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Is the example of neutrino entering the event horizon of BH quoted from this article a valid possible example of CPT violation due to the presence of event horizon in BH ?

Please, note that there is a very similar previous Question here . I don't think this is a duplicate, meaning that I have specified a counter example of possible CPT violation in BHF, as presented in the article I quoted.

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  • $\begingroup$ I think you should narrow down your question? $\endgroup$
    – jinawee
    Feb 2, 2014 at 11:44
  • $\begingroup$ The first paragraph alone looks now like an ok question to me, if it were the only text I would retract my close and downvotes ... $\endgroup$
    – Dilaton
    Feb 2, 2014 at 12:09
  • $\begingroup$ What exactly are the assumptions of the CPT theorem? If it works in Minkowski space-time, why should it be an argument against event horizons? $\endgroup$
    – MBN
    Feb 2, 2014 at 13:42
  • $\begingroup$ Ok, seems the opinionated part is edited out now (not by the OP though), so I remove my votes with negative sign. The question itself can no longer be blamed for getting bad answers... $\endgroup$
    – Dilaton
    Feb 2, 2014 at 19:45
  • $\begingroup$ I think that this paper titled "Black holes as a source of neutrino asymmetry in Universe" contains a detailed analysis. They say: "for the propagation of fermions in Kerr black hole space-times the interaction term is CPT violating" $\endgroup$
    – user31807
    Feb 2, 2014 at 23:58

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The article you are quoting is asking for a test of Charge conjugation, Parity transformation and Time reversal (CPT) invariance at high energies at the LHC and presumes that violations of this will be the signal for the sought for black holes of large extra dimensions. This violation is argued on the lines I am arguing against, below, and certainly is not a strict prediction of such large extra dimension models.

I am a simple minded experimentalist having worked with the analysis of various experiments in the large CERN collaborations for forty years+. The brain gets cluttered with all the details of detectors and their errors, programs and their errors so when it comes to reading theories

a) I keep it simple

b) I try to think of an experiment that would validate the theory.

As far as elementary particles and General Relativity goes, a) tells me that General Relativity says nothing about elementary particles, and a subset of GR, special relativity, applies to elementary particles and the theories evolved to describe and predict the data.

Now CPT invariance of a function is a theorem that applies to the theories and the functional forms developed to describe elementary particle dynamics, very successful theories.

Elementary particles come one by one to start with. The collective behavior of systems of elementary particles has been studied and functional forms found, but still the theories DO NOT contain gravitational effects. CPT has been tested and holds for the experiments we have done.

Is the thought experiment of a neutrino crossing an event horizon a valid thought experiment?

To start , in my simple minded experimentalist's view, we are on dangerous ground because we are mixing GR ( event horizon) and elementary particles. That is, at best, we will have a semi classical ( hand waving) approximation of what may really be the case. Can one test the validity of a theorem validated in particle physics while mixing GR and quantum mechanics?

My intuitions says not, if we go by precedent of such semi classical approximations. They are not a strict theoretical tool and are heuristic. They may seem to work as in the Hawking radiation case because no contradictory data has been found but to base a violation argument on the approximation seems to me a game with many probable outcomes. Suppose when the four forces are unified in a quantized theory of everything ( TOE) the event horizon comes out to be quantized, as an example of a bizarre outcome. It will be a complete game change. In fig2 of the neutrino example, how do we know that the black hole does not increase its lepton number by 1 if we do not have a quantized theory of gravity? After all an electron captured in a nucleus keeps all the quantum number sums correct.

We were at the same impasse with the black body radiation and thermodynamics, the ultraviolet catastrophe. When a complete model of quantum statistical mechanics was developed the catastrophe disappeared. ( actually it was the reason the quantization of photons was proposed). So I am proposing, in this semiclassical handwaving, that the black hole gains a lepton number when a neutrino falls in ( or a baryon or whatever) and that each black hole is characterized ( is in an eigenstate of ) by all the quantum numbers falling in it. I can hand-wave with the best of them, as an experimentalist.

