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Nature abhors a paradox, which is just as well. Otherwise you might be zapped by a naked singularity or go back in time and kill your own grandmother. Paul Davies opens a can of worms
Nature abhors a paradox, which is just as well. Otherwise you
might be zapped by a naked singularity or go back in
time and kill your own grandmother. Paul Davies
opens a can of worms NOTHING can escape from a black
hole. Yet Stephen Hawking
famously proved that black holes are not truly black-instead they glow with
heat. But how can this heat energy possibly be flooding back out from what
should be a one-way street? The answer is every bit as exotic as the phenomenon
it explains: the heat radiated by a black hole is paid for, not by normal
energy flowing out of the hole, but by negative energy flowing in.
A mathematical sleight-of-hand? Far from it-negative energy really does exist.
The trouble is, generating and manipulating large enough quantities of negative
energy could threaten some of nature's most sacrosanct laws-the second law
of thermodynamics, for instance. It is easy to dream up scenarios that produce
unphysical or paradoxical consequences-building perpetual motion machines,
or even travelling backwards in time. To physicists, these are alarming notions.
But nature seems to have a trick or two up its sleeve. Intriguingly, if you
look carefully at any of these scenarios, some effect always seems to intrude
in the nick of time to stymie the would-be law-breaker. It is as if there
is a deeper principle of nature at work that permits negative energy, but
proscribes its worst effects.
The concept of energy is familiar to all engineers and scientists. But when
you are keeping track of where it goes, what normally matters is the energy
differences. For example, you can calculate the energy expended in lifting
a weight from A to B, without bothering about what the total energy was at
A.
There is one known exception to this rule, and it concerns
gravity. Einstein's famous
formula E = mc2 states that energy has mass. Because mass
is a source of gravitation, you can imagine an "absolute zero" energy state,
like the absolute zero for temperature. All you need is a state with no
gravitational field-completely empty space is one example. A state with negative
energy would then simply have less energy than one with zero gravitational
field.
But how is it possible to have less mass, or energy, than empty space? The
secret lies with quantum theory. According to this, what appears to be empty
space is in fact teeming with all manner of "virtual" particles that exist
only fleetingly. The so-called quantum vacuum state cannot be stripped of
these countless ghostly entities, but they reveal themselves only when something
disturbs the vacuum state ("Nothing like a vacuum", 25 February 1995, p
30).
It is these ghostly particles that hold the key to creating a flux of negative
energy-in effect a beam of cold and dark, rather than heat and light. The
best way to picture negative energy beams is in terms of a phenomenon called
interference. In a normal interference experiment, when light waves pass
through two nearby slits in an opaque screen, they create a series of bright
and dark stripes on the wall beyond. The bright regions occur where the waves
from the two slits arrive at the wall in step and reinforce each other-so-called
constructive interference. The dark regions occur where the waves are out
of step and cancel each other out-destructive interference. Now think about
the virtual photons in the quantum vacuum. In just the same way, you can
create states in which normal "real" photons from a laser, say, interfere
with virtual vacuum photons. In this case, destructive interference would
form regions where the energy is less than the normal quantum vacuum-in other
words, negative. If there is no wall to stop the light, you then have a beam
of negative energy.
This much was known back in 1970s, and I realised along with Stephen Fulling,
now at Texas A&M University, that a negative energy flux could create
the power source for Hawking's black hole radiation. At a distance, the heat
radiation represents positive energy streaming away from the black hole.
But we knew that this energy could not be traced all the way back inside
the hole, as that would violate the rule that nothing can get out. We found
that negative energy continually streams into the hole from the surrounding
region. Black holes create negative energy around themselves because the
curvature of space-time due to their intense gravitational field disturbs
the virtual particles in the quantum vacuum.
Unfortunately, beams of negative energy don't just
solve problems. They create them too. Suppose you directed such a beam at
a hot object-an oven, say, with an opening protected by a shutter. The contents
of the oven would lose energy and cool down. But this would be a clear breach
of the celebrated second law of thermodynamics, which concerns a property
called entropy. Roughly speaking, entropy is a
measure of how much disorder there is in a given system, and the rule is
that, taken as a whole, the total entropy can never fall. If the oven cooled
down, its entropy would drop. Usually, this process would be accompanied
by a rise in entropy elsewhere, but the negative energy beam has no associated
entropy and nothing changes in the world outside the oven. This would mean
that the total entropy of the Universe would fall, violating the second law.
But since this law is the linchpin of thermodynamics, any violation would
open the way to serious problems-such as the ability to create a perpetual
motion machine, which could conjure up useful work from a system without
any cost.
