Information and a Black Hole

Classical information and quantum information are not the same. Why? Because QM rule 2 tells us that in QM there can be a coherent superposition of quantum states. No such state exists in classical physics. So quantum information supersedes classical information.

The classical and the quantum information content in a system, such as a chair, can be determined or estimated by standard techniques of classical and quantum information theory. Suppose the chair is tossed into a black hole. The quantum information in the chair seems to have gone with the chair into never-never land. Why should we worry about this information loss?

Answer

For certain, one should worry about quantum information loss, especially if quantum mechanics is to provide a complete explanation for everything in the world. Does the black hole information increase with the inclusion of the chair? Let’s see. A black hole has mass, spin, and possibly electric charge, weak charge, or color charge. That’s all! We cannot determine the information content of the black hole from these quantities only. That is a problem. The most likely solution that would prevent quantum information loss is that the surrounding space just outside the event horizon of the black hole takes care of the information equation to make everything correct, emitting particles to compensate correctly.

The actual physics calculation of information change in the gravitational field of a black hole is much more complex and difficult. Among the necessary concerns is the fact that the black hole has performed a non-unitary transformation on the state of system when it devoured the chair. A non-unitary evolution is excluded in a quantum theory because it fails to preserve probability that is, after a non-unitary evolution, the sum of the probabilities of all possible outcomes of an experiment may be greater or less than 1. Quantum mechanics could not survive. Perhaps the QM of a black hole will eventually be done and quantum gravity will save us from this catastrophe!