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.

      Dear Professor Corda,

      I have read your essay but unfortunately I am not properly qualified to make a judgment on it, sorry.

      I was reading through your blog and I was pleased to see that you are kind enough to reply to everyone and also curious enough to read everyone's essays.

      It is my first time in this contest and I am completely a non-specialist. I have written an essay but so far I haven't received a proper feedback from a professor of theoretical physics.

      I would be delighted if you would accept to take a look at it (I have also written a complete theory here, but I don't want to abuse your kindness).

      Best regards and good luck with the contest.

      Patrick

        Dear John,

        Thanks for your kind comments. Actually, I do not see contradiction between theoretical physics and abstractions. Abstractions and conjectures arises from intuition which is the basis for constructing theoretical physics. Hence, I totally agree not only with the statement by Coleman on the "ever-increasing levels of abstraction", but also with the famous aphorism by Einstein that "Information is more important than knowledge".

        I am going to read, comment and rate your Essay in next days.

        Cheers,

        Ch.

        Dear Prof. Corda

        I read with great interest your essay (the parts that I could understand, you loose me in math). The issue of information and BH is essential in science and I try to follow all the evolvements in this area.

        The latest information I got was from New Scientist of 22 june 2013 (www.newscientist.com/article/dn23611-quantum-gravity-takes -singularity-out)

        where Juan Maldacena and leonard Susskind come up with a new kind of wormhole, they pose that there is no singularity in the "center" of a BH, this perception is endorsed by Abhay Ashtekar who couples this view with LQG where space-time after the Planck Length 10^-35m is rendered to "chunks". The center of a BH should so be the threshold to another "universe" and information coming in would never be lost because it just "goes" to that other dimension.

        I am curious what is your opinion about this theory .

        This theory is touching my own perception as is written in my essay "THE QUEST FOR THE PRIMAL SEQUENCE". I should be very obliged if you could eventually read, comment and/or rate my view.

        respectfully

        Wilhelmus

          Dear Patrick,

          Thanks for your kind comments. Yes, I think that the spirit of this Essay Contest is to stimulate discussions, as much as possible, among various authors on the various issues that can emerge from various Essays. Thus, in my opinion is important to reply to everyone and to read everyone's essays. I will be happy to read, comment and rate your Essay in next days. I will also take a look to your The 3D Universe Theory.

          Thanks again an good luck in the Contest!

          Cheers,

          Ch.

          Dear Wilhelmus,

          Thanks for your kind comments. Actually, I have not yet read the paper by Maldacena and Susskind. By reading the abstract, I think that their approach to solve the BH information paradox concerns the framework of the "AMPS" firewall, which is a hypothesis of quantum gravity. In general, the approach by Maldacena and Susskind on quantum gravity is the one of String Theory while the approach by Ashtekar is the one of LQG, as you correctly emphasize. I am not an expert neither of String Theory, nor of LQG. In my Essay the approach is different and completely semi-classic. In any case, I agree with them that there should be no singularity in the "center" of a BH. I worked on this issue again at the classical level in my paper C. Corda and H. J. Mosquera Cuesta, Removing black hole singularities with nonlinear electrodynamics, Mod. Phys. Lett. A 25, 2423-2429 (2010). I will surely read, comment and rate your Essay in next days.

          Thanks again and good luck in the Contest!

          Cheers,

          Ch.

          Dear Christian,

          I read and reread your essay with great interest. Although I did not comprehend all of the mathematics and am unfamiliar with some of the references (I am an attorney, but deeply interested in the subject of information, physics, and reality), I think I understood the basics of your essay and was impressed with your depth of knowledge and direction of your thinking.

          I have a question that I hesitate to ask (out of concern that my ignorance is such that the question may appear nonsensical to you), but I will ask it anyway. In your technical endnotes, you stated, "In other words, QNMs frequencies are the eigenvalues of the system. The Hawking quanta are then interpreted as the 'jumps' among the levels." My question is this: are the 'jumps' among the levels perhaps somewhat analogous - in principle - to the jumps in levels or 'shells' of atomic orbitals? Again, I apologize if my question makes no sense, but I wondered, after reading your essay, if such might be the case.

          Thank you for your contributions to the subject. I'm going to attempt to learn more about some of the things you mentioned.

          Best,

          Ralph

            Ch,

            There's a side that I am not aware of being argued with the info-being-lost paradox where because info goes beyond a boundary, it is just completely gone when the black hole evaporates and gets small like a puddle. Mainly, I see a case for information, which has a energy or heat equivalent, going into a black hole being analyzed by the same method that information leaving a universe would. You know both apparently vanish, so I would think that makes them equivalent for analysis and thinking about then. Which brings up another question I'm not sure about. Do light rays, which have info, go indefinitely outwards from the view of quantum mechanics? I ask because in General Relativity, since gravity is king at long distances, everything loops back on itself, if you will. So getting down the behavior of data as it goes into a black hole incident is important before even getting to the rest of the issue presented in this pap.

