but bent around in a gentle curve, far away from the
wormhole, so that the connection really is a shortcut from one part of
the Universe to another (Figure 4). If you imagine unfolding this
geometry to make the entire Universe flat except in the vicinity of the
wormhole mouths, you get something like Figure 5, in which a curved
wormhole connects two separate regions of a completely flat Universe
-- and don't be fooled by the fact that in this drawing the distance from
one mouth to the other through the wormhole itself seems to be longer
than the distance from one mouth to the other through ordinary space;
in the proper four-dimensional treatment, even such a curved wormhole
can still provide a shortcut from A to B.

Or at least, it could if the wormhole stayed open for long enough,
and if passage through the wormhole didn't involve travelling at speeds
faster than that of light. But this is not the end of the story of
hyperspace connections. A simple Schwarzschild black hole has no
overall electric charge, and it does not rotate. Intriguingly, adding
either electric charge or rotation to a black hole transforms the nature
of the singularity, thereby opening the gateway to other universes, and
makes the journey possible while travelling at speeds less than that of
light.

Adding electric charge to a black hole provides it with a second
field of force, in addition to gravity. Because charges with the same
sign repel one another, this electric field acts in the opposite sense to
gravity, trying to blow the black hole apart, not pulling it more tightly
together. Rotation does much the same. There is a force, in either
case, that opposes the inward tug of gravity.

Although gravity still tries to slam shut the door opening to other
universes, the electric field, or rotation, holds the door open for
travellers to get through. But there is still a sense in which this is a
one way door; you could not get back to the universe you started from -
- you would inevitably emerge into another region of spacetime, usually
interpreted as another universe. What goes in one end (the black hole)
comes out of the other end (sometimes dubbed a white hole). Turning
around to go back the way you came would require travelling faster
than light.

Until Sagan made his innocent enquiry about wormholes to Thorne,
this was the nearest the mathematicians had come to describing a
plausible traversable, macroscopic wormhole.

New speculations, encouraged by Sagan's wishful thinking and
developed by the CalTech researchers and others, suggest that it might
indeed be possible to construct traversable wormholes artificially,
just as Sf writers have been telling us for decades, given a suitably
advanced technological civilization.

Wormhole engineering

There is still one problem with wormholes for any hyperspace
engineers to take careful account of. The simplest calculations
suggest that whatever may be going on in the universe outside, the
attempted passage of a spaceship through the hole ought to make the
star gate slam shut. The problem is that an accelerating object,
according to the general theory of relativity, generates those ripples in
the fabric of spacetime itself known as gravitational waves.
Gravitational radiation itself, travelling ahead of the spaceship and
into the black hole at the speed of light, could be amplified to infinite
energy as it approaches the singularity inside the black hole, warping
spacetime around itself and shutting the door on the advancing
spaceship. Even if a natural traversable wormhole exists, it seems to
be unstable to the slightest perturbation, including the disturbance
caused by any attempt to pass through it.

But Thorne's team found an answer to that for Sagan. After all, the
wormholes in "Contact" are definitely not natural, they are engineered.
One of his characters explains:

There is an interior tunnel in the exact Kerr solution of the
Einstein Field Equations, but it's unstable. The slightest
perturbation would seal it off and convert the tunnel into a
physical singularity through which nothing can pass. I have
tried to imagine a superior civilization that would control
the internal structure of a collapsing star to keep the
interior tunnel stable. This is very difficult. The civilization
would have to monitor and stabilize the tunnel forever.

But the point is that the trick, although it may be very difficult, is not
impossible. It could operate by a process known as negative feedback,
in which any disturbance in the spacetime structure of the wormhole
creates another disturbance which cancels out the first disturbance.
This is the opposite of the familiar positive feedback effect, which
leads to a howl from loudspeakers if a microphone that is plugged in to
those speakers through an amplifier is placed in front of them. In that
case, the noise from the speakers goes into the microphone, gets
amplified, comes out of the speakers louder than it was before, gets
amplified... and so on. Imagine, instead, that the noise coming out
of the speakers and into the microphone is analysed by a computer that
then produces a sound wave with exactly the opposite characteristics
from a second speaker. The two waves would cancel out, producing
total silence.

For simple sound waves, this trick can actually be carried out, here
on Earth, in the 1990s. Cancelling out more complex noise, like the
roar of a football crowd, is not yet possible, but might very well be in a
few years time. So it may not be completely farfetched to imagine
Sagan's "superior civilization" building a gravitational wave
receiver/transmitter system that sits in the throat of a wormhole and
can record the disturbances caused by the passage of the spaceship
through the wormhole, "playing back" a set of gravitational waves that
will exactly cancel out the disturbance, before it can destroy the tunnel.

