Carlo,

I agree with you that if one writes a Schroedinger equation one gets in turn unitarity without many calculations (in fact I stressed that my calculations in my Essay are on the same level of university studies on quantum mechanics). On the other hand, the vice versa, i.e. that unitarity permits to ALWAYS write a Schroedinger equation is not so trivial as you claim. I recall you that Maldacena, Susskind and the same Hawking claimed that unitarity is restored in black hole evaporation through the ADS/QFT duality, that Mathur claimed that unitarity is restored through the "fuzzball" approach and that Zhang, Cai, Zhan and You claimed that unitarity is restored through the correlations among Hawking quanta. In any case, neither Maldacena, Susskind and Hawking, nor Mathur, nor Zhang, Cai, Zhan and You wrote down explicitly a Schroedinger equation which permitted them to find a pure final state. In fact, unitarity is also permitted WITHOUT obtaining a Schroedinger equation as in some cases one obtains a final mixed state but information is preserved trough correlations among the subsystems. I did NOT construct the Schroedinger equation by assuming unitarity. I constructed the Schroedinger equation by using my result in Int. Journ. Mod. Phys. D 21, 1242023 (2012), where I have shown that black holes quasi-normal modes can be interpreted in terms of quantum levels. I do not think that such a result automatically implies unitarity, because in that case, I should have won a Prize in the 2012 Gravity Research Foundation Competition rather than a "simple" Honorable Mention as in that case the black hole information paradox was implicitly automatically solved in my Essay Int. Journ. Mod. Phys. D 21, 1242023 (2012)!! On the other hand, you claims that "In the classical theory, there is no time translation invariance at infinity. Information can fall in, instead than out." But here I am not using neither the classical theory nor the full quantum theory. I am using a semi-classical approximation. Maybe time translation invariance at infinity is restored in my result Int. Journ. Mod. Phys. D 21, 1242023 (2012), I have not checked. You can check it if you like.

Cheers,

Ch.

Dear Eckard,

I am happy to read that you are seeing Carlo's objection logically justified. Why don't you ask Carlo if he, in turn, see your objections against the theory of relativity logically justified too? In any case, I am going to see your view concerning unitarity in a reply to my comment on your Essay in next days.

Cheers,

Ch.

Hi Doug,

Thanks again for your insightful comments.

1) Concerning your question on the reverse absorption process, yes, you are correct in saying that equation (16) for m > n corresponds to emission and the BH losing mass. In fact, I have emphasized both between eqs. (9) and (10) and between eqs. (10) and (11) that I assume m > n. On the other and, for an absorption, the sign of the variation of energy changes in both eqs. (11) and (15). This implies that, when one switches m and n in formula (16) also the sign in the argument of the exponential must change and one gets again exp[2pi(n-m])= exp[-2pi(m-n)]. In any case, I am going to read again the paper by W&P to see in detail what concerns the outgoing/ingoing modes.

2) Concerning the AMPS firewall framework, I must confess that my understanding of this issue is even pretty poorer than your one. But I am pleasured to have some comment/discuss with you. In my knowledge, the idea that information does not leak out until more than half way through the evaporation process i.e. little information leaks out until >=t/2, is originally due to this paper by Don Page. This recent paper by Maldacena and Susskind verbatim claims that "we believe that the AMPS conclusion is unwarranted" and "we claim that there is no convincing argument in favor of firewalls". Recently also Mathur and Turton claimed that there is a flaw in the firewall argument. A point that surprises me is that all these researchers, i.e. Almheiri, Marolf, Polchinski, Sully, Mathur, Turton, Maldacena, Susskind, Van Raamsdonk, Giddings, Page, etc. NEVER consider the correction to the thermal spectrum by Parikh and Wilczek but continue to consider the strictly thermal spectrum of Hawking original computations. It is my personal opinion that, instead, the non-strict thermality is fundamental to solve the paradox. On the other hand, this paper by Braunstein and Pati looks to show that the paradox arises immediately after the black hole starts to emit Hawking quanta. This looks in contradiction with the idea that information does not leak out until more than half way through the evaporation process and, in turn, makes the paradox more severe.

Although I have read your FQXi Essay some weeks ago, I am going to re-analyse in detail, comment and rate it in next day.

Good luck in the Contest!

Cheers,

Ch.

Dear Tom,

Yes, it could be a similar result if every singularity should be guaranteed to be extinguished in finite time. But we must be careful on which "time" we are referring to. In fact, singularities can be time-like too.

Cheers,

Ch.

Dear John,

1) Gravity is not described as the contraction of space. Instead it is described as the curvature of spacetime.

2) Historically, the Cosmological Constant was inserted by Einstein in the right hand side of his Field Equation in order to prevent the Universe to collapse under the action of gravity. In fact, he originally did not realize that his Field Equation implies that the Universe is expanding rather than contracting.

3) You must show quantitatively that you gravity wells can take into account the Cosmological Redshift. Your qualitative claims are not sufficient.