            Also, boundaries seem unnatural to exist in reality when the goal of science is to make the most complete picture. The same thing goes for points. Here is another question. What in science is a singularity. I could guess a point where no existence, no mass or distance or grounds for rates, took place, or even a minute region where everything is localized on a very small scale. But beyond guesses, I like most people, am clueless. And since the speed of light is not constant in G.R., could a black hole not yet have adequate conceptual understanding? It seems like since info can go not faster than light in curved spacetime, and since there is a point where the grid just curves too much, that a new description is in order geometrically. Something has to give in this uncharted territory eventually.

            Does your paper go on the idea that info hangs out on the outside of the B.H. by that weird 1/4 area to volume rule? I would see evaluating extreme or end behavior near the "edge" of the universe as only appropriate if the case is that info somehow gets past the point of no return around a black hole.

            A lot of the information deals with heat theory which has developed quantum mechanically from the starters of it like Boltzmann. Is there attempted generalizations of relativity applied to thermodynamics which might shed new light on the issue here. For all the math here, it seems a little one-sided, the other side maybe not even existing! I read more abstract math here than pictorial verbiage, which vaguely results because some maths just don't condense to easy imaging. One last point is that the reason black holes evaporate didn't poke out at me. In fact, I'm still not entirely sure if they are presented here as giving off info because non is lost and thus shrinking, or rather if info just chills and shifts about like little grains or units and is exchanged, but the real radiation is due to some thermal process that does not fit thermal ideas so is called "non-thermal" behavior. Please clarify my mix up.

            The mass equations are quite interesting.

            Best,

            Amos.

              Hi Christian,

              Without stretching too much I think our viewpoints are the same. Here goes:

              1. Start with: "Information tells physics how to work. Physics tells information how to flow"?

              2. Change physics to "it" and change information to "Bit" and you get:

              "Bit tells "it" how to work. "It" tells Bit how to flow"?

              3. Lastly change tells to determines and we get:

              "Bit determines "it" how to work. "It" determines Bit how to flow"?

              4. This is a little awkward so we make it smooth:

              "Bits determine how "it" acts. "It" determines how Bits respond.

              5. This is close enough for me to say we are saying the same thing. IT and BIT are two side of the same coin.

              What do you say will "Russell and Whitehead" accept this logic? Siri says the logic is OK!

              Don L.

                Dear Dr. Corda,

                (Google translation)

                You are deservedly at the top of this competition for a number of reasons. Solution "black hole (BH) information paradox" is a very important issue. Aside from that I think that the production of paradoxes, then to be solved wrong way. Just so because my completely different approach to your, I was grateful to get a comment on my article from you. Negative comment is also welcome as positive (ignore the two errors in typing in formulas). Thus, the formulas (2) is:

                gamma = 2 ^ {[cy / 2 + p / 2 +3 * log (2pi, 2) / 2] / [1 +137.035999074 ^ 2 * log (I, 2)]} = 1.00137841920431

                Rating is irrelevant.

                Regards,

                Branko

                  Dear Ralph,

                  Thanks for your kind words and also for appreciating my Essay. Do not worry, your question is indeed very reasonable and it permits me to give more explanations. The analogy that you cited is very profound although we must be very careful in discussing it. I try to explain this issue. It is a general conviction that black holes should result in highly excited states representing both the "hydrogen atom" and the "quasi-thermal emission" in quantum gravity. At the present time, we do not yet have a full theory of quantum gravity, thus, we have to be content with the semi-classical approximation. In fact, as for large n Bohr's correspondence principle should hold, such a semi-classical description should be adequate. In this framework, my black hole model is somewhat similar to the semi-classical Bohr's model of the structure of a hydrogen atom. In fact, during a quantum jump a discrete amount of energy is radiated and for large values of the principal quantum number n the analysis becomes independent from the other quantum numbers. In a certain sense, QNMs represent the "electron" which jumps from a level to another one and the absolute value of the QNMs frequencies represent the energy "shells". In Bohr's model, electrons can only gain and lose energy by jumping from one allowed energy shell to another, absorbing or emitting radiation with an energy difference of the levels according to the Planck relation E=hf, where h is the Planck constant and f the transition frequency. In my black hole model, QNMs can only gain and lose energy by jumping from one allowed energy shell to another, absorbing or emitting radiation (emitted radiation is given by Hawking quanta) with an energy difference of the levels according to eq. (15) in my Essay. On the other hand, Bohr model is an approximated model of the hydrogen atom with respect to the valence shell atom model of full quantum mechanics. In the same way, my model should be an approximated model of the emitting black hole with respect to the definitive, but at the present time unknown, model of full quantum gravity theory. In any case, this analogy looks intriguing. Let me know if my replies are OK or if you need more details.

                  Thanks again for your important question.

                  Cheers,

                  Ch.