But where do the wormholes come from in the first place? The way
Morris, Yurtsever and Thorne set about the problem posed by Sagan was
the opposite of the way everyone before them had thought about black
holes. Instead of considering some sort of known object in the
Universe, like a dead massive star, or a quasar, and trying to work out
what would happen to it, they started out by constructing the
mathematical description of a geometry that described a traversable
wormhole, and then used the equations of the general theory of
relativity to work out what kinds of matter and energy would be
associated with such a spacetime. What they found is almost (with
hindsight) common sense. Gravity, an attractive force pulling matter
together, tends to create singularities and to pinch off the throat of a
wormhole. The equations said that in order for an artificial wormhole
to be held open, its throat must be threaded by some form of matter, or
some form of field, that exerts negative pressure, and has antigravity
associated with it.

Now, you might think, remembering your school physics, that this
completely rules out the possibility of constructing traversable
wormholes. Negative pressure is not something we encounter in
everyday life (imagine blowing negative pressure stuff in to a balloon
and seeing the balloon deflate as a result). Surely exotic matter cannot
exist in the real Universe? But you may be wrong.

Making antigravity

The key to antigravity was found by a Dutch physicist, Hendrik Casimir,
as long ago as 1948. Casimir, who was born in The Hague in 1909,
worked from 1942 onwards in the research laboratories of the
electrical giant Philips, and it was while working there that he
suggested what became known as the Casimir effect.
The simplest way to understand the Casimir effect is in terms of
two parallel metal plates, placed very close together with nothing in
between them (Figure 6). The quantum vacuum is not like the kind of
"nothing" physicists imagined the vacuum to be before the quantum era.
It seethes with activity, with particle-antiparticle pairs constantly
being produced and annihilating one another. Among the particles
popping in and out of existence in the quantum vacuum there will be
many photons, the particles which carry the electromagnetic force,
some of which are the particles of light. Indeed, it is particularly easy
for the vacuum to produce virtual photons, partly because a photon is
its own antiparticle, and partly because photons have no "rest mass" to
worry about, so all the energy that has to be borrowed from quantum
uncertainty is the energy of the wave associated with the particular
photon. Photons with different energies are associated with
electromagnetic waves of different wavelengths, with shorter
wavelengths corresponding to greater energy; so another way to think
of this electromagnetic aspect of the quantum vacuum is that empty
space is filled with an ephemeral sea of electromagnetic waves, with
all wavelengths represented.

This irreducible vacuum activity gives the vacuum an energy, but
this energy is the same everywhere, and so it cannot be detected or
used. Energy can only be used to do work, and thereby make its
presence known, if there is a difference in energy from one place to
another.

Between two electrically conducting plates, Casimir pointed out,
electromagnetic waves would only be able to form certain stable
patterns. Waves bouncing around between the two plates would behave
like the waves on a plucked guitar string. Such a string can only
vibrate in certain ways, to make certain notes -- ones for which the
vibrations of the string fit the length of the string in such a way that
there are no vibrations at the fixed ends of the string. The allowed
vibrations are the fundamental note for a particular length of string,
and its harmonics, or overtones. In the same way, only certain
wavelengths of radiation can fit into the gap between the two plates of
a Casimir experiment (Figure 7). In particular, no photon corresponding
to a wavelength greater than the separation between the plates can fit
in to the gap. This means that some of the activity of the vacuum is
suppressed in the gap between the plates, while the usual activity goes
on outside. The result is that in each cubic centimetre of space there
are fewer virtual photons bouncing around between the plates than
there are outside, and so the plates feel a force pushing them together.
It may sound bizarre, but it is real. Several experiments have been
carried out to measure the strength of the Casimir force between two
plates, using both flat and curved plates made of various kinds of
material. The force has been measured for a range of plate gaps from
1.4 nanometers to 15 nanometers (one nanometer is one billionth of a
metre) and exactly matches Casimir's prediction.

In a paper they published in 1987, Morris and Thorne drew attention
to such possibilities, and also pointed out that even a straightforward
electric or magnetic field threading the wormhole "is right on the
borderline of being exotic; if its tension were infinitesimally larger ... it
would satisfy our wormhole-building needs." In the same paper,
they concluded that "one should not blithely assume the impossibility
of the exotic material that is required for the throat of a traversable
wormhole." The two CalTech researchers make the important point that
most physicists suffer a failure of imagination when it comes to
considering the equations that describe matter and energy under
conditions far more extreme than those we encounter here on Earth.
They highlight this by the example of a course for beginners in general
relativity, taught at CalTech in the autumn of 1985, after the first
phase of work stimulated by Sagan's enquiry, but before any of this was
common knowledge, even among relativists. The students involved
were not taught anything specific about wormholes, but they were
taught to explore the physical meaning of spacetime metrics. In their
exam, they were set a question which led them, step by step, through
the mathematical description of the metric corresponding to a
wormhole. "It was startling," said Morris and Thorne, "to see how
hidebound were the students' imaginations. Most could decipher
detailed properties of the metric, but very few actually recognised that
it represents a traversable wormhole connecting two different
universes."

