Pedagoguery

The defining issue in 21st century physics is the incompatibility between general relativity and quantum mechanics. General relativity rules on large scales while quantum mechanics rules on the scales of molecules, atoms, and smaller scales. Given the weakness of gravity as a force, it plays almost no role on such small scales – with one exception. There is a place where the issues of general relativity and quantum mechanics come together, and that is in a black hole.

Black holes are fundamentally constructs of general relativity. They are a place where matter has attained infinite density, forming a singularity surrounded by an event horizon. However, the fact that a singularity exists points to the fact that the theory is incomplete. It was Stephen Hawking who first applied some principles of quantum mechanics to black holes, and he discovered something unexpected – black holes evaporate due to quantum effects.

To explain why this happens, we need to understand the effects of one of the fundamental principles of quantum mechanics: The Heisenberg Uncertainty Principle. It states that for a particle, there are certain pairs of values that you cannot know to an arbitrary level of certainty. For example, you cannot know both the position and the momentum of a particle at the same time. The more you know about its position, the less you know about its momentum, and vice versa. Another such pair of values is time and energy, and this applies to an empty region of space as well as to a particle. As a result, you cannot know the total energy of a region of space at a given instant of time, and the smaller the region of space, the greater the uncertainty. As a result, you get “virtual particles”, particles that appear, separate, come back together, and annihilate with each other within such a short span of time that they cannot be directly observed. Their effects can be detected indirectly, however, and the existence of virtual particles has been verified in this way.

What Hawking asked is what happens when virtual particles are formed just outside the event horizon of a black hole? There is a chance that one of the particles will fall into the event horizon while the other escapes. If that happens, the survivor carries off mass. Since the total amount of mass has to equal what was started with (zero), the particle that fell into the black hole carries negative mass, and thus the black hole gets just a little smaller. The chance of such an event happening depend on the precise curvature of the space at the edge of the event horizon, and larger black holes have less curved space, and so emit less Hawking radiation, as the phenomena came to be known. This has the counter intuitive effect that the smaller a black hole is, the hotter it is.

Another effect that Hawking described involves information. There is information in everything, including everything that falls into a black hole. However, according to general relativity, nothing that falls into a black hole can escape. Hawking radiation carries away mass, but conveys no information about the black hole at all. Thus, black holes destroy information. However, another foundational principle of quantum mechanics is unitarity, which is essentially conservation of information. According to quantum mechanics, you cannot destroy information, only transform it. Thus, another conflict is born.

There is a possible answer, however, and it relates to another quantum effect called vacuum polarization. To demonstrate this effect, think of a positively charged particle in empty space. It will have an effect on the virtual particles that form near it, attracting negatively charged virtual particles and repelling positively charged ones. The net effect is a cloud of negative charge surrounding the particle. This cloud is not enough to fully cancel out the positive charge of the particle, but it does partially cancel it out. Interestingly, mass works the same way, in that around every mass in empty space, there is an effective cloud of negative mass, produced by the curvature of spacetime. This negative mass produces a repulsive gravitational force. How would this effect influence the collapse of a black hole?

As particles fall together in the collapse of a stellar core, they start to slow as they enter each others' clouds of negative mass. If the vacuum polarization effect is large enough, then fall would continue to slow until it stopped. The result would be a black star, which is a star that would have many of the properties of a black hole as seen from the outside, but which would be solid, with a material surface. They would be extremely dim due to the redshifting of the light they emit. The temperature of the star would match the predicted Hawking temperature of a black hole of a similar mass, thus as you got deeper into the star, it would get hotter. Information would be retained in the structure of the star, and in theory it could be observationally determined, thus no information loss. The only question is whether the vacuum polarization effect is large enough to cause this arrested collapse.

This is not the only theory being developed to reconcile the issues of quantum mechanics and general relativity in the realm of black holes, and the others involve their own exotic physics. Only further observation and experimentation will be able to resolve them.

Next time, out sun's long lost siblings.