The quantum hair appears on the event horizon, or really the quantum membrane called the stretched horizon, as seen by a stationary observer. For a distant observer the tortoise or time delayed coordinate r' = r - 2m ln|r' - 2m| means these are redshifted enormously. However, an observer on an accelerated frame close to the horizon will observe more of this physics. Of course this requires an observer or probe on a frame with an enormous acceleration up to 10^{30}m/s^2.

In the collision of black holes quantum hair participates in the production of gravitons or quantum signatures in gravitational radiation. This is one big thrust of my essay; quantum gravitational signatures at the foundations of the universe are potentially detectable.

There is this problem with how gravitation and quantum mechanics merge or function in a single system. It is often said we understand nothing of quantum gravity, and this is not quite so. Even with the based canonical quantization of gravity from the 1970s in a weak limit is computable and tells you something. This theoretical understanding is very limited and big open questions remain. Of course since then far more progress has been made. The AdS/CFT correspondence, the Raamsdonk equivalence between entanglement and spacetime and the RT formula are some of the more recent developments. These indicate how spacetime physics has a correspondence or maybe equivalency with quantum mechanics or quantum Yang-Mills fields. However, an obstruction exists that appears very stubborn.

The vacuum is filled with virtual pairs of fields. With a black hole the gravity field causes one of these pairs to fall into the black hole and the other to escape. This means the quantum particle or photon that escapes as Hawking radiation is entangled with the pair that falls into the black hole, and so this means Hawking radiation is entangled with the black hole. So at first blush there seems to be no problem. However, if we think of a thermal cavity heated to high temperature photons that escape are entangled with quantum states of atoms composing the cavity. Once the entanglement entropy reaches a maximum at half the energy released the subsequent photons released are entangled with prior photons released. This would hold with black holes as well, but because of the virtual pair nature of this radiation it means Hawking radiation previously emitted in a bipartite entanglement are now entangled not just with the black hole, but with more recently emitted radiation as well. This means a bipartite entanglement is transformed into a tripartite entanglement. Such transformations are not permitted by quantum unitary evolution. This is called quantum monogamy requirement, and what this suggests is unitarity fails. To prevent the failure of quantum mechanics some proposed a firewall that violates the equivalency principle. This is called a firewall.

The firewall occurs when half the possible radiation is emitted, which is also the Page time. This also corresponds to the failure of a quantum error correction code. Error correction codes involve some deep mathematics; it is connected with the RT formula and I illustrate in my essay the connection with Mirzakhani's mathematics on the geodesics in hyperbolic spaces. Error correction is also tied with the packing of spheres or how oranges stack at the grocery store, the Kepler problem. This gets into the guts of what my paper is about. However focusing in an error correction corrects the mixing of information. Think of a library, in particular an elementary school library with little kids, and the patrons scramble up the order of books. The distance a books ends up from its right position is the Hamming distance. As the library gets mixed up an algorithm can manage this disordering. However, at about half mixing up things break down. The librarian has to virtually start over.

The solution with Susskind and others is to say spacetime variables and quantum states are equivalent. I do not disagree completely, but I think this is a complementarity instead of an equivalency. It means with either spacetime or quantum states you can account for the system, but at the expense of abandoning a description of the system by the other. You can't describe quantum gravity completely by both in the same measurement description. So this is a sort of Heisenberg uncertainty, if you will.

Cheers LC

Dear Lawrence

[I have sent this post to both our threads.]

Thank you very much for your reply. Making and breaking of space metrics are a minor part of my essay (pages 3 and 5). My employment background includes making metrics for examination scores using Rasch pairs analysis [fortunately I never encountered FQXI-style 1-bombing ratings there]. Obviously trying to make a connection between psychometric metrics and the spacetime metrics of BH hairs is a long and tenuous stretch. I have followed all of Susskind's online "theoretical minimum" courses including SR, GR and cosmology which includes BHs but only the starting point basics. I have read your reply but will need to work at it extensively to follow it. I still have some points though which you might kindly clarify.

You mention the Raamsdonk equivalence between entanglement and spacetime:that equivalence sounds somewhat similar in aim to an idea I wrote in sci.physics .foundations in 2011.

".... two entangled binary spins of electrons with random total spin, but perfectly correlated within the pair, seems a little like looking at the raw data for a rasch [pairs] analysis. ... Surely the binary spin data can't be the raw decisions which determine the emergent space [?]..."

https://groups.google.com/forum/#!msg/sci.physics.foundations/UIpgAj43QXg/lmXQajBksZUJ

I tried the idea in a Rasch pairs analysis soon afterwards and reported it in my 2016 paper at http://vixra.org/abs/1609.0329

where I was trying to see if I could compress the emergent space metric [arising from a Rasch pairs analysis] near a large 'mass': it seemed to work OK. Alas, the paper is not aimed at physics and has hardly any discussion. I need to re-write it to discus GR and CCC physics.

