Bohr-like model for black holes: the route for quantum gravity by Christian Corda

The main point here is that the entropy of a black hole is S ~ A/4 + ln(A) + ..., where the area A ~ M^2 is such that for large M this is essentially the Bekenstein bound S = A/4. The logarithmic part is much smaller that the A/4 for the mass large. For tiny black holes the logarithmic part becomes significant. This part of the formula and the rest is what is of interest.

There is an underlying physical meaning to this. The Bekenstein bound is based on the idea that quantum phases of Hawking radiation are random. Bekenstein formulated this as a black hole form of black body radiation by counting up harmonic oscillators. The phases of oscillators are ignored or considered to be random. This was carried further by Hawking with his estimate of the back reaction of the black hole with the emission of radiation. When the black hole becomes very small so that its mass is less than ~ 10^3M_p this approximation begins to fail. The phase of the oscillators on the horizon of the BH is entangled with the Hawking radiation and its physics is more prevalent

An approximate form of the partition function of states on the black hole horizon is

Z = sum_n e^{-E}p(n)

for p(n) ~ e^{sqrt{n}ОІ} as n --- > в€ћ. The E = GM^2ОІ is the energy distribution of states and p(n) is the degeneracy of states. This little part with the number n ~ A is responsible for that ln(A) term I think.

This work hints at a deep connection between the degeneracy of states on a black hole as an integer partition and the density of states on a string. The scattering of two closed strings, with graviton modes, gives an intermediate state of a black hole that decays into a spray of particles (strings) that are the Hawking radiation. This seems to indicate a connection between string theory and LQG, where LQG gives the constraint condition for physical states.

Cheers LC

Christian,

You're aware I certainly agree that all the information entering a black hole re-emerges. In my view as the significant 'AGN' outflows, mostly re-ionized, but I see no inconsistency with the description you utilise. Do you?

I suspect there may have been more reason for the passing over of your essay last year than just failed understanding of BH information retention. You've done an excellent job again, and at least clarified that point. I do hope it gets more recognition.

I prefer a mode pedagogical approach but see you may have perceived the need to include comprehensive mathematics to satisfy questioning by the judges. I do hope that works and doesn't compromise popular peer scoring support. Certainly I think it worth the same good score as last years and hope it does well. I see it's been badly 'trolled', as has mine, but a troll can only hit once.

I look forward to your valuable advice on my own, deriving the predictions of QM from a classical mechanism, circumventing Bells theorem, but in a less 'scientific paper' style to hopefully allow Joe average an insight into a logical version of QM and convergence with SR.

Best of luck in the contest.

Peter

First off I found the following essay very interesting. I gave this a 9, and while that pulls the essay way ahead of the rest of ours this hits a lot of nails on the head. It has nothing to do with physics, but with sociopaths (he calls psychopaths) in power as psychocracy. Due to personal circumstances I have almost an advanced degree in the psychology of sociopaths.

The deviation from the Bekenstein bound is due to I think an error correction code system. The interior of black holes is entangled with the exterior, and this leads to troubles with quantum information. The old standby idea of the EPR particle pair near the horizon implying that Hawking radiation entanglement with the BH means the BH runs out of quantum information at about half its mass, or with certain modifications at the Page time. The additional quantum entanglement with the interior permits a quantum error correction code (ECC) to run, but this runs into troubles as the number of occupation states with the Hilbert space for the ECC increases beyond the Bekenstein bound.

The interior spacetime of the BH has curious properties, such as winding of geodesics that are on Cauchy horizons. From an information mechanics perspective it means this is a hyper-Turning machine. This quantum machine can compute second order λ-calculus, which is beyond the power of Turing machines or quantum computers. There is an entanglement between these states and the exterior. The exterior states are ordinary quantum machines, but their limited power is entangled with a second order λ-calculus system. This makes the system an "open system" which is able to overcome the problem of the ECC limitation.

I'll send some references to ideas along these lines.

Cheers LC

Dear professor Corda,

The solution of the almost insurmountable problem of unifying SR and quantum physics is surely one of the corner stones for humanity to build a new comprehension of our reality.

Your progressive thinking is surely helping us further forward, together with Stephen Hawking and the new perception of Carlo Rovelli (Planck Stars as the core of Black holes) I think we make an approach to a fresh way of thinking.

I thank you for your submission and hope that there will be this time more understanding for your insurgent thinking.

I also thank you for your comprehensive comment on my essay.

good luck this time with the FQXi judges.

Wilhelmus

Hi Christian,

Nice to see you in the essay contest forum again. I have not had time to read over your entire essay yet but I did have two comments/questions from the early part which I read which I wanted to already ask.

The first is a quibble in that "Will it really help humanity if we understand BH radiation, get a theory of quantum gravity, etc.?" In other words how important is the really? Note I am playing devil's advocate (the same thing I mentioned on Phil Gibbs) discussion, since as a theoretical physicist I spend a large percentage of my time thinking about these things. And then if people ask me what I do *and* if they stick around for the full answer the response from them is usually "Can you build a better iPhone, flat screen TV, etc. with this knowledge?" To which the answer is "Yes, maybe eventually, but isn't this of intrinsic interest without the need from some kind of gadget as the outcome?"

OK now to the second more substantive question -- in equation (3) you are proposing a modification of the usual Fermi-Dirac and Bose-Einstein distributions and therefore (I think) this would mean some modification of the underlying FD and BE statistics. Might not this lead to some observable consequences. For example, white dwarfs and neutron stars are held up by Fermi degeneracy pressure. If one modifies the statistics this might lead to a potentially observable chance in the mass-radius relationship of such objects. Or maybe one might be able to see a deviation from BE statistics in systems which exhibit such behavior (although usually in such system as superconductors or superfluid helium gravity is a completely ignorable interaction so that the astrophysical objects might be a better bet in regard to looking for deviations.

Anyway good luck and I will more fully read and comment in less than a week (I hope since now we are entering the end of semester gauntlet).

Best,

Doug

Dear Christian,

Congratulations for the results! I read your essay with much interest, and I think that quantum black holes should indeed be similar to Bohr's model, at least semi-classically. As your work shows, this would explain some results which otherwise seem to be disconnected, concerning BH thermodynamics, the entropy, its (approximate) proportionality with the area etc. One of my future plans is, at some point, to invest more time in the problem of quantum behavior of black holes, and to study more thoroughly yours and other results. I am happy to see your progress, and how this research spreads in the community.

Best regards,

Cristi

Dear Christian,

Your essay is excellent, so my words are well deserved. My admiration to your work is great, and I would be deeply honored if we will collaborate, or at least exchange ideas. I wish you all the best and good luck with the contest.

Best regards,

Cristi

Ch,

I would be curious to know which of the essays in last year's program are the one's you think are rubbish.

I seem to be doing pretty well this year. I think this is better than the previous attempts. There is no guarantee that will translate into winning anything.

Cheers LC

Also the experimental test for these fundamental theories generates not only jobs but a host of heretheto unknown technologies that benefit everyone. The touch screen, internet etc came from cern and other research centers. So yes there are benefits to be derived from investing in fundamental research.

Regards

Stuart

Ch

If nothing is allowed to fall into a BH then we do not have the information paradox and firewall problems.Recall that it is the surface area of a BH that is important and not its volume.So from my investigations a BH is BEC of planck sized BHs wich constitute the surface of a BH.

regards

Stuart