Our current understanding of black holes would seem to indicate
that they could never be used in practice as windows or bridges to
other universes, or to other parts of our own universe, even if we
could ever get to one. They remain a fertile subject for science
fiction writers who are not usually deterred by the objections
of physicists or even experimental evidence. However, not all
science fiction writers disregard the latest findings and predictions
of the physicists. Many sci-fi authors are themselves professional
scientists and would require of their stories that they at least did
not blatantly flout the laws of physics. This was the case in 1985 when the celebrated astrophysicist, author and TV personality
Carl Sagan was writing his novel Contact. In the story, which has
recently been made into a movie, humans make contact with an
advanced alien civilization using a tunnel through hyperspace (a
wormhole2) that links two distant parts of the Galaxy through
which the heroes of the story travel. Sagan was aware of the
possibility of an Einstein–Rosen bridge or a Kerr singularity for
this purpose but wanted his story to be as realistic as possible and
needed to get his facts straight. After all, despite the whole idea
of fiction being that we can make things up as we go along, being
a trained scientist he was determined to only include what was
considered at least possible by general relativity.
Sagan therefore sent an early draft of the manuscript to
his friend Kip Thorne in the Theoretical Astrophysics Group at
California Institute of Technology. Thorne is one of the world’s
leading experts on general relativity and Sagan hoped that he
could at least come up with a suggestion or two based on the
latest scientific ideas that would add credence to the story. Neither
man was prepared for what was to follow. Sagan’s request
aroused Thorne’s curiosity and, with the help of his PhD student
Michael Morris, Thorne decided to tackle the problem from an
original angle. To understand his approach I should explain what
Einstein’s equations of general relativity roughly look like. On
one side of the equations is information about mass and energy
while the other side of the equations describes the curvature of
spacetime in the presence of this mass and energy—suffice it to
say that the equations are far richer and more complex than his
special relativity equation E = mc2. Usually, physicists will start
by defining the mass and energy content of a particular region
of spacetime, such as a star, then solve Einstein’s equations to
find out how the surrounding spacetime is affected and what
properties it might have. Thorne began thinking about whether
wormholes were allowed in theory, but he didn’t follow the traditional approach. After all, he was well aware of the problems
that plagued the usual solutions for black holes, such as event
horizons, tidal forces, unstable singularities, tunnels that pinch
shut before you can get across and so on. Instead, he decided to
start with a wish list. He knew that for the purposes of Sagan’s
story the wormhole would have to be stable, constantly open, not
have event horizons at either end to allow for two-way travel, not
have any singularities and not have any uncomfortable tidal forces
that would kill any traveller before they could enter. He then set
about, with his colleagues at Caltech, to (mathematically) design
the shape that spacetime must have to satisfy all his requirements.
To his surprise he found that this was indeed possible.
Thorne realized he could design just the sort of wormhole
Sagan was looking for. It turned out to be possible in theory to have
a link between two parts of the Universe that looked, schematically,
just like Wheeler’s quantum wormholes of thirty years earlier.
But this time the tunnels would be large enough for humans to
travel through in a spacecraft without feeling any discomfort. For
instance, a traveller could enter one mouth of the wormhole near
Earth and within a short time he or she would emerge from the
other end on the opposite side of the Galaxy. The traveller would
then be able to return through the wormhole and report back.
This ‘connection’ was thus dubbed a ‘traversable wormhole’ to
distinguish it from non-traversable ones like the Einstein–Rosen
bridge. From now on, when I refer to such structures I will simply
call them wormholes, implying the traversable variety.
Such a wormhole is shown in figure 8.1 in which space is
depicted as a two-dimensional sheet. The two entrances into the
wormhole are known as its mouths, while the neck (or handle)
in between them is referred to as the wormhole’s throat. A
difficult concept to grasp is that, while the distance through
normal space between the two mouths of the wormhole may
be arbitrarily long (say a thousand lightyears), the length of the
wormhole tunnel itself may be arbitrarily short (a few kilometres
or even metres). This is not apparent from figure 8.1 where it
looks like the path through the wormhole is actually longer than
the one going straight across. However, you must remember that the wormhole is really a connection between two regions in
curved four-dimensional spacetime which is impossible for us to
visualize.
