Dear Doug,

Not only I completely agree with you concerning the issue of thermality/non-thermality, but I have recently finalized the W&P approach in my paper Ann. Phys. 337, 49 (2013) by showing that the W&P probability of emission is indeed associated to two non-strictly thermal distributions for both bosons and fermions. I would like to bring to your attention that a lot of researchers that I previously cited are string theorists. It is enlightening what Motl wrote on this issue in ref. 21 of my Essay: "We find it hardly acceptable to reject Hawking's semi-classical calculations (on highly thermal radiation), in part because they have been confirmed by many developments in String Theory". Thus, it looks that string people endorse the strict thermality of the spectrum.

I also agree on the issue that it is puzzling that the remarkable work by Zhang, Cai, Zhan and You received little attention. This has been partially compensated by their First Award at the 2013 Gravity Research Foundation Essay Competition. Mathur was a strong opponent of their results as he thinks that the only solution to the information loss paradox is his "fuzzball" framework which, again, arises from string theory. Instead, I think that, as Hawking's original introduction of the information puzzle arose from a pure semi-classical approach, it is a good thing if it can be solved by remaining within such a semi-classical approach. This is the reason because I appreciate both your Essay with Vagenas and Zhu and the work by hang, Cai, Zhan and You.

Cheers,

Ch.

  • [deleted]

Hello Christian,

I enjoyed your essay greatly, and I think you are insightful to point out a subtle duality between the inhaling and exhaling modes of the Black Hole, which are modulated by variations upon its surface. I note that the condition of n being much greater than 1 is probably easily met any time the BH is feeding, because there would of course be higher harmonics to the Quasinormal Mode vibrations as soon as the energy is high. But I am assuming that lower values of n correspond to a resting BH in a space devoid of matter to feed upon, and are indistinguishable from thermal or Hawking radiation.

I guess it only matters to consider what goes in when feeding takes place, in terms of information loss, but it seems there would be a ramping up of higher n modes. Regardless; I think that on the whole your analysis is sound, and I respectfully disagree with Professor Rovelli about it being trivial to write a Schrödinger equation and declare the evolution is therefore unitary, as I think what you have done is supplied missing terms, without which a true unitary equation could not be written. You are assuming that any emanation from the BH must be a quantized vibration so that QNMs provide a way to encode things rather than having them be lost, and that the QNM variations then modulate what comes out.

You have done something clever, by taking Coleman's advice seriously, and treating the BH QNM vibrations as a kind of harmonic oscillator, but then you took things a step further - which is nice. It appears that what you did was recast the oscillator problem in Hamiltonian form, and in effect Hamiltonized the variables to put the QNM term in Schrödinger equation format. I first read about this trick in a paper by Steven Kauffmann, but you use it here to great effect - in order to supply the missing term of the full equation. It would be nice to see a graph of how QNM radiation might be distinguishable from pure Hawking radiation, as in the paper by Barrau et al Probing Loop Quantum Gravity with Evaporating Black Holes.

An excellent paper overall.

Regards,

Jonathan

    T'was I, who commented above.

    I thought I was still logged in, but it appears not. However, the words in the comment above are mine.

    All the Best,

    Jonathan

    Christian,

    I do not fully understand the connection between the broad universal theme of this contest and this precise, technical essay about a phenomenon limited to black holes. It would be helpful to link the nature of information in a black hole to information in the rest of the universe.

    The evaporation of a black hole due to Hawking radiation creates particles and the wavefunctions of associated with those particles. I did not see how the wavefunctions going into the black hole are the same as the ones going out. I did not see anything about wavefunctions going in. As an example, an electron beam travels through a double slit then into a black hole. Would we see a double slit pattern radiating from the black hole when it evaporates?

    Thank you for this essay.

    Jeff

      Dear Jonathan,

      Thank you very much for your kind words and compliments and for giving a well written "referee report" on my paper. In particular, I am grateful to you to be returned on Professor Rovelli's comment. At the end of such a comment, Professor Rovelli asks if he is missing something. The answer to this question is yes, he is missing what you correctly emphasize, i.e. I supply missing terms without which a true unitary equation could not be written. Such missing terms arise from my previous research work, published in various important international peer review journals, which are correctly cited in my Essay. I strongly suspect that Professor Rovelli have ONLY read the abstract of my work, and this generated to him the misunderstanding that I derived the Schrödinger equation based on an abstract and constructed on air assumption of unitarity. Instead, I derived it by using such missing terms which arise from my previous research work. In other words, in my Essay I did NOT made an abstract assumption of unitarity, but I finalized my previous research work by constructing a Schrödinger equation for a well defined system that I discussed and analysed in my previous papers. I will further bring back on this issue in detail in next days, in order to remove all potential misunderstanding, but here I thank you again to have raised this point. Thanks also for signalling the paper by Barrau et al. which looks connected to my work. I will surely read it in next days.