For examinations one often has two metrics which one needs to link together, such as for two parallel alternative tests. They need to be linked for comparability of grading outcomes. One way is to put a small amount of overlapping data in both of the alternative tests.

In the BH context this amounts to having pairs of entangled particles in both spaces simultaneously i.e. both inside and outside the BH simultaneously. But both entangled particles need to be in both spaces. I cannot simulate, in a Rasch pairs analysis, the use of only half of one pair in one metric. So I suspect that it may be impossible in general to use entangled pairs to make a metric when the two single particles, of an entangled pair, are in different spaces.

At a Penrose CCC node, all the stuff in the universe is in the form of photons in a single state at almost infinite wavelengths. The metric breaks down at the node in his model and I agree with that. But the stuff in the photons continues to exist even though the metric has gone. So a broken metric does not imply destruction of the 'stuff' in the old metric.

Page time etc is all new to me, but I am familiar with a metric breaking down gradually (your library books analogy). I suggested in my essay that the breakdown of the space metric may occur gradually before the CCC node is reached. The metrics I produced in my 2016 paper (ref above) show that, in special circumstances, some pairs of data do not get included in the metric. And sometimes the metric fails completely to plot any data. And I agree that this is connected to a sort of Heisenburg uncertainty. But in my psychometric area the problem is referred to as the problem of Guttman data. Guttman data kills metrics. And Guttman data is data with zero uncertainty.

As an example one could use Rasch pairs analysis to construct a metric for ratings in this contest. One datum point is where essay A is deemed to be better than essay B. Deemed, that is, by contestant C. Repeat for all pairs of essays and all contestants as raters. The metric would be most compressed if all the ratings of 'better' or 'worse' were at random. Corresponding to large uncertainty. But on the other hand, if every rater put the scripts is the same order of merit as every other rater than the analysis would collapse because there was no error in the system: corresponding to Guttman data and zero uncertainty. This is a nice explanation for the need for the existence of uncertainty as we would not be placed in our space metric without it.

I looked at the wikipedia site on Rasch model. It does look similar to statistical mechanics. I am not sure where it can go from there with respect to physics and physical modeling.

LC

Yes, a hero of mine, seen all his lectures. But quantum optics etc have now moved on rather a lot.

"The real question is how it is that classical mechanics is built up from the quantum world." Yes, that's exactly what I address, and the quantum scale mechanism I identify shows the quantum world can be mechanistic to! (John Bell said the Bohr version should really be called 'quantum NON-mechanics!) Now ALL can then be 'real'.

If you can see any flaw in the new mechanism please do identify it for me. (Nobody's been able to yet and the papers half written).

Very best

Peter

Dear Fellow Essayists

This will be my final plea for fair treatment.,

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

    We have probably exhausted my Rasch comments (and your patience).

    But first I should add for the record that it is not a simple Rasch model but a hybrid of Rasch and Thurstone pairs with a wiki page at https://en.wikipedia.org/wiki/Pairwise_comparison.

    I enjoyed your paper and thought it of high quality on both interest and relevance to the contest topic. It also makes me want to study the topic of hairs on BHs.

    Best wishes

    I am sorry I have not gotten to reading your paper yet. In fact I am not very active in reading many of them. I am working on a problem with a partner in Brazil. Read papers by Strominger for how quantum hair has a bearing on information content in gravitational radiation.

    Cheers LC

    To be honest I have absolutely no idea what you keep writing about with this.

    LC

    I enjoyed this essay Lawrence,

    It is more readable than some of your past efforts and demonstrates your point well, so I give you kudos and high marks for that. As a special aside; it appears you are now more glib at filling in some of the descriptions less Math literate people require to understand what all the Math is about, or at least more mindful of when such comments and explanations about applicability are needed. This essay is still a bit Math intensive for average readers and requires a certain level of proficiency to understand. You lost me a few times, starting with the reference to time crystals, but you pulled it together later each time.

    You impressed me linking RT and Mirzakhani, but not so much by showing the fundamentality of the correspondence, or its relationship to fundamental issues in Physics. I think there is a connection to press there, but you did not highlight it so well. I think you more wish to celebrate that Mirzakhani made some important advances in fundamental Physics that also tell us something about the black hole hair issue. I think it is interesting that from such a different construction, you also arrived at the result it reduces to a harmonic oscillator problem, just as Christian Corda did in earlier work.