It is also important to appreciate that Thorne’s wormhole is
not formed from black holes, nor does it have event horizons.
So presumably we cannot expect to find one lying about in
the Universe. If so, how would we go about constructing one
ourselves? First of all, and before you get too excited, building
a traversable wormhole is not a job for twentieth or even twenty
first century technology. It may indeed never be possible. But
since this chapter is dealing in speculation, allow me to speculate.
One way of creating a wormhole would be to enlarge a quantum
wormhole. Down at the very tiniest length scale and trillions
of times smaller than atoms, is what is known as the Planck
scale where the concept of length loses its meaning and quantum
uncertainty rules. At this level all known laws of physics break
down and even space and time become nebulous concepts. Any
and all conceivable distortions of spacetime will be popping in
and out of existence in a random and chaotic dance which is
going on all the time everywhere in the Universe. Terms such as
‘quantum fluctuations’ and the ‘quantum foam’ which are used to It is clear that, however inflation worked just after the
Big Bang, it must have opposed the inward pull of gravity by
providing an outward pressure (or antigravity) that would cause
space to stretch and the Universe to expand. This idea should
sound familiar. It is the work of Einstein’s cosmological constant
which he first proposed to stabilize the Universe against collapse,
and which has been in and out of favour among cosmologists
ever since. If we were able to apply such ‘negative pressure’ to
a tiny region of space and cause our own controlled mini-inflation
of space we might produce, among other ‘things’, a wormhole.
This means of course that such wormholes may have been created
naturally in the Universe. Even so, it is highly unlikely, although
not impossible, that some might still be around today as they
would have very quickly collapsed.
Of course if naturally occurring wormholes do exist then apart
from the difficulty of actually finding one (or one of its mouths
at least), we would have no control over where it might lead
to. We would just have to try it out and see. The alternative
to finding a ready-made wormhole, either a tiny one that we
would have to inflate or one left over from the Big Bang, would
be to start from scratch and manipulate spacetime ourselves.
Even by the speculative standards of this discussion it would
appear to be highly unlikely that this would ever be possible.
Of course, researchers in ‘wormhole physics’ are not currently
concerned with how to make wormholes since the field is still in its
infancy and they are more interested in what their properties are.
Scientific papers on this subject often start with phrases such as:
“We consider a traversable wormhole joining two asymptotically
flat regions of spacetime . . . ”, which basically means “Take one
wormhole . . . ”. They then go on to work through the complex
equations of general relativity. Because of the highly theoretical
and speculative nature of wormhole physics, such papers often
talk about ‘cutting and pasting’ two regions of spacetime together
as a way of creating a wormhole. This conjures up an image of using scissors and tape on a spacetime treated as a 2D sheet of
paper. Even the theoretical physicistswhowrite these papers often
have this sort of simple image in mind.
As for Kip Thorne, he is no longer as interested these days
in wormholes as he was in the late 1980s when his papers started
the whole field off. Since then, and throughout the 1990s, many
serious and highly technical papers have appeared in the leading
scientific journals dealing with wormholes of all shapes and sizes,
and interest in the subject shows no signs of abating just yet. Today,
it is fair to say that the best known expert on wormholes is Matt
Visser at Washington University in St Louis who has written the
first textbook devoted to the subject.
Visser has compiled a whole taxonomy of wormholes. He
has shown that wormholes come in different phyla and species.
The phylum of interest here is known as Lorentzian wormholes
(based on the way spacetime is warped to give rise to the
wormhole). Lorentzian wormholes are then divided into two
species: permanent and transient—we are naturally interested
in permanent ones. Each of these species consists of two
subspecies depending on whether it is a wormhole that connects
two different universes (known as an inter-universe wormhole)
or two, possibly distant, regions of the same universe (an intrauniverse
wormhole). Each of these subspecies is then divided
into macroscopic and microscopic varieties. The ‘macroscopic’
tends to mean traversable, while ‘microscopic’ implies quantum
wormholes of the type first studied by Wheeler. In general of
course, Wheeler’s quantum wormholes are of the transient type
since they pop in and out of existence according to the rules of
quantum mechanics. But, due to quantum mechanical uncertainty,
it may be that wormholes of the permanent variety (by which I
mean having the right spacetime curvature that allows them to
last much longer than normal) might occasionally be created.
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