Everything you always wanted to
know about Time Travel
by John Gribbin
Time and the Universe
How to build a time machine
A beginner's guide
Ruling time travel in
Does time exist?
Another point of view
Wormholes
The ultimate proof
Quantum time waits for
no cosmos
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.
Is time travel possible?
by John and Mary Gribbin
In one of the wildest developments in serious
science for decades,
researchers from California to Moscow have
recently been
investigating the possibility of time travel.
They are not, as yet,
building TARDIS lookalikes in their laboratories;
but they have realised
that according to the equations of Albert
Einstein's general theory of
relativity (the best theory of time and space
we have), there is nothing
in the laws of physics to prevent time travel.
It may be extremely
difficult to put into practice; but it is
not impossible.
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 --".
And Kaku's description of a time machine is
something fans of Dr
Who and H.G. Wells would be happy with:
[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?
Time travel for beginners
by John Gribbin
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.
Time travel back on the agenda
CLAIMS that time travel is impossible in principle
have been shown to
be in error by an Israeli researcher. Amos
Ori, of the Technion-Israel
Institute of Technology, in Haifa, has found
a flaw in the argument put
forward recently by Stephen Hawking, of Cambridge
University,
claiming to rule out any possibility of time
travel.
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."
Is time an illusion?
JUST because we perceive time flowing in one direction,
does that
mean there "really is" a difference between
the past and future? The
old philosophical question has been re-examined
by Huw Price, of the
University of Sydney, in the context of quantum
mechanics. He
concludes that the idea that the past is not
influenced by the future is
an anthropocentric illusion, a "projection
of our own temporal
asymmetry". By allowing signals from the future
to play a part in
determining the outcome of quantum experiments,
he can resolve all
the puzzles and paradoxes of the quantum world.
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".
For the more mathematically inclined, Price
offers a discussion of
John Bell's famous inequality, in which two
widely separated quantum
systems seem to be connected by what Albert
Einstein called a "spooky
action at a distance". The action at a distance
is real, on this picture,
and is essentially Cramer's handshaking process.
But there is no
limitation on free will, according to Price.
We are free to make any
decisions we please, and to take any actions
we choose. The past
already knows what those decisions will be,
but that does not affect
our freedom in making them, and "we shouldn't
expect to 'see' backward
influence in action," which may be bad news
for Stapp, after all.
"It is time," says Price, "that this neglected
approach [to quantum
mechanics] received the attention it so richly
deserves."
Time Machines
Paul J. Nahin
American Institute of Physics p408 Pound??
Distributed in UK by OUP; ISBN 0883189356
John Gribbin
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.
There are, though, two major weaknesses in
Nahin's treatment of
the science. The lesser is his discussion
of black holes, which is weak
and sometimes a little confused. Much more
importantly, though, he
fails to appreciate how the "many worlds"
interpretation of quantum
mechanics allows a time traveller to go back
in time and alter the past
without producing problems such as the notorious
grandfather paradox.
In the conventional version of the paradox,
a traveller goes back and
murders his grandfather as a young boy, so
the traveller could never
have been born, so grandfather never died
-- and so on. But in the many
worlds version (championed today by David
Deutsch, of the University
of Oxford), the act of killing grandad creates
a new reality, so that
when the traveller then goes forward in time
he is no longer in his own
world, but in the universe "next door". This
explains, for example, some
of the more subtle touches in the "Back to
the Future" trilogy of
movies, which Nahin comments on while missing
their point entirely.
But although the book is flawed, it is still
welcome. It does not
lend itself to being read from front to back
like a novel, but is ideal to
dip in to and hop around in, like a time traveller
dipping in to history.
It is also a first class reference book for
anyone interested in the Sf
side of time travel, and one that will be
welcomed by the fans -- at
least, they will welcome it when and if it
becomes available in
paperback at a sensible price.
Hyperspace connections:
Black holes, white holes, wormholes
by John Gribbin
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."
For those with less hidebound imaginations,
there are two remaining
problems -- to find a way to make a wormhole
large enough for people
(and spaceships) to travel through, and to
keep the exotic matter out of
contact with any such spacefarers. Any prospect
of building such a
device is far beyond our present capabilities.
But, as Morris and Thorne
stress, it is not impossible and "we correspondingly
cannot now rule
out traversable wormholes." It seems to me
that there's an analogy
here that sets the work of such dreamers as
Thorne and Visser in a
context that is both helpful and intriguing.
Almost exactly 500 years
ago, Leonardo da Vinci speculated about the
possibility of flying
machines. He designed both helicopters and
aircraft with wings, and
modern aeronautical engineers say that aircraft
built to his designs
probably could have flown if Leonardo had
had modern engines with
which to power them -- even though there was
no way in which any
engineer of his time could have constructed
a powered flying machine
capable of carrying a human up into the air.
Leonardo could not even
dream about the possibilities of jet engines
and routine passenger
flights at supersonic speeds. Yet Concorde
and the jumbo jets operate
on the same basic physical principles as the
flying machines he
designed. In just half a millennium, all his
wildest dreams have not
only come true, but been surpassed. It might
take even more than half a
millennium for designs for a traversable wormhole
to leave the
drawing board; but the laws of physics say
that it is possible -- and as
Sagan speculates, something like it may already
have been done by a
civilization more advanced than our own.
Why time travel is possible
by John Gribbin
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.
So self-consistency is a consequence of the
Principle of least
action, and nature can be seen to abhor a
time travel paradox. Which
removes the last objection of physicists to
time travel in principle --
and leaves it up to the engineers to get on
with the job of building a
time machine.
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