Discussing on "What Is Fundamental" with Albert Einstein by Christian Corda

Hi Christian,

Great essay! It is a nice overview of normal modes. Check out my essay and in particular equations 7 through 8. I derive the states of quantum gravitons associated with quantum hair on black hole coalescence as Hermite polynomials. This is an approximation, where the full solution is far more difficult and complex. However, this overlaps with the normal modes model. If you want more details I have attached to my first comment a mathematical supplement. Your work here is a path along these lines as I see it.

There should by one means or the other a way of looking at the quantum transition of a black hole to a black hole plus radiation quanta or particle as sharing basic features seen in how a hydrogen atom emits photons. I do think that quantum information is conserved, but I agree with the Hawking idea that it is in a form that appears concealed or unavailable to everyone but an observer capable of the most complete possible set of measurements.

I see you got slammed down right away. Welcome to FQXI essay contest. Here there is a whole avalanche of papers that are pure balderdash, and some of them are near the top voting ranks. This happens every time.

In this work I was motivated by Maryam Mirzakhani's death. She died of breast cancer last July, and the news for various reason made me angry. I had read one of her paper's back in 2014 when she won the Fields medal, and at the time I thought this had something maybe to do with physics. Last spring I studied the Ryu-Takayanagi (RT) formula and for some reason the day I heard of Maryam's death the insight on how her work connects with this hit me.

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

The normal modes occur from the small arc approximation I employ. This results in Hermite polynomial solutions that correspond to quantum harmonic oscillator modes. This segues into the concept of normal modes, at least as an approximation, as a description of black hole quantum mechanics. A full set of solutions is obviously bewilderingly complex, but I don't think these dominate the made features of quantum black holes.

A part of the idea is that in black hole coalescence so called quantum hair or quantum topological charge associated with event horizons is magnified and emitted within gravitational radiation. It may be possible to detect this with LISA or the ESA eLISA. This will occur in signatures of so called gravitational memory.

I read Maryam's papers back in 2014 when she won the Fields Medal. At the time the thought occurred to me that this may have some important role in physics. When she died July 14 last year I was sort of angered and depressed about this, given how news of the world of late has been a bit sour. Then later this idea on how this might connect with quantum hair and the RT formula. So for several months I worked pretty hard on this. This paper is based on a loose set of notes and writing I did on this last October. I decided to fold this into an FQXi paper, even though I really thought I would no longer submit papers to these contests.

Cheers LC

Hi, Christian

This is one of your most entertaining essays yet- and the caveat of normal modes is actually quite on target as a serious issue

What I would like to know, as an extension of your ideas is due to the question of quantum entanglement. Do you view that as fundamental, and the entire EPR business, or do you have more of a semi classical treatment of gravity in mind?

If you could, please review my small essay. It was put in December 21st. i.e. materially it is very similar to what I have published with you earlier

As I indicate in my response quasi-normal modes are necessary as an approximation because the full solution set is virtually impossible. Maybe to some other form of intelligent life in the universe where what might be called an IQ of 250 is considered by them retarded this is tractable. To be honest the full set of solutions in QCD are largely a blank unknown. Maybe some sort of perturbation series can be worked up.

BTW, if Trump manages to win the next election here I am packing my bags. Not sure what is cooking out there in S. Europe, but it can't be as crazy as what is happening here.

Cheers LC

Dear Dr Christian Corda,

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.

Joe Fisher, Realist

Dear Christian;

Beautiful work. It makes you completely understand the analogy between Bohr's atom theory and your gravitational atom of BH theory. But you did not address the issue of the contest. That's why I have to disagree with herr Doktor Einstein.

You are a great scholar in physics, I respect you for that, but some time we have to understand the very basic to come down to the level of children and be able to teach them. Otherwise they would not get it. And that's when you fail.

Anyway, I wish you luck this time.

Truly yours;

Diogenes

Dear Christian,

I enjoyed very much reading your essay, you manage to transmit so much about the foundations of physics in such an entertaining way! I think you evoked Einstein so convincingly that maybe he visited you indeed :) Now, beyond the entertaining factor, I think the explanations are clear and the idea is excellent. I find very convincing the role of the oscillations of the horizon in this elegant explanation, which doesn't introduce new factors in the game, such as giving up an important principle of physics, as it is often considered the black hole information paradox implies we should do. I think both unitarity and the principle of equivalence are essential.

I have some questions. (1) You refer to your solution as "Bohr-like", but you use Schrödinger's equation. Why "Bohr-like" and not "Schrödinger-like"? (2) The radiation takes place similarly to how an excited atom emits a photon. In the case of the atom, the spontaneous emission is described in a good approximation by the Weisskopf-Wigner model. How do you think this happens in the BH case? Of course, to calculate the transition amplitudes you don't need this, but I am interested what is your view about this. (3) Do you think your solution can be related with the BMS symmetry? (4) Your proposal seems to me very natural, and minimalist in the sense of not requiring changes to the laws of physics. Your articles about the subject collected a beautiful number of citations, considering that they are recent. But I think this model deserves more attention. Instead, various proposals of giving up one principle or another, or built by artificially patching solutions, or by counting states made of artificial hypothetical objects, seem to receive much more interest. I think most of these constructions work just because the bound of entropy of quantum systems, you can put there anything as long as this is quantum. But I think yours is much more natural and simpler. So I think this preference is rather sociological, considering that so many people have their own group agendas of quantum gravity. What's your opinion about this? (5) In the notebook Einstein showed you, the final unified theory has as central equation a formula whose left hand side is "something like the Einstein tensor". Did you get the time to notice whether or not there are some tiny hats on those symbols?

Your essay made my day, I wish you success with the contest!

Best wishes,

Cristi

Dear Dr Christian Corda,

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe consists 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.

Joe Fisher, Realist

Dear Dr Christian Corda,

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.

Joe Fisher, Realist

Dear Dr Christian Corda,

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe consists 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.

Joe Fisher, Realist

Dear Christian,

Thank you very much for the reply, I am very interested in the future developments of your idea. I'm a bit sad that you didn't see the right hand side of the Equation. At least it seems that no modified gravity is in the left side, so no f(R) or W^2, although I am interested in conformal gravity. Sadly, you didn't have enough time to see if the Einstein tensor is classical or a quantum operator. So in this case the next best thing is to ask you, what is your opinion about this?

Warm regards,

Cristi