                  Dear Prof. Corda,

                  Its my privilege to comment on your essay.

                  Regarding your arguments on BH information restorations, I like to add some thing here which may support yours, and equally I invite you in my essay http://fqxi.org/community/forum/topic/1855)to have some comments.

                  It is well known that basic problem for not receiving any information from the opposite end of an event horizon of BH is due to its superluminal range of escape velocity. Special Relativity restricts the superluminal speeds of particles to emerge out of that event horizon. If in any way we can get the superluminal speeds to overtake that range of high escape velocities around the BH, the information sharing issues with the BH by penetrating the event horizon to the outside world could be instantly resolved.

                  That is why I sincerely like to invite you in my essay, particularly I request in Eqs.(28)-(31)and paragraph no.5.2 there, where we can get such superluminal speeds of particles in the same frames of special relativity (which is now we have respect to c).

                  With my regards

                  Dipak

                    Dear Amos,

                    Thanks for your kind comments.

                    Actually, we do not know if the final result of the black hole evaporation is a puddle (having dimensions of order of the Planck scale) or if, instead, the black hole completely evaporates. In fact, avoiding evaporation is usually claimed when one invokes the Generalized Uncertainly Principle which should stop evaporation at the Planck scale. In any case, in quantum physics the complete information in a system is encoded in the wave function representing the quantum state of the system. i.e. in eq. (36) of my Essay. The wave function (36) represents a pure final state rather than a mixed final state. Thus, information is surely preserved because the evaporation process rigorously obeys the laws of quantum mechanics.

                    In general, it is possible to apply method of analysis concerning black holes to the whole universe, but one has to be very careful because, although they have similar features, a black hole is different from the whole universe. In General Relativity the analogy depends on the issue that in both universe and black holes the ratio between mass and radius is of order 1 in natural units. I did not worked on information leaving a universe, thus I do not know if the analogy works also in this case.

                    I do not think that in General Relativity, although gravity is king at long distances, everything loops back on itself, if you will. In fact, for example, particles can be attracted by others gravitational fields. We see the light of the sun and of distant stars on Earth. Thus, those photons do not loop back on them-self. Instead, they arrive to us. Then, one does not need quantum mechanics in order to have light rays going indefinitely outwards.

                    The definition of singularity in science is not simple. From an intuitive point of view, a singularity is visualized as a point at which a particular mathematical object is not defined. For example, the function 1/z is not defined in z=0. A rigorous definition of singularity in the gravitational collapse can be obtained following B. G. Schmidt, Gen. Rel. Grav. 1, 269-280 (1971). For example, in standard Schwarzschild coordinates one tells that in the internal geometry all time-like radial geodesics of the collapsing star terminate after a lapse of finite proper time in the termination point r = 0 and it is impossible to extend the internal space-time manifold beyond that termination point. I suggest you to search further details in the book C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Feeman and Company (1973).

                    Although in General Relativity the speed of light can be different for different coordinates, an event horizon is defined as "the point of no return", i.e. photons emitted from beyond the horizon can never reach an outside observer.

                    What do you mean with "weird 1/4 area to volume rule"? The famous formula of Bekenstein-Hawking entropy claims that the entropy of a black hole is 1/4 of its area in Planck units, but this is not connected with the information paradox.

                    I regret for your statements claiming that "For all the math here, it seems a little one-sided, the other side maybe not even existing!" and that "I read more abstract math here than pictorial verbiage, which vaguely results because some maths just don't condense to easy imaging". In my Essay I used mathematics and physics on the same level of university studies on quantum mechanics. I read that you are currently an undergraduate physics student. Maybe, you have not yet completed your studies on quantum mechanics. On the other hand, rules of FQXi request verbatim that the Essay must be "Accessible to a diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature." I think that readers of Scientific American and review articles in Science or Nature should know mathematics and physics on the same level of university studies on quantum mechanics. Of course, this is not a criticism for you! In fact, I invite you to read again my Essay when you will end your graduate studies. I am sure that you will completely understand it.

                    Finally, black holes evaporate because of quantum effects near the event horizon. Hawking provided a theoretical argument for this effect improving ideas by Parker, Zeldovich and Starobinski. In Hawking's original computation black hole radiation was a perfect black body radiation (purely thermal) which has a specific spectrum and intensity that depends only on the temperature of the body. By using arguments of energy conservation, Parikh and Wilczek have instead shown that the black hole emission is not exactly the one of a perfect black body. Hawking claimed that because of the strict thermality, information should be loss in black hole evaporation. As the radiation is, instead, not exactly the one of a perfect black body, Hawking's claim breaks down.

                    I hope to have partially clarified your mix up.

                    Cheers,

                    Ch.

                    Thanks Don.

                    As I told you in your page Essay, I agree with Siri that the logic is OK. It should be OK for "Russell and Whitehead" too. Definitively, our viewpoints are the same!

                    Cheers,

                    Ch.