Time dependent Schrödinger equation for black hole evaporation: no information loss by Christian Corda

Dear Christian,

Time Lord Dr. Louis von Essen should be renowned since he developed in 1955 the first caesium clock. He criticized in particular that Einstein did not bother to quote Michelson, Lorentz, and Poincaré and that he speculated without having performed own experiments. Maybe, von Essen underestimated the importance of clean reasoning. Our library does not have v. Essen's booklet "The Special Theory of Relativity: A Critical Analysis", Oxford Univ. Press and other dissident literature. This was rather helpful because I had to deal with the matter myself on the basis of books e.g. by Bohm and by Feynman. In the end I arrived at an insight beyond what v. Essen wrote, see my current endnotes.

By the way, because Einstein's theory of relativity got famous, some people claimed having found out that already Woldemar Voigt and Ferdinand Lindemann invented it.

You wrote: "It is not correct that Einstein in the end confessed being seriously worried by the now. He ALWAYS was uncertain on his results during his life."

I referred to written utterances of the late Einstein, and I compare them with his anything than thoughtful attitude in his discussion with Ritz, belonging photos of the young Einstein's rather self-confident or even cheeky face, culminating in a photo of Einstein as a professor when he sticked out his tongue at us. Don't get me wrong. I don't see a weak point in Einstein's personality but in theoretical positions he adopted.

The idea of an a priori (God-) given time goes back to Newton, Descartes, the old testament of bible, and perhaps even elder beliefs.

I can only guess that Einstein's misleading synchronization was stolen from Poincaré who used it in a manner that I consider still logically correct under the wrong assumption of a light-carrying aether.

What about the cowards, it often happens that there are many mutually excluding theories and at best one out of them can be correct. That's why I consider any kind of hasty prejudice unfair. As a rule, I feel not in position to compellingly reveal mistakes already from the abstract. Of course, there are knowing-alls too. If I made mistakes then presumably not those you have made in the past. I look forward ...

Cheers,

Eckard

Dear Professor Corda,

Your essay is an awesome contribution and cornerstone in theoretical physics - in a very well formulated and lucid manner you spell out how black hole evaporation still preserves information. I'm going to reread it to fully incorporate all the technical analysis, perhaps with some friends in a discussion group. I appreciate your originality in your approach throughout, while incorporating the concepts of other experts historically as well as currently.

My essay briefly touches on some black hole concepts such as the entropy to area relationship, but does so as part of an analysis of the second law of thermodynamics. I suggested a symbiotic relationship between information and physical reality too, but you stated it much more strongly especially in your comments, and I really like your parallelism of: '"Matter tells space how to curve. Space tells matter how to move". In the same way, "bits" and "its" are complementary, "Information tells physics how to work. Physics tells information how to flow"' And again, showing this technically for example through the unitary evolution like you did, without having to handwave, is truly the mark of an expert physicist and professional.

One of the experiments my essay reviews utilizes entanglement to show increasing the physical effect that can be extracted through information, i.e. in a sense pushing up the bound on how much we can tell physics to work based on information. Your paper and comments inspire me about approaching the flip side: experiments that can be formulated regarding entanglement and black hole complementarity, to obtain an increased bound on extracting information practically after BH evaporation, i.e. pushing up the bound on how much information can be told to flow based on physics.

Thanks again for contributing this piece, I want to check out your other papers too. I hope you have a chance to review and rate my essay as well - I do really appreciate feedback from people such as yourself who are directly involved in fundamental physics.

Sincerely,

Steve Sax

Professor Corda,

Your essay approaches the density of a BH and doesn't evaporate.

"The physical state and the correspondent wave-function are written in terms of an unitary evolution matrix instead of a density matrix."

So the "heat death" prediction by some physicists after billions of years is off? What does your pure quantum state concept do with Big Bang prediction literature, considering the relationship oft made between BHs and the BB? And is there a difference between super-massive black holes and solar black holes?

Jim

Dear Christian,

Your interesting essay provides a thorough and clear description of the developments on the paradox. I always had doubts about Hawking's results, but my arguments are altogether different: The

quantization of the right hand side of Einstein's equations, in a given spacetime, has yielded the interesting effects of the Hawking radiation [SW Hawking, Comm. Math. Phys. 43, 199, 1975]. (However, even here the role of back reaction has not been fully understood.) Recently it has been shown that the right hand side of Einstein's equations, i.e., the energy-stress tensor T^ik, has serious problems [arXiv:1204.1553]. Hence, the results obtained by using it also become doubtful.

Your essay makes important contribution to this subject. I rated your essay high and wish you best of luck in the contest.

___Ram

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 ")

Hi Christian,

Great essay and completely in line with the intent of the contest.

Could I over simplify your work by saying BHs evaporate via quantum jumps with no blackbody

radiation involved?

Don Limuti

Hi Christian,

There is something about your work that reminds me of a though I had about black body radiation and emission spectra of gases. Your work is very different, but there is something about it that may apply to other areas of physics besides BHs. It is just a hunch but take a look at:

http://www.digitalwavetheory.com/DWT/31_Thermodynamics.html

And please forgive my unsophisticated techniques, but quasi thermal kinda fits.

Don L.

Hello Christian,

The main task of contests FQXi - new fundamental ideas. You are fine, revolutionary ideas on the fundamental issues of the Universe, primarily in «one of the most famous and intriguing scientific controversies in the whole history of Science is the so called BH information paradox». You had a brilliant analysis of the problem in the spirit of Descartes: "has come under question." You made sweeping conclusions. They provide an opportunity to take a fresh look at the nature of the information and its essence, a deeper understanding of the concepts of 'matter' and 'energy' and their limits and states.

I wish you every success and respect,

Vladimir

Much pleased to have discussions with you, dear Prof. Corda,

Hawking radiation itself is indicative of the continuum nature of information, in that we may differentiate information paradox in general from specified BH information paradox. This implies that in particle scenario the observational information is not observational in continuum, which has been defined as information paradox in general. Thus we recommend an alternative cosmological model in a scenario of eigen-rotational segments of string-matter continuum is expressional to resolve these information paradoxes, in that the relationship of Planck constant with energy and frequency is not been altered though the Reduced Planck constant is not applicable. Thus time dependent Schrödinger equation is not descriptive in this paradigm, yet unitary matrix is much germane in describing the observational information continuum, in that discrete incident time from linear flow of time may be quantised for near-reality observations.

With best wishes

Jayakar

Christian,

Your response was quite adequate. Being somewhat of a neophyte in physics and cosmology, I marvel that I can begin to understand some of the issues. Thank you for your research reference.

Jim