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

    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.

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

    Cheers,

    Ch.

    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

      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.

      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

        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.

        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.

        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

          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.

          Dear professor Christian Corda:

          Thanks for your nice essay, well done, i enjoyed reading it very much

          I am not expert about black hole, i have two questions:

          1The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed,

          why not use relativistic dirac equation?

          2 BH evaporation must be information preserving.

          then information is preserved for other system? for what kind of system? for the whole universe? how to define it like energy to the symmetry of time

          Anyway, I believe BH evaporation is a very important issue, which deserve more future research

          Thanks for your nice essay, i rated it with high mark

          and from a different point view, my essay may interest you

          Bit: from Breaking symmetry of it

          http://fqxi.org/community/forum/topic/1906

          While symmetry is kind of redundancy which means loss of information, breaking of symmetry gives rise to information.

          Hope you enjoy it

          Regards,

          Xiong

          Dear Xiong,

          Thank you very much for your kind comments with interesting questions and for rating my Essay with high mark. Concerning your questions:

          1 Dirac equation describes relativistic fields which correspond to fermions, i.e. elementary particles with half-integer spin. Elementary relativistic particles with integer spin, i.e. bosons, instead obey to the Klein-Gordon equation. Black hole physics is extremely difficult, thus, at the present time, it is impossible to give a complete description of it by considering the full quantum and relativistic effects. Then, by invoking Bohr's correspondence principle, one argues that a semi-classical description should be adequate for large values of the principal quantum number even without considering such full quantum and relativistic effects. In my Essay I have shown that a semi-classical description for the system composed by Hawking radiation and quasi-normal modes can be achieved through a time dependent Schröedinger equation.

          2 The principle of the conservation of information, i.e. the claim that "in both classical and quantum world, information cannot appear or disappear" is in general considered a fundamental principle in the evolution of all physics systems in our Universe. The information loss paradox claimed that such a principle is questioned for black hole evaporation.

          Thanks again, I am going to read your Essay in next days.

          Cheers,

          Ch.

          Mr. Christian Corda hello,

          I read Your essay and it is very interesting but very heavy and full of equation. It will take a lot of time.

          I used a very low quantity of equation into My essay. Can I have Your opinion Mr. Corda ? Or at least some impressions ?

          http://fqxi.org/community/forum/topic/1903

          My Best Regards.

          Dear Giacomo,

          Thanks for finding my Essay very interesting and also for taking your time to analyse details of equations. I will surely read, comment and rate your Essay in next days.

          Cheers,

          Ch.

          Greeting Christian,

          I wanted to let you know that I am happy to see your entry, and that it is doing well in the contest, as I intend to read it this weekend. It appears you have attempted to grapple with a foundational information Physics question, rather than deal with the "It from Bit" paradigm head-on, but that appears to be germane here. Should you have time, my humble effort bears inspection, and I invite your comments.

          All the Best,

          Jonathan

            Dear Dr. Corda -

            My view is that we need to be able to think in physical (less-abstract) terms about these issues: Our assumptions need to be revisited before we can venture to ask whether or not information is lost when energy-mass enters a BH. This is not to take away anything from your achievement - but no doubt many will say that the debate continues, and so we should check if, under the assumptions that have prevailed for the last several generations, we can possibly achieve a concrete answer?

            Energy conservation enters into our ideas about BH's, for instance. In my essay, I describe a paradigm consisting of energy vortices that are correlated in a larger (omni-dimensional) energy field. The law of conservation is then amended into a perpetual energy exchange between the field and the Cosmos. If you agree with the logic, then you will see that BH's do not need to shrink when radiation is emitted - since they must be energy portals between the Cosmos and the greater energy field.

            Stated in such an abbreviated fashion the paradigm acquires a science fiction flavor, I know, but the argument is entirely logical, and clearly shows how the Correlation of distinct energy vortices must be the unifying element of the cosmos.

            It then becomes explicable (and no doubt the math needs to be evolved) that Information going into a black hole is scrambled, and that radiation re-emerging from it is also scrambled - but then orders itself as it is distributed between the principal vortices that form the Cosmos.

            I believe you will be interested by the Vortex System I describe - and I look forward to your feedback. I have rated your essay, of course, and I wish you the best of luck in the contest -

            John

              Hi Jonathan,

              Nice to meet you here in the Contest again.

              Thanks for your kind comments. Although the statement "It from bit or bit from it" is the title of the Contest, the object is more general as it concerns the general role of information in physics. On the other hand, the black hole information paradox was a fundamental issue for the popolarization of the connection between physics and information within the Scientific Community.

              I will be pleasured to read, comment and rate your Essay in next days.

              Thanks again and good luck in the Contest.

              Cheers,

              Ch.