Some definitions.
Dear professor Corda ,
because FQXi contest is not pure scientific forum, I'd like to introduce some common definitions on BHIP ( may be, for readers - poets and philosophers if You agree )
Following Hawking, the black hole (BH) information paradox started in 1967 when Werner Israel showed that the Schwarzschild metric was the only static vacuum black hole solution. Later generalizations showed that all information ( i.e. hypothetical quantities about the collapsing body , which we can define as "pseudo-bits of BH information ") ) was lost from the outside region apart from three conserved quantities: the mass, the angular momentum, and the electric charge. This loss of pseudo-bits of information wasn't a problem in the classical theory ( A classical black hole would exist for ever and the information could be thought of as preserved inside it, but just not very accessible ). However, the situation changed when Hawking discovered that quantum effects would cause a black hole to radiate at a steady rate Such sort of the radiation from the black hole would be completely thermal and would carry no pseudo-bits of information. Hence, as is known,
BHI paradox : What would happen to all that pseudo-bits of information locked inside a black hole that evaporated away and disappeared completely? It seemed the only way the information could come out would be if the radiation was not exactly thermal but had subtle correlations. No one has found a mechanism to produce correlations but most physicists believe one must exist.
Hawking predicted that if information were lost in black holes, pure quantum states would decay into mixed states and quantum gravity wouldn't be unitary.(1975)
In other words, any information that falls in a black hole ( in anti de Sitter space ) must come out again. But it still wasn't clear how information could get out of a black hole. Later Hawking (and Hartle ) showed that the radiation could be thought of as tunnelling out from inside the black hole." It was therefore not unreasonable to suppose that it could carry information out of the black hole.
As the next step, as is known, Hawking invented new
Law of information conservation - "The information remains firmly in our universe. Thus, If you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the information about what you were like but in a state where it can not be easily recognized. It is like burning an encyclopaedia. Information is not lost, if one keeps the smoke and the ashes. But it is difficult to read. In practice, it would be too difficult to re-build a macroscopic object like an encyclopaedia that fell inside a black hole from information in the radiation, but the information preserving result is important for microscopic processes involving virtual black holes. If these had not been unitary, there would have been observable effects, like the decay of baryons" ( 2005 )
Let us take here initial definition of Shannon's foundational principle : "One device with two stable positions can store one bit of information, correspondingly, n such devices can store n bits, since the total number of possible states is 2ⁿ and log 2 2ⁿ = n " (1948). Thus, using Shannon-like association between bit and "one device with two stable positions" ( transistor), we can make global generalizations on entity Information in theoretical physics and philosophy of physics. For example,
we always can translate Hawking law of information conservation in the following form :
Universe could be considered as a set of transistors with two at least stable positions which can store n bit of information. Because it is based on analogy, we can say that the Universe as a set of transistors can store n pseudo-bit of information. Pseudo-bit information remains firmly in our universe. Thus, If you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the pseudo-bits of information about what you were like but in a state where it can not be easily recognized. It is like burning an encyclopaedia ( another poetical metaphor ) Information is not lost, if one keeps the smoke and the ashes. But it is difficult to read because there is no such thing as physical measurement of pseudo-bits of BH thermal radiation ( thermal information ). Hence, thus, BHIP could be understood also as pseudo-problem, indeed.
As a consequence, your mathematical solution of BHIP based on non-Weyl solution of Schrodinger equation cannot provide final resolution of this kind of pseudo-problem.
Respectfully,
Michael (" Bit from It. Mathematical Clarification ")