      Cheers,

      Ch.

      Dear Jonathan,

      I wrongly replied to your comments by writing a new post below. Hence, I will copy and past here my reply:

      Dear Jonathan,

      Thank you very much for your kind words and compliments and for giving a well written "referee report" on my paper. In particular, I am grateful to you to be returned on Professor Rovelli's comment. At the end of such a comment, Professor Rovelli asks if he is missing something. The answer to this question is yes, he is missing what you correctly emphasize, i.e. I supply missing terms without which a true unitary equation could not be written. Such missing terms arise from my previous research work, published in various important international peer review journals, which are correctly cited in my Essay. I strongly suspect that Professor Rovelli have ONLY read the abstract of my work, and this generated to him the misunderstanding that I derived the Schrödinger equation based on an abstract and constructed on air assumption of unitarity. Instead, I derived it by using such missing terms which arise from my previous research work. In other words, in my Essay I did NOT made an abstract assumption of unitarity, but I finalized my previous research work by constructing a Schrödinger equation for a well defined system that I discussed and analysed in my previous papers. I will further bring back on this issue in detail in next days, in order to remove all potential misunderstanding, but here I thank you again to have raised this point. Thanks also for signalling the paper by Barrau et al. which looks connected to my work. I will surely read it in next days.

      Cheers,

      Ch.

      Dear Amazigh,

      Thanks for your kind message and for rating my Essay. I will surely read, comment and rate your Essay in next days.

      Cheers,

      Ch.

      Thank you Christian,

      I have no axe to grind with Carlo Rovelli, and I respect his work highly, but after a careful review I find no fatal flaws to your reasoning, and it appears you aptly address the caveats of your findings in comments - such as the conciliatory remark regarding Mitra's work and the possibility an event horizon would never be formed. One must make some standard assumptions to proceed with answers to questions like the information loss paradox, and carefully vary a few analytic parameters to reveal something others have not.

      It appears you have done this. But graphs contrasting the spectra of pure Hawking radiation with the emanations from QNMs, as in the paper cited, would be extremely helpful. As luck would have it; I met Aurelien Barrau at FFP11 in Paris, and the work cited (then still in preparation) came up in answer to a question. I'll comment further after a bit.

      Regards,

      Jonathan

      Who deleted several posts here and at 1793 and why? For instance, I criticized that Christian Corda first wrote that Wheeler dubbed the phrase it from bit in the 1950, after I questioned this, he admitted he did not know when, and nonetheless he reiterated his old text without providing a reference he referred to.

      More importantly, we disagreed about the notion unitarity, and I tried to further explain my also missing post belonging to R. Kastner's paper "The Broken Symmetry of Time" in the blog "What can't be sensed?". I argued that it might be more natural to consider time as an abstraction from measurable elapsed time and future time as a continuation of it than ad hoc assuming time as given a priori from minus infinity to plus infinity, sharing Einstein's worry about the now and bother to explain why elapsed time is a special case of abstract time. I see the border between past and future the only natural border. My position might be unwelcome. Is it a sign of strength if belonging posts are brutally deleted?

      Eckard Blumschein

      Dear Jeff,

      Thanks for your interesting comments/questions. Concerning the connection between the broad universal theme of this contest and this precise, technical essay about a phenomenon limited to black holes, this criticism has been previously raised by D'Ariano and Heinrich. I rewrite here my reply to them almost verbatim. Although "It From Bit or Bit From It" is the title of the Contest, one easily checks that topics like "How does nature (the universe and the things therein) "store" and "process" information?" and "How does understanding information help us understand physics, and vice-versa?" are fully taken into account in my Essay. On the other hand, it is historically well known and also stressed in the interesting Essay by Singleton, Vagenas, & Zhu, which looks to be complementary to my one, that (verbatim from the Essay by Singleton, Vagenas and Zhu) "much of the interest in the connection between information, i.e. "bits", and physical objects, i.e. "its", stems from the discovery that black holes have characteristics of thermodynamic systems having entropies and temperatures." In fact, if Hawking's original claim was correct, black holes should destroy bits of information. By showing the unitary evolution of black hole evaporation instead implies that bits of information are preserved. On the other hand, the worst consequence of destruction of bits of information by a physical process is that quantum mechanics breaks down. I have instead shown that quantum mechanics works in black hole evaporation and bits of information are in turn preserved in that process. I also think it is not a coincidence that the great scientist who coined the phrase "It from bit or Bit from It?" in the 1950s, i.e. John A. Wheeler, was the same scientist who popularized the term "black hole" in the 1960s. Also, attempts to solve the black hole information loss puzzle opened the road to various interesting physical ideas concerning information, like for example the Holographic Principle. Hence, by using your words, this precise, technical essay about a phenomenon limited to black holes is strongly connected with the broad universal theme of this contest. In order to have further details on this issue, I suggest you to read the pretty book by Leonard Susskind "The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics", Little, Brown and Company (2008). It is not simple to link the nature of information in a black hole to information in the rest of the universe. In any case, an important point is that, as it is supposed that there is a big number of black holes in the universe, the idea that black holes destroy information should lower the global information in the universe. A recent model of cosmology, proposed by Roger Penrose, i.e. The Conformal Cyclic Cosmology, looks to strongly depend on the condition that information should be indeed lost in black holes.

