Scharnhorst Black Holes

Hawking’s black hole information paradox is one of the biggest examples of quantum mechanics and gravity not playing well with each other. Special relativity states that no particle, even a massless one, can travel faster than the speed of light c. If the gravitational attraction of an object is strong enough to make the escape velocity greater than c, then clearly no particles can escape a black hole.

Information must be destroyed. As soon as a particle enters, no experiment can be performed to determine if the particle was a photon, electron, or quark. The no-hair theorem states that the only inference one could make is the particle’s mass, charge, or angular momentum.

Quantum mechanics is a probabilistic deterministic theory, since the time translation operator is always unitary. As soon as the state at one point in time is known, some information of every particle will be known at later times. Quantum mechanically, information should not be spontaneously lost at some special instant of time corresponding to the particle passing the Schwarzschild radius. This seems to be quite paradoxical.

But what if information could escape the black hole? Clearly that would be impossible, right?

A paper by Klaus Scharnhorst shows how boundary conditions and external fields make the quantum vacuum become a refractive material, with a dispersive index of refraction. He also shows how certain systems can result in group and phase velocities greater than c, such as Casimir plates.

(http://arxiv.org/abs/hep-th/9810221)

The black hole event horizon acts as a boundary condition. The allowed number of momentum states on the inside of a black hole decreases, as particles cannot escape. Cutting out these possible vacuum modes is similar to how Casimir plates cut out vacuum modes. Perhaps the index of refraction is less than 1, and the “speed of light” in a vacuum on the inside of a black hole is slightly greater than c. Would this allow for some information to escape a black hole?!

I would like to pursue this calculation and see what the index of refraction would be on each side of the horizon, but two theorists have suggested that this is not an avenue worth pursuing. They could not show that it was wrong though.

It seems that Scharnhorst’s effect has not gotten to be mainstream in the physics community, but it must be true. People claim that this effect violates causality, as it allows for faster than c signals, but causality is NOT violated. Whenever people approach solving the information paradox by saying something moves faster than c, they immediately assume it violates causality. The Scharnhorst effect does not do such a thing!

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