Wormholes—keeping the star gate open

Of all the properties of wormholes, the one that has been aired the
most is the issue of their stability. You might find this surprising given that we are not even sure how to make one in the first place,
and in a sense you would be right. But wormhole physics is
all about what is possible—or rather what is not impossible. It
is enough that wormholes of the type first proposed by Thorne
can exist theoretically. How they are created is of secondary
importance. What is not yet clear however is whether the
wormhole can be kept open long enough for someone moving
at a comfortable speed (considerably less than the speed of light)
to get through.
One of the conditions that Thorne wished to impose on his
traversable wormhole was that it would not pinch off quickly like
an Einstein–Rosen bridge or snap shut as soon as we tried to go
through like a Kerr singularity. However, he discovered that this
would not be an easy matter. The throat of the wormhole would
not stay open of its own accord and needed a lot of help. You
might think that this would be the least of his problems since we
can imagine having to erect some sort of scaffolding within the
wormhole that would be of such strength that it could withstand
the immense gravitational forces trying to close it. This would
obviously be way beyond our technological capabilities, but not
impossible. Unfortunately, it turned out that no known matter in
the Universe could fulfil Thorne’s requirements. He realized that
the only way his wormhole would stay open would be if it was
threaded with a very strange kind of material that would have to
have negative mass! What could this mean? How can something
have a mass that is less than zero? Technically, it is said to
have negative energy since mass and energy are interchangeable,
which is just as preposterous. In typical scientific understatement,
Thorne dubbed this material ‘exotic’.
Acommon confusion that many people have when they hear
about this is that it is the same thing as antimatter. Far from
it. Antimatter is a piece of cake compared with exotic matter.
Antimatter has sensible positive mass and is every bit the same as
normal matter in its effect on spacetime. The difference between
matter and antimatter is that they have other opposite properties,
such as electric charge. So, just as a subatomic particle such
as an electron is negatively charged, there exists its antimatter equivalent, the positron, which is identical to the electron in every
way apart from being positively charged. If a lump of matter is
brought together with a lump of antimatter they will mutually
annihilate in a burst of pure energy. But an isolated lump of
antimatter will fall towards the Earth obeying the laws of gravity
just like normal matter. Exotic matter, on the other hand will, if
dropped, experience a force of antigravity repelling it away from
the Earth’s surface!
So where would you go to buy a sufficient amount of this
exotic material to use in your wormhole? Well, we do know how
to make a very tiny amount of negative energy. Not much, but
it’s a start. Work on traversable wormholes has rekindled interest
in an obscure yet fascinating, and experimentally proven, effect
discovered by the Dutch physicist Hendrik Casimir in 1948. It
involves a property of what we would consider to be completely
empty space.
If all the air is pumped out of a chamber then we say that
we have a vacuum, meaning that there is no matter inside and
hence, I hope you’d agree, zero energy. But down at the quantum
level, even the empty vacuum is a busy place. I recommend at this
point that you go back and reread the section in Chapter 4 entitled
‘Not so black after all’ where I discuss Hawking radiation. That
is where I describe how particles and their antimatter partners are
continuously popping into existence from nothing before quickly
disappearing without a trace. Casimir showed how to harness
this process to extract energy from the vacuum even though it has
nothing to give.
As most of us know only too well, if we borrow money from a
bank we must soon pay it back. The rules of quantum mechanics,
as expressed within the Heisenberg uncertainty principle, operate
in a similar way. But unlike a bank loan wherewe are free to choose
the period over which we make the repayments, the uncertainty
principle is rather more strict. It states that energy can be borrowed
from the vacuum provided it is paid back very quickly. The more
energy that is borrowed, the quicker the dept must be repaid.
Now consider what is going on in a vacuum if we could zoom
down to the microscopic level. Among the myriad of subatomic particles that are forming from this borrowed energy are photons
(the particles of light). What’s more, photons of all energies are
being created, with the higher energy ones, corresponding to short
wavelength light, being able to stick around for much less time
than the lower energy, longer wavelength, ones. Thus at any given
moment, the vacuum contains many of these photons (and other
particles) and yet will have an average energy equal to zero since
each particle has only temporarily borrowed the energy needed
for it be created.
Casimir showed how the vacuum can be coaxed into giving
up a tiny amount of its energy permanently. This is achieved by
taking two flat metal plates and placing them up close to each
other inside a vacuum. When the distance between the plates is
not equal to a whole number of wavelengths, corresponding to
photons of a particular energy, then those photons will not be able
to form in the gap because they will not fit. This is a rather difficult
concept to appreciate, sincewemust consider both thewavenature
of light (wavelengths) and its particle nature (photons) at the same
time. Nevertheless, the number of photons forming in the vacuum
between the plates is less than the number on the other side of the
plates and it will therefore have a lower energy. But since the
vacuum outside the gap has zero energy already then the region
between the plates must have less than zero (or negative) energy.
This causes the two plates to be pushed together with a very
weak force that has nevertheless been experimentally measured3.
Unfortunately, the amount of negative energy that can be made
in this way is very tiny and is nowhere near enough to keep a
wormhole open. But it’s a start.
In keeping with the spirit of this chapter, I am not proposing
that the Casimir process will one day lead to enough exotic matter
to line a wormhole’s throat, but rather that such negative energy
material, albeit very tiny and extracted from empty space, is not
ruled out by the laws of physics. In fact, some physicists have
proposed that there might be a way of squeezing the vacuum and
pumping energy out of it in a more systematic way, but this is by
no means clear yet. Just to give you a feel for the amount of exotic material that is needed, Matt Visser has calculated that we would
need exotic matter equivalent to the mass of Jupiter just to hold a
one metre wide wormhole open.
Another way of getting hold of exotic material is from
something called cosmic string. This is material that might have
been left over from the Big Bang but whose existence is highly
debatable. It should not be confused with the string of superstring
theory which I will discuss further in the last chapter, but is much
more impressive. Cosmic string would either be in the form of
a loop or would stretch right across the Universe (and thus may
be infinitely long if the Universe is infinitely large). Either way,
this is string that doesn’t have an end! Its diameter is much less
than the width of an atom yet it is so dense that just one millimetre
of it would weigh a million billion tonnes. The hope would be
that if the Universe went through an inflationary period, driven
by antigravity due to a non-zero cosmological constant, then the
state of the Universe at that periodmayhave been frozen within the
cosmic string. The string would therefore contain exotic matter, or
whatever it was that caused the antigravity driven inflation during
that time. If we could find such string in the Universe it would be
just right to thread through our wormhole.