Black Hole Thermodynamics

One of the features of Hawking and Bekenstein's development of black hole thermodynamics is that it ties many many pieces of physics together. Among those pieces are:

The realisation from Quantum Mechanics that we can think of all matter-energy as waves.

The realisation from classical physics that in a confined region, waves exist as standing waves.

The realisation from thermodynamics that the entropy can be viewed as a measure of the number of combinations or permutations of an ensemble that are equivalent. This is equivalent to viewing the entropy more conventionally as a measure of the heat divided by the temperature of a body. According to the Second Law of Thermodynamics, in a closed system the entropy never decreases.

The realisation from Heisenberg's Uncertainty Principle that we can violate the principle of Conservation of Energy so long as we do it for only a short period of time.

The realisation from classical physics that all objects with a temperature above absolute zero radiate away energy as electromagnetic radiation.

Feynman's theory of antimatter as regular matter going backwards in time.

Virtual Pair Production

Recall Heisenberg's Uncertainty Principle. It basically puts a limit on how much we can reduce the disturbance we introduce in a system by doing a measurement on it. There are a number of forms of the principle, and here we shall use only one of them:

The uncertainty in any measurement of the energy of an object times the uncertainty in when the object had that energy will always be at least equal to a universal constant.

Technical note: The universal constant is Planck's constant h divided by 2 pi.

A moment's reflection on the implications of this form of the Uncertainty Principle may convince you that this means that the energy does not even have a definite value but only a lower and upper bound.

Thus the principle of conservation of energy can be violated so long as the violation occurs for only a brief period of time.

Now consider Dirac's infinite sea of negative energy electrons. One of those electrons can violate conservation of energy by spontaneously jumping into a positive energy state provided it falls back into the hole quickly enough. You will recall that we interpret the hole in the sea as a positron. Thus, we believe that this virtual pair production is occurring everywhere in the universe. The pair can only exist for a time of about 10-35 seconds, i.e. 34 zeroes followed by a 1 to the right of the decimal point; this is called the Planck time.

Similarly we believe virtual pairs of proton-antiprotons, neutron-antineutrons etc. are continually being formed and disappearing everywhere in the universe. Wheeler, then, characterises the vacuum at a scale of very small distances as being quantum foam.