Negative energy also threatens to create difficulties in a quite different
situation. If you drop an object into a black hole, you generally lose all
sight of its physical properties. One exception is electric charge; any charge
carried by a sacrificed object is retained by the hole, and sets up an electric
field around it. This electric field has energy, which modifies the gravitational
field of the hole. If a black hole has an electric charge so great that its
electric force rivals its gravitational force, then you have a problem. According
to the general theory of relativity, if the charge-to-mass ratio exceeds
a critical value, the black hole will abruptly disappear. This rings alarm
bells, because lurking at the heart of a black hole is a so-called singularity,
a point with infinite density where space-time is infinitely curved. A
singularity is effectively a boundary or edge to space-time. If this edge
were exposed-a "naked"singularity-unknown and unpredictable physical influences
could emerge and invade the Universe. Fortunately, when the singularity is
safely trapped inside a black hole, the wider Universe is safe. But if the
black hole were removed, and the singularity let loose, then all bets would
be off. A negative energy beam could do just that by lowering the mass of
a black hole without affecting its electric charge until the critical limit
is reached.
Cosmic flashing
Larry Ford of Tufts University in Massachusetts has studied these disturbing
scenarios, and found something curious. Although you can imagine ways of
sending negative energy into ovens and black holes, in practice you can't
keep it up for long enough to cause real trouble. Ford used a simple example
of a negative energy flux formed by interference between real photons and
virtual photons in the vacuum. Just as every dark stripe in a conventional
interference experiment has a neighbouring bright stripe, so a region of
negative energy created by destructive interference has a nearby region of
positive energy created by constructive interference. So in a beam like this,
every pulse of negative energy will be followed soon after by a pulse of
positive energy. It's true that a pulse of negative energy could temporarily
lower the entropy of an oven, but the next positive pulse would raise it
again. Although the beam would create a fluctuation in the total entropy,
the second law of thermodynamics is a statistical law that permits small
fluctuations . Ford managed to prove that, for the states he investigated,
the strength and duration of the entropy fluctuations stayed safely within
permitted statistical boundaries. In the black hole scenario the situation
is rather less clear cut. It looks as if a
space-time singularity might be momentarily exposed,
a situation that Ford describes as "cosmic flashing". Whether such flashes
would compromise the rationality of the cosmos is still uncertain.
You might wonder whether it is possible to improve on Ford's scenario, for
example by opening the oven's shutter only when a pulse of negative energy
approaches, and shutting out the positive energy pulses. That way the negative
energy would gradually accumulate inside the oven and the positive energy
would be kept out. There is, however, yet another snag. Just operating the
shutter will itself create a disturbance in the quantum vacuum, and a short
calculation shows that the disturbance serves to create a burst of photons
from the vacuum. When the sums are done, you find that the entropy of the
newly made photons more than outweighs the reduction in entropy due to the
negative energy. More elaborate strategies designed to chop out the negative
energy parts of a beam and stockpile them all run into similar obstacles.
Once again, nature seems to find ways of confounding experimenters' attempts
to use negative energy to achieve more than a token reduction in entropy.
However, there are other ways to create sustained negative fluxes. One of
these was discovered by Fulling and me, and uses a single moving mirror (see
Diagram, left).
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| Trick of the light: could negative energy from a moving mirror evaporate a black hole and expose the singularity within? |
The effect depends once again on the invisible virtual photons in the quantum
vacuum. It's all down to the Doppler effect-the same principle used
by police to trap speeding motorists by reflecting laser light or radar waves
off an approaching vehicle. When light waves reflect off the moving mirror,
the wavelengths change towards the blue end of the spectrum for an approaching
mirror, and towards the red for a receding one. So a speeding mirror scrambles
the wavelengths, and hence energies, of all the virtual photons. Depending
on the details of the mirror's motion, the overall effect can add to or subtract
from the total energy of the vacuum. In an idealised model in one dimension,
our calculations showed that if a mirror moves to the right with increasing
acceleration, negative energy flows in the same direction at the speed of
light, whilst positive energy flows to the left.
Such a beam would be continuous rather than pulsed, so does that mean you
could you use it to cool down the oven and violate the second law? Curiously,
you would still run into problems sustaining the negative flux. Picture the
experiment: the accelerating mirror produces a beam of negative energy as
it heads towards the oven, but eventually it collides with the oven, halting
the experiment. The greater the acceleration the bigger the flux, but the
shorter the duration before collision. Again, the sums show that the total
accumulated negative energy at the oven is not enough to exceed the allowed
entropy fluctuations. A different approach is to station an oven close to
the surface of a black hole, in the hope of scooping up some of the negative
energy before it's sucked in (see Diagram below).