    I like that you talked about a means of verification, and that it is possibly within the sensitivity range of current or pending instruments. Your writing continues to improve. I had to give you partial credit in some areas, but I elevated your score.

    All the Best,

    Jonathan

      As a further comment,

      I understand that gravitational memory also occurs in models where the event horizon is treated as the quantum critical point of BEC formation, as studied by Dvali and colleagues. There is a correspondence with BMS supertranslations and modes at the horizon, as I recall. My talk at FFP15 was on Gravitation by Condensation, so I talked a lot about the Bose-Einstein condensation model for Schwarzschild EHs and briefly touched on the other.

      My current essay incorporates a large subset of what I presented in Spain, in relation to the question of whether gravity is fundamental or emergent. You will probably find my offering a bit too wordy, for your taste, but I do reference some interesting Maths and explain part of it with full rigor in the endnotes.

      All the Best,

      Jonathan

      Dear Gary,

      I have yet to read your paper I hate to say. I have been not as able to get to papers easily this contest cycle.

      LC

      I scored your essay a week or two ago. It makes a bold proposition about how fractal geometry, and Julia/Mandelbrot sets enter into physics. I will in the ensuing year or so be introducing concepts along these lines. This does play a role in renormalization group flow, and in one sense time is a form of RG flow.

      Cheers LC

      I have rated your paper and also left a comment on both our papers on my own thread.

      Austin

      Dear Lawrence,

      First I want to thank you for commenting on my essay. I appreciate your mentioning epiphenomenalism. I regard it as a serious alternative, although I also consider it strange and somewhat paradoxical. Overall I am puzzled by the issue of the relationship between consciousness and the rest of things.

      Concerning your essay, I have to say that I cannot comment on the mathematical details. As you stated, you are presenting some "serious physics." However, I did learn from your general conceptual structure. I think I understand the point with which you begin, namely, the two ways of characterizing what is fundamental for physics. If two physical systems apply to the same phenomena, the more fundamental of the two allows for fewer degrees of freedom. The way this is accomplished is through the dynamical laws of the more fundamental system. Those laws show how what were previously thought to be independent degrees of freedom are not in fact independent but "are related to each other by some transformation principle." At any rate, that is how I read your statements. I had not thought of this way of looking at fundamentality. You can correct me if I have misinterpreted. As I said, I will not comment on the further development of your ideas, but I appreciate the opportunity to become acquainted with your work.

      Laurence Hitterdale

        Your description of two descriptions with different degrees of freedom is right. That is in one sense how one can assign which is more fundamental. The description with the fewer is often most fundamental. What I am finding is that two descriptions of quantum gravitation may be equivalent. One description has spacetime variables, while the other has quantum mechanical observables. This is the duality between unitarity of quantum mechanics and the equivalence principle of general relativity.

        The application of this is not so clear. I suspect the quantum mechanical variant that upholds unitarity is compatible with string theory. The description with the equivalence principle might be some form of loop variables with something like Penrose's R-process for collapse. I have yet to get to this phenomenological aspect of things.

        Currently I am finding the RT formula has information theoretic properties analogous to chaotic and open thermodynamic (Prigogine etc) systems. That is what currently I am finding interesting.

        Cheers LC

        Dear Lawrence B. Crowell

        Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.

        My essay is titled

        "Darwinian Universal Fundamental Origin". It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my effort judged on both the basis of prospect and of novelty.

        Thank you & kind regards

        Steven Andresen

        With the measurement issue a quantum system with some set of states, usually rather small in number or with a few number of degrees of freedom, by a classical-like system. By the use of "like" it is a reference to the fact this system is really in fact quantum mechanical. In the sense that Zurek outlines there is a form of quantum decoherence that induces superposition or entanglement phase of the system to enter into a large reservoir of states. Hartle then illustrates how decoherence leads to a form of macrostates that are decoherent sets of states. These are subjectively assigned groups of states, similar to the idea of macrostates in phase space in statistical mechanics. We then see in this physics the split between objective physics, which might be seen as the dynamical evolution of quantum states, and subjective physics that occurs with the phenomenological report observers make.

        I do not think it is unreasonable to see this as a case of quantum states encoding information about quantum states. In order to fully understand this process it requires some understanding of how the reservoir of quantum states define the final needle states, which requires a measurement system of the measuring system, which then of course gets into this recursion. The many world interpretation has this feature in it of a product structure of increasingly entangled states. This ψ-ontological interpretation has its mirror in ψ-epistemic interpretations, such as in GRW objective collapse models. Further, quantum interpretations tends to be incomplete and contradict each other. I see this as a possible feature of a Gödelian nature of quantum physics.