4) Cosmic rays and other radiation are taken into account in the right hand side of Einstein Field Equation. Their effect is negligible with respect to the global evolution.

Cheers,

Ch.

Christian,

I know gravity is described as the curvature of spacetime, but does that explain it, or just model it?

One problem I have with spacetime is that it is based on treating time simply as a measure of duration, which is based on the perception of time as a vector from past to future, along which this point of the present moves/exists, depending on your interpretation. Yet it seems much more rational to consider time as an effect of action, so it is the changing configuration of what is, that turns future potential into past circumstance. For example, rather than the earth traveling/existing along some dimension from yesterday to tomorrow, it is that tomorrow becomes yesterday because the earth rotates. This makes time an effect of action, similar to temperature. In essence, time is to temperature what frequency is to amplitude.

Duration does not transcend the state of the present, but is what is presently occurring between events, like the wave cycling between peaks.

Therefore there is no metaphysical "fabric of spacetime" and so no conceptual basis for an expanding universe, or blocktime, or wormholes, or multiverses, or any of the other speculative fantasizing arising from this conjecture.

Spacetime is simply correlation of measures of duration and distance and is mathematically accurate for the same reason epicycles are mathematically accurate; Perspective is inherently relative. There is no such thing as objective perspective. One could, with sufficient complexity, create a self-centric cosmology, for the quite logical reason we are the center of our view of the universe, but that wouldn't mean there are Titans pushing the entire universe in the other direction, every time one walks across the room, just as there is no giant cosmic gear wheels, or fabric of spacetime, pushing and pulling.

If time were a vector from past to future, logically the faster clock would move into the future more rapidly, but the opposite is true. Since it thermodynamically ages/burns quicker, it recedes into the past more rapidly.

Now the temporal vector is the basis of both narrative and linear logic, which are the basis of civilization, so it isn't an easy idea to put in context and I understand why it would be incorporated into foundational theories, but then we still see the sun as moving across the sky and it was only five hundred years ago we began to understand it is the earth spinning the opposite direction.

According to measurements of background radiation, overall space appears flat. This was proposed decades ago and measured by COBE and WMAP. The explanation given is that Inflation initially blew the universe up so much larger than is visible, it only appears flat on local scales, much as a local area of the earth's surface appears flat.

I could speculate as to the various relations between radiation and mass, but I will stop with the above observations as to why current theories may have to be reconsidered, not just continually patched.

Looking at the literature appearing in the popular press, Smolin et al, it might be worth your while to consider thinking about alternatives. I'm just offering some suggestions.

Again, pardon the rant.

Regards,

John

Hi Stephen,

Thanks for your comments and for rating my Essay quite highly. I well understand your perplexities on the issue that information remains, in a certain sense, random. I think that such perplexities can be generalized to the whole quantum theory and this was exactly the reason for which Einstein claimed that quantum mechanics should not be definitive. I am not an expert on Popper. Did he claim something concerning the determinism/indeterminism issue and concerning the discrete/continue issue? My idea on black holes is that they are exactly harmonic states that remains in contact with the outside, with no singularity!

Cheers,

Ch.

Hi Christian,

In regard to the excitation/de-excitation or ingoing/outgoing modes W&P find at the semi-classical level that for ingoing modes Gamma~1 which they equate with there being unit probability for an ingoing photon to "tunneling into" the BH since there is no barrier at the semi-classical level for something to fall into the BH. However this statement they make is based on their semi-classical approximation.

I'll have to look at the use of thermal spectra by these researcher. It seems "obvious" that due to back reaction the spectrum will have to deviate from thermal/Planckian. I put obvious is in scare quotes since there are examples where due to a collaboration of factors a dynamic/changing space-time can have a Planckian spectrum. The FRW Universe is such an example since there the way in which the photon frequency and temperature come into play works in such a way that as the Universe expands the spectrum remains Planckian just at an ever lower temperature. But this feature depends on an interplay of f and T which may not occur in general. Thus I agree with you - I am puzzled that the assumption is the spectrum remains thermal as the evaporation proceeds. Especially at the end stages it is hard to believe (modulo some specific calculation to the contrary) that the spectrum will remain thermal. And certainly the W&P result indicates that at some level the spectrum should wander away from pure thermal. Also it is a bit puzzling how little attention the work by Zhang, Cai, Zhan and You has received (at least initially). There is a question of what happens to their mechanism at the very end stages of the evaporation since they ignore QG corrections and these are thought to play some role in this regime. But overall their result is very suggestive.

By the way there was an earlier work by Zurek which obtained the same (or maybe only similar?) deviation of thermality of BH radiation using entropy arguments. The paper is

"Entropy Evaporated by a Black Hole", W.H. Zurek, Phys.Rev.Lett. 49 (1982) 1683-1686

It makes sense one could obtain that deviation of the spectrum from entropy arguments since as W&P show there is a close connection between the tunneling rate Gamma and the entropy, S.

Anyway interesting stuff.

Best,

Doug

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]

  • Post #143

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