      I am going to answer your other questions later.

      Cheers,

      Ch.

      Hi Christian,

      "But we must be careful on which 'time' we are referring to. In fact, singularities can be time-like too."

      Exactly so. Which is the precise reason I pointed out that Baez is wrong to dismiss Mitra's "metric of a test particle" on the event horizon of a black hole. For if the trajectory of a massless particle traces a timelike curve of measure zero on that trapped surface, and a distant free observer receives back a frozen image -- the observer's time relative to the test particle is also measure zero. Thus the singularity {0,0} is a complex point between the observer's spacelike state and the timelike curve on the event horizon -- a pure quantum spacetime relation.

      As Hawking explained many years ago, imaginary time in complex space is just as real as the linear time we experience under our ordinary low energy conditions. At the extremis of black hole dynamics, time becomes space and -- because the observer cannot go "north of the North Pole" as Hawking so elegantly put it -- all singularities are extinguished in finite time. The freely falling observer will eventually join the 1-dimension information channel (Bekenstein-Mayo) described by the metric trace, and all information of observer interaction with the test particle trajectory will fall into an ordered line.

      All best,

      Tom

      Thank you for your response.

      I do not look at the other posts before I post because I want to see if I can understand an essay on my own. Sorry that I made you repeat past statements.

      I do find the topic of this contest is not clear. Your theme is clear and concise. My trouble making the connection has more to do with contest theme than your essay theme.

      All the best,

      Jeff

      Dear Christian,

      On Jul. 2 you wrote to Stuart Heinrich: "the great scientist who coined the phrase "It from bit or Bit from It?" in the 1950s, i.e. John A. Wheeler, was the same scientist who popularized the term "black hole" in the 1960s.

      On Jul. 4 I asked you: Did Wheeler really already coin "the phrase "It from bit or Bit from It?" in the 1950s"? If so I have to correct my essay ..."

      On Jul. 7 you wrote to me: "Actually, I did not know when Wheeler coined the phrase It from Bit or Bit from it.

      On Aug. 1 you wrote again to Jeffrey Schmitz: "the great scientist who coined the phrase It from bit or Bit from It? in the 1950s, i.e. John A. Wheeler ..."

      Well, there are many other reasons for me do distrust the Wheeler glorification, and I appreciate your courage to try and defend his idol against my endnotes. In particular I am waiting for your reply concerning unitarity.

      When you did not take issue concerning Gupta's question concerning singularity, I see this justified because he equated black holes with singularities. However, don't singularities have measure zero like anything that does not exist?

      By the way, did you read Schroedinger's reasoning in the fourth of his original papers? He made a trick that reduced an equation of fourth order to second order. And he got famous because this correctly described the spectrum of hydrogen - without Einstein's relativity.

      Cheers,

      Eckard

      Having read so many insightful essays, I am probably not the only one to find that my views have crystallized, and that I can now move forward with growing confidence. I cannot exactly say who in the course of the competition was most inspiring - probably it was the continuous back and forth between so many of us. In this case, we should all be grateful to each other.

      If I may, I'd like to express some of my newer conclusions - by themselves, so to speak, and independently of the logic that justifies them; the logic is, of course, outlined in my essay.

      I now see the Cosmos as founded upon positive-negative charges: It is a binary structure and process that acquires its most elemental dimensional definition with the appearance of Hydrogen - one proton, one electron.

      There is no other interaction so fundamental and all-pervasive as this binary phenomenon: Its continuance produces our elements - which are the array of all possible inorganic variants.

      Once there exists a great enough correlation between protons and electrons - that is, once there are a great many Hydrogen atoms, and a great many other types of atoms as well - the continuing Cosmic binary process arranges them all into a new platform: Life.

      This phenomenon is quite simply inherent to a Cosmos that has reached a certain volume of particles; and like the Cosmos from which it evolves, life behaves as a binary process.

      Life therefore evolves not only by the chance events of natural selection, but also by the chance interactions of its underlying binary elements.

      This means that ultimately, DNA behaves as does the atom - each is a particle defined by, and interacting within, its distinct Vortex - or 'platform'.