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| No go: if in oven could trap negative energy flowing into a black hole, the laws of physics would be threatened. But positive energy around the hovering oven would creep in and outweigh the negative energy |
This time another effect saves the second law from violation.
The gravitational pull of the black hole is enormous, so if you want to keep
the oven from plunging into the hole, you have to subject it to a huge outwards
acceleration. William Unruh of the University of British Columbia and I have
shown that, if you are accelerating, the virtual photons in the quantum vacuum
make you feel as if you are immersed in a bath of heat radiation-and the
faster the acceleration, the hotter it will seem. An object hovering outside
the surface of a black hole, will experience an enormous acceleration, and
thus an effective heat bath. It turns out that the oven would let in more
heat from the bath than it would negative energy, and the entropy would not
fall, but rise. It's not just fluxes of negative energy that threaten
paradoxes-static negative energy could cause trouble too. One such scenario
is a worm-hole in space. Wormholes are hypothetical tubes of space that create
a shortcut between distant points ("Planes, trains and wormholes", 23 March
1996, p 28). If they exist they can be used as time machines-astronauts who
pass through the wormhole and return home via normal space, could get back
before they left.
Opening up
Kip Thorne and his colleagues at Caltech have shown that wormholes are
theoretically possible, but they need something to keep their throats open.
A wormhole is basically an adaptation of a black hole, and has an intense
gravitational field. Under normal circumstances, with only ordinary positive
energy around, any wormhole that formed would collapse under gravity before
anything could pass through it. But because negative energy has negative
mass it exerts a negative gravitational force, so it could oppose the pinching
effect of positive energy and keep the throat open. If unrestricted negative
energy states were possible, they could be used to make a time machine that
would enable us to change the past-an absurd prospect in many people's eyes.
But here, the problem is how to make the static negative
energy. One way could be to exploit the Casimir
effect, discovered by Dutch physicist Hendrick Casimir back in 1948.
Two mirrors placed face-to-face trap a slab of quantum vacuum between them.
While mirrors reflect real photons of light, they also reflect ghostly virtual
photons too. According to quantum theory, every photon is associated with
an electromagnetic wave whose wavelength corresponds to the photon's energy.
Electromagnetic waves sandwiched between Casimir mirrors form patterns of
standing waves, which are restricted to certain values-in the same way that
plucked guitar strings play only certain notes. Because of this, many virtual
photons that would exist in unbounded empty space cannot be trapped between
the mirrors because their wavelengths don't fit. The energy associated with
all these missing' photons is absent from the region between the plates,
and the total energy of the quantum vacuum is lower there than in unbeunded
empty space. In other words, a static negative energy state exists between
the plates.
But this would probably not be good enough to keep a wormhole open. You might
think that the Casimir effect would offer unrestricted negative energies,
if the mirrors have a large enough area and a small enough separation. However,
the mirrors themselves are made of normal, positive-energy matter. Moreover,
no mirror is perfectly flat, infinitely smooth and perfectly reflecting.
It is unlikely that the total energy of the entire Casimir system could ever
be negative. Whether or not there are any configurations of matter that can
form large, stable, regions of negative energy is an open question still
being investigated by theoretical physicists interested in time travel. My
hunch is that the same deep principle that protects the second law of
thermodynamics from negative energy abuse will intervene here too.
So what is this deep principle and where does it come from? I think that
it all stems from the concept of information. All the paradoxical scenarios
we have explored relate to the subject of information. Reducing entropy is
like creating order, which is equivalent to creating information, and naked
singularities are a source of gratuitous information. Wormhole time travel
is paradoxical because it enables information to be generated out of thin
air.
Consider the professor who travels ahead to the year 2000 and
jots down a new theorem from a journal. The professor then returns to 1998
and promptly writes up the theorem in a paper. When published, this work
constitutes the very paper that the professor inspected in the year 2000.
The question is, where did the information in the new theorem come from?
Not from the professor, who read it in the journal. But not from anyone else.
It came into existence spontaneously and paradoxically. So if there is a
hidden law at work in the Universe banning excessive negative energy, then
it would seem to ban information from appearing out of nothing. Since the
spontaneous appearance of information is tantamount to a miracle, and deeply
irrational, such a principle goes to the very heart of the scientific description
of nature.
If this principle does exist, it will continue to protect us from the vagaries
of negative energy. But nobody has yet proved for sure that it's impossible
to create sustained negative energy fluxes that you could manipulate to make
mischief. Until a no-go theorem is proved, the subject will continue to be
a fertile ground for the imaginative inventor.
Author Paul Davies is a physicist and writer who is based in Adelaide. Further Reading The Matter Myth by Paul Davies. |