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).

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).

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.


Paul Davies is a physicist and writer who is based in Adelaide.

Further Reading

The Matter Myth by Paul Davies.





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