        When it comes to quantum gravity there is a similar gap. Currently the firewall is a major obstruction to the unital description of quantized gravity. Hawking bet that information, here information as the number of quantum bits, qubits or qu-Nits for N >= 2, is not conserved. The conservation of information appears to be a reasonable requirement of physics, which was the stance of Susskind. Susskind won a bet with Hawking, but then Almheiri, Marolf, Polchinski, and Sully demonstrated something interesting. A failure of accounting for entanglements of states meant that either unitarity of quantum mechanics or the equivalence principle of general relativity fails. In my essay I illustrate how these two principles are complementary and not compatible in a classical sense.

        The vacuum is filled with virtual pairs of fields. With a black hole the gravity field causes one of these pairs to fall into the black hole and the other to escape. This means the quantum particle or photon that escapes as Hawking radiation is entangled with the pair that falls into the black hole, and so this means Hawking radiation is entangled with the black hole. So at first blush there seems to be no problem. However, if we think of a thermal cavity heated to high temperature photons that escape are entangled with quantum states of atoms composing the cavity. Once the entanglement entropy reaches a maximum at half the energy released the subsequent photons released are entangled with prior photons released. This would hold with black holes as well, but because of the virtual pair nature of this radiation it means Hawking radiation previously emitted in a bipartite entanglement are now entangled not just with the black hole, but with more recently emitted radiation as well. This means a bipartite entanglement is transformed into a tripartite entanglement. Such transformations are not permitted by quantum unitary evolution. This is called quantum monogamy requirement, and what this suggests is unitarity fails. To prevent the failure of quantum mechanics some proposed a firewall that violates the equivalency principle. This is called a firewall.

        The firewall occurs when half the possible radiation is emitted, which is also the Page time. This also corresponds to the failure of a quantum error correction code. Error correction codes involve some deep mathematics; it is connected with the RT formula and I illustrate in my essay the connection with Mirzakhani's mathematics on the geodesics in hyperbolic spaces. Error correction is also tied with the packing of spheres or how oranges stack at the grocery store, the Kepler problem. This gets into the guts of what my paper is about. However focusing in an error correction corrects the mixing of information. Think of a library, in particular an elementary school library with little kids, and the patrons scramble up the order of books. The distance a books ends up from its right position is the Hamming distance. As the library gets mixed up an algorithm can manage this disordering. However, at about half mixing up things break down. The librarian has to virtually start over.

        In the end it may be that the equivalence principle and the unitary principle are complementary and in a quantum setting are not observable in a simultaneous observation. This is similar to the Heisenberg uncertainty principle with position and momentum. Back to the Gödelian issue, this means the universe presents itself in entirely different ways depending on the type of measurement performed. This is also a sort of form of "collapse" if thought of in a ψ-epistemic sense, which would agree with Hawking and Penrose. A ψ-ontological perspective would be more in line with Susskind. These perspectives are I think ultimately a form of G and NOT-G for G a true but undecidable Gödelian proposition.

        Cheers LC

          quote

          The many world interpretation has this feature in it of a product structure of increasingly entangled states. This ψ-ontological interpretation has its mirror in ψ-epistemic interpretations, such as in GRW objective collapse models. Further, quantum interpretations tends to be incomplete and contradict each other. I see this as a possible feature of a Gödelian nature of quantum physics.nWhen it comes to quantum gravity there is a similar gap.

          end of quote

          Excellent point. THe incompleteness of quantum interpretation you allude to is actually why I used Klauders enhanced quantization in my esssay

          Could you please give me your expert opinion of if the enhanced quantization procedure I appealed to in my essay is akin or different from what you are intending to reference in your above quote?

          Thanks

          Andrew

          P.S. my essay is as of December 21st, 2017

          quote

          The many world interpretation has this feature in it of a product structure of increasingly entangled states. This ψ-ontological interpretation has its mirror in ψ-epistemic interpretations, such as in GRW objective collapse models. Further, quantum interpretations tends to be incomplete and contradict each other. I see this as a possible feature of a Gödelian nature of quantum physics.nWhen it comes to quantum gravity there is a similar gap.

          end of quote

          Excellent point. THe incompleteness of quantum interpretation you allude to is actually why I used Klauders enhanced quantization in my esssay

          Could you please give me your expert opinion of if the enhanced quantization procedure I appealed to in my essay is akin or different from what you are intending to reference in your above quote?

          Thanks

          Andrew

          P.S. my essay is as of December 21st, 2017