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

Christian Corda

Dear Jim,

Thanks for your kind comments with interesting questions.

Actually, the unitary evolution discussed in my Essay does not imply that the BH does not evaporate, but only that the evaporation process is information preserving. Avoiding evaporation is usually claimed when one invokes the Generalized Uncertainly Principle which should stop evaporation at the Planck scale.

I did not yet work on potential consequences of the paradox solution on the Big Bang, but they could be intriguing. Mathur recently started to work on this issue. I suggest you to read his paper Awarded in the 2012 Gravity Research Foundation Competition that can be easily download in the Foundation web-site.

My analysis works for both solar and super massive BH. The difference is that for the latter the evaporation time is much longer.

Let me know if my replies are OK or if you need more details.

Thanks again.

Cheers,

Ch.

Don Limuti

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

Christian Corda

Hi Don,

Thanks for your kind congrats. Concerning your question, we can say that BHs evaporate via quantum jumps generating a quasi-thermal radiation.

I will surely read your Essay in next days.

Cheers,

Ch.

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.

Christian Corda

Thanks Don. OK, I am going read something on your Digital Wave Theory.

Cheers,

Ch.

Stephen Anastasi

Hello Dr Corda

I found your essay very challenging due to the dense equation set with (necessarily due to page constraints) insufficient description of what prompted each equation. What was unfortunately not clear to me was the reasoning behind each step made. My own work had to recreate mathematics from the ground up, and placed natural constraints on physics that would question the possibility of a singularity (not shown in my essay, but follows immediately from it) and for that matter, the Schrodinger equation as a differential (rather it ought to align with CDT). As such, one wonders at the effect the absence of a singularity within a black hole would have on information that would otherwise be lost within a finite time.

I would love to know your line of thinking that gave you the approach to this problem, and guided you through the application of the equations used.

PS. Is there a typo in equation (20) or (22) exp - (...) rather than exp(-...)?

PPS. I would be keen to receive critical feedback on my essay: http://fqxi.org/community/forum/topic/1904

Christian Corda

Hi Ram,

Thanks for your kind comments and for the high rate you gave to my Essay.

You know that I have a high opinion on your ideas concerning the deletion of the stress-energy tensor in the right hand side of Einstein Field Equation. It could be interesting to develop your approach in the framework of the gravitational collapse in order to see if Hawking's prevision of black hole radiation is again confirmed.

Thanks again.

Cheers,

Ch.

Christian Corda

Dear Michael,

Thanks for your particular approach to the BHPI. The metaphor of an encyclopaedia works in my case too. Here, the difference with Hawking's approach is that the emitted radiation is not strictly thermal. Now, the encyclopaedia is not more burned. Instead, one can think as its internal pages have been cutted and cutted and cutted. .. an enormous number of times. Inother words, the encyclopaedia becomes an enormous puzzle. My mathematical solution permits to reconstruct the puzzle. Thus, it also a final solution of your pseudo-problem.

I am going to read your Essay in next days.

Cheers,

Ch.

Vladimir Rogozhin

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

Christian Corda

Dear Vladimir,

Thank you very much for your kind congrats. I am very honoured by them. I am going to read your Essay in next days. I wish you good luck in the Contest, every success and respect to you too.

Cheers,

Ch.

Christian Corda

Dear Stephen,

Thanks for your comments. Yes, page constraints limits description of what prompted each equation. On the other hand, after a rigorous definition of the quantum problem, I used a standard method of calculation in quantum mechanics following the textbook by Sakurai. Concerning the line of thinking that gave me the approach to this problem, and guided me through the application of the equations used, actually, I started to work on the problem of black hole quantum levels from two years. I had the intuition to replace the Hawking temperature with the effective temperature in order to take into account the non-strictly thermal character of the radiation spectrum in my paper JHEP 1108, 101 (2011). After this, I refined my results in my Essay Int. Journ. Mod. Phys. D 21, 1242023 (2012), which received an honorable mention in the 2012 Essay Competition of the Gravity Research Foundation, by discussing in detail the correspondence between Hawking radiation and BH QNMs. This winter, I had another intuition, i.e. that energies of Hawking quanta should be proportional to the effective temperature instead of to the Hawking temperature in case of deviation from the strict thermality of the radiation spectrum. At that point, by interpreting the absolute values of the QNMs in terms of total emitted energies, and, in turn, in terms of quantum levels, I developed my Essay by using standard techniques of quantum mechanics.

Cheers,

Ch.

P.S.

I checked eq. (22), it should be the same writing exp - (...) rather than exp(-...), or not?

P.P.S.

I am going to read your Essay in next days.

Jayakar Joseph

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 Corda

Dear Jayakar,

Thanks for your comments. Yes, you are absolutely right. The issue that in particle scenario the observational information is not observational in continuum is exactly the core of the information paradox. I am surely going to read your Essay in next days. Thanks again.

Cheers,

Ch.

Jayakar Joseph

Thank you

James Hoover

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

Thomas Ray

Dear Christian,

It was a happy moment for me, among others, when Hawking reversed himself on the issue of black hole information loss.

What I could never make sense of, is why the transition from initial to final state in black hole thermodynamics (ground to excited state) should be equivalent to a quantum jump -- where we lose information of the time evolution -- because if Hawking radiation exists at all, it should be a classical map t --> T, for the reason that the extreme condition of the black hole horizon gives us a perfect t = 0 potential that is lacking when we choose t arbitrarily.

So I am all in favor of 't Hooft's efforts to unite classical determinism with quantum mechanics, and I so appreciate your careful argument from pure potential to pure kinetic state. I'm always impressed with your essays and as usual wish you the best in the compeitition! You can count on a high score from me.

Tom

Christian Corda

Hi Tom,

Nice to re-meet you here. Thanks for your kind congrats and for giving an high score to my Essay. I am very honoured by this. I am surely going to read your Essay in next days.

All the best in the Contest to you too!

Cheers,

Ch.

Héctor Gianni

Dear professor Christian Corda:

Thank you for reading my essay as you promise and rating my essay so high. I am glad you enjoy reading it. Well I am convince you would enjoy reading Dr. Elliot McGucken self conscious essay, "Where is the Wisdom we have lost in Information? Returning Wheeler's Honor and Philo-Sophy--the Love of Wisdom--to Physics". as you know he was a good John Wheeler student at Princeton, maybe after reading it, you would like to read again mine. Personally and probably without the necessary authority, I agree to many things he said about modern physics, I agree with many of his concepts about , to me , the so called "time", also that is not the fourth dimension, but I disagree with the Moving Dimension Theory, being the so called "time" the moving dimension. The so called "time" is just a remnant word, don't have physical existence, is not a physical entity, is not an expanding dimension, the fourth dimension is just as Einstein said an imaginary dimension. The so called "time" Is not a moving dimension, but "motion itself " I think like him that this new position can make a big difference, and knowing that the so called "time" in fact is "motion" can change many things. Probably the contest itself is the less important thing we are doing here.

With my very best wishes

Héctor

Christian Corda

Hi Héctor,

Thanks for signalling McGucken's Essay. I am going to read it in next days. Yes, I remember that he was a "Wheeler boy" and now he has various interests on arts science and technology. I appreciate your statement that "Probably the contest itself is the less important thing we are doing here". On the other hand, thing we are doing here ennoble the Contest in the same way!

Cheers,

Ch.

Christian Corda

My pleasure dear Jim!

Cheers,

Ch.

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