      However, as the cosmic system expands, simple sensory activity is transformed into a third platform, one that is correlated with the Organic and Inorganic phenomena already in existence: This is the Sensory-Cognitive platform.

      Most significantly, the development of Sensory-Cognition into a distinct platform, or Vortex, is the event that is responsible for creating (on Earth) the Human Species - in whom the mind has acquired the dexterity to focus upon itself.

      Humans affect, and are affected by, the binary field of Sensory-Cognition: We can ask specific questions and enunciate specific answers - and we can also step back and contextualize our conclusions: That is to say, we can move beyond the specific, and create what might be termed 'Unified Binary Fields' - in the same way that the forces acting upon the Cosmos, and holding the whole structure together, simultaneously act upon its individual particles, giving them their motion and structure.

      The mind mimics the Cosmos - or more exactly, it is correlated with it.

      Thus, it transpires that the role of chance decreases with evolution, because this dual activity (by which we 'particularize' binary elements, while also unifying them into fields) clearly increases our control over the foundational binary process itself.

      This in turn signifies that we are evolving, as life in general has always done, towards a new interaction with the Cosmos.

      Clearly, the Cosmos is participatory to a far greater degree than Wheeler imagined - with the evolution of the observer continuously re-defining the system.

      You might recall the logic by which these conclusions were originally reached in my essay, and the more detailed structure that I also outline there. These elements still hold; the details stated here simply put the paradigm into a sharper focus, I believe.

      With many thanks and best wishes,

      John

      jselye@gmail.com

        Dear Dr. Corda. I enjoyed your paper very much. An original idea and very competent description. In my view, this is one of the best papers in the contest.

        It was perhaps an accident that I read your paper back to back with the essay by Carlo Rovelli, in which he says something very similar (to your description in the technical endnotes). I mentioned this to him on his site. You might find it useful to review his essay also.

        My favorite paragraph in your essay:

        "In principle, a process in which pure states evolve in completely mixed states does not contradict the laws of quantum mechanics because the apparent information loss is instead hidden by quantum entanglement. The term entanglement means that the quantum state of a quantum system composed by two (or more) subsystems depends on the quantum state of each subsystem even if they are spatially separated. When one sums up the information in the two subsystems the result will be less than the information in the original system. The apparent information loss results hidden inside correlations between the subsystems."

        In my essay I introduced a very similar idea that the apparent information loss is hidden by quantum entanglement. I described a "background free" conceptualization of time where subtime flows only down the 1-dimensional path, e.g. The flow of a photon between an emitter and absorber atom. And that this subtime will be reversed in all ontological respects if the energy/information in that photon is now returned to the original atom.

        A trapped photon bouncing back and forth between two atoms will therefore trap energy/information and for all intents and purposes will be "dark"; i.e. outside of (classical) time. It appears to me that this description is capable of yielding similar measured results of entanglement, and I have thus described it so (even though I imagine I may endure the wrath of a conventional quantum mechanic).

        I believe there may be congruence between our ideas, and I would thus be honored by your comments on my essay if you have time.

        Kind regards, Paul

        Dear Paul,

        Thanks for your kind words. Your idea on a "background free" conceptualization of time looks quite intriguing. I am going to surely read, comment and score your Essay in next days. Thanks also for signalling me the Essay by Rovelli. I will read it in next days too.

        Cheers,

        Ch.

        Dear Christian,

        I risk to be naive, but I must ask you. I'm skeptical, what's going on Schwarzschild radius. All just talk about gravity. As if on that radius, repulsion indifferently waiting, what do attraction? Acording Rudjer Bošković maby there are chaingin of atraction/repulsion not only once.

        Regards,

        Branko

          Dear John,

          Thanks for your comments. I will surely read, comment and rate your Essay before the vanishing of the deadline of Community Rating.

          Cheers,

          Ch.

          Dear Christian,

          Congratulations on maintaining a clear lead as the number one essay. I've read your essay and had several questions which have been covered in comments above, so I will simply convey my congratulations. I did very much appreciate your summary of the problem and recent results on pages 2 and 3. In light of Coleman's remark, I find it fascinating that it has taken until now to perform a QNM analysis of the problem. Again congratulations on formulating the Schrodinger approach.

          I found the comments on this page very stimulating and enlightening and add very much to your essay. I've read Susskind and many other papers (including Susskind and Maldecena's latest on the "firewall") but have no expertise in, or strong opinion on, black holes. I do rather have an interest and theory of non-linearity of gravito-magnetism and a new approach as outlined in my current essay, which I hope you find the time to read.

          Best regards,

          Edwin Eugene Klingman

            Dear Corda,

            We are at the end of this essay contest.

            In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

            Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

            eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

            And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

            Good luck to the winners,

            And see you soon, with good news on this topic, and the Theory of Everything.

            Amazigh H.

            I rated your essay.

            Please visit My essay.