Physicists have found the law of nature which prevents time travel
paradoxes, and thereby permits time travel. It turns out to be the same
law that makes sure light travels in straight lines, and which underpins
the most straightforward version of quantum theory, developed half a
century ago by Richard Feynman.

Relativists have been trying to come to terms with time travel for
the past seven years, since Kip Thorne and his colleagues at Caltech
discovered -- much to their surprise -- that there is nothing in the
laws of physics (specifically, the general theory of relativity) to forbid
it. Among several different ways in which the laws allow a time
machine to exist, the one that has been most intensively studied
mathematically is the "wormhole". This is like a tunnel through space
and time, connecting different regions of the Universe -- different
spaces and different times. The two "mouths" of the wormhole could be
next to each other in space, but separated in time, so that it could
literally be used as a time tunnel.

Building such a device would be very difficult -- it would involve
manipulating black holes, each with many times the mass of our Sun.
But they could conceivably occur naturally, either on this scale or on a
microscopic scale.

The worry for physicists is that this raises the possibility of
paradoxes, familiar to science fiction fans. For example, a time
traveller could go back in time and accidentally (or even deliberately)
cause the death of her granny, so that neither the time traveller's
mother nor herself was ever born. People are hard to describe
mathematically, but the equivalent paradox in the relativists'
calculations involves a billiard ball that goes in to one mouth of a
wormhole, emerges in the past from the other mouth, and collides with
its other self on the way in to the first mouth, so that it is knocked out
of the way and never enters the time tunnel at all. But, of course, there
are many possible "self consistent" journeys through the tunnel, in
which the two versions of the billiard ball never disturb one another.
If time travel really is possible -- and after seven years' intensive
study all the evidence says that it is -- there must, it seems, be a law
of nature to prevent such paradoxes arising, while permitting the self-
consistent journeys through time. Igor Novikov, who holds joint posts
at the P. N. Lebedev Institute, in Moscow, and at NORDITA (the Nordic
Institute for Theoretical Physics), in Copenhagen, first pointed out the
need for a "Principle of Self-consistency" of this kind in 1989 (Soviet
Physics JETP, vol 68 p 439). Now, working with a large group of
colleagues in Denmark, Canada, Russia and Switzerland, he has found
the physical basis for this principle.

It involves something known as the Principle of least action (or
Principle of minimal action), and has been known, in one form or
another, since the early seventeenth century. It describes the
trajectories of things, such as the path of a light ray from A to B, or
the flight of a ball tossed through an upper story window. And, it now
seems, the trajectory of a billiard ball through a time tunnel.
Action, in this sense, is a measure both of the energy involved in
traversing the path and the time taken. For light (which is always a
special case), this boils down to time alone, so that the principle of
least action becomes the principle of least time, which is why light
travels in straight lines.

You can see how the principle works when light from a source in air
enters a block of glass, where it travels at a slower speed than in air.
In order to get from the source A outside the glass to a point B inside
the glass in the shortest possible time, the light has to travel in one
straight line up to the edge of the glass, then turn through a certain
angle and travel in another straight line (at the slower speed) on to
point B. Travelling by any other route would take longer.

The action is a property of the whole path, and somehow the light
(or "nature") always knows how to choose the cheapest or simplest path
to its goal. In a similar fashion, the principle of least action can be
used to describe the entire curved path of the ball thrown through a
window, once the time taken for the journey is specified. Although the
ball can be thrown at different speeds on different trajectories (higher
and slower, or flatter and faster) and still go through the window, only
trajectories which satisfy the Principle of least action are possible.
Novikov and his colleagues have applied the same principle to the
"trajectories" of billiard balls around time loops, both with and
without the kind of "self collision" that leads to paradoxes. In a
mathematical tour de force, they have shown that in both cases only
self-consistent solutions to the equations satisfy the principle of
least action -- or in their own words, "the whole set of classical
trajectories which are globally self-consistent can be directly and
simply recovered by imposing the principle of minimal action"
(NORDITA Preprint, number 95/49A).

The word "classical" in this connection means that they have not yet
tried to include the rules of quantum theory in their calculations. But
there is no reason to think that this would alter their conclusions.
Feynman, who was entranced by the principle of least action,
formulated quantum physics entirely on the basis of it, using what is
known as the "sum over histories" or "path integral" formulation,
because, like a light ray seemingly sniffing out the best path from A to
B, it takes account of all possible trajectories in selecting the most
efficient.