We shall reach b) if the experiments trying hard to find large dimension black holes in the LHC have some candidates. That will be fun, checking the quantum numbers and designing new experiments.

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  • $\begingroup$ My argument is the same as above. Neutrinos are elementary particles absolutely governed by quantum mechanics. General relativity has been validated only in classical dimensions. Mixing quantum mechanical concepts with non-quantized gravity and talking about breaking symmetries like CPT is in my opinion mixing apples and oranges. For such a conclusion to hold ( CPT violation) one needs to examine the statement in a quantized theory which includes both elementary particles and (at its classical limit) GR. A string theory model would do, but I do not know if anybody is looking at this. $\endgroup$
    – anna v
    Feb 3, 2014 at 20:41
  • $\begingroup$ The paper is more sophisticated than in fig2 of the other reference, it looks at interactions not just adding quantum numbers, but still, how a black hole looks if gravity is quantized will be different then just looking at background metrics deviating from spherical symmetry. There might be new conservation rules, and who knows what else that would ensure CPT conservation. A rigorous statement can come only from a unified quantum theory of everything, in my opinion. $\endgroup$
    – anna v
    Feb 3, 2014 at 20:46
  • $\begingroup$ I think that we are on a long road towards a quantized theory of everything, which will really be a model fitting existing data ( the standard model and astrophysical data) validated by a good fit to known and predictions for new observations. Until then everything is a mathematical game based on hypothesis assumed. A black hole will have an enormous number of these unified fields. In quantum physics up to now enormous numbers are treated thermodynamically, the quantized states through a density matrix give such a small probability for reversibility as to be in effect zero. $\endgroup$
    – anna v
    Feb 4, 2014 at 5:16
  • $\begingroup$ It would look like CPT violation but it is just a statistical effect of treating very large numbers of quantized states. See here motls.blogspot.gr/2014/02/… . Why would this state change when gravity is quantized? i.e. why should we think that once we have a TOE there will be no density matrix describing the black hole interior is not evident to me, has not been demonstrated rigorously, as far as I am concerned. Now for small black holes ( from large extra dimensions) at the LHC where the no of particls will be limited, if they are ever found, $\endgroup$
    – anna v
    Feb 4, 2014 at 5:20
  • $\begingroup$ one might get an experimental handle on the problem. If a violation appears there one has to choose a TOE model that includes it. Until then it is all theorists playing games, in my opinion. $\endgroup$
    – anna v
    Feb 4, 2014 at 5:22
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ok, dear user: You are probably confused by the long, correct but superficial and naive discussion of the blogger you quote above that disagrees with Hawking. Of course, in most of the cases I agree with the blogger, or, better said, I would agree with him if it happened to have the same biases and beliefs about nature... fortunately this is not the case. First, the blogger is right: time reversal symmetry is a symmetry in the dynamics and it is NOT the entropic idea of time. However, time reversal of the dynamics in the presence of strong space-time alterations is not independent on the entropic time definition. The things may appear different when analyzed from a classical point of view but entropy can be generalized in a quantum mechanical and quantum informational sense that escapes the blogger up there... This being said, a correct formulation of quantum gravity appears to be necessary even for aspects considered as "effective" before, and maybe Hawking is right after all... the problem lies again in how exactly one quantizes a theory, be it 0, 1 or 2 dimensional... I learned to be cautious about calling Hawking an idiot... this happened with... time...

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  • $\begingroup$ You are right and certainly CPT is not just T or CP. CPT is equivalent to local Lorentz invariance. Good luck in defining "local" close to a BH horizon in a general way... arxiv.org/pdf/hep-th/9506138v1.pdf this paper may be useful, although I have some other opinions about the problem discussed... $\endgroup$
    – user33923
    Feb 2, 2014 at 15:22
  • $\begingroup$ being in a hurry: maybe this is helpful... (my opinion about the subject is different but I just show it to the public) prd.aps.org/abstract/PRD/v39/i2/p683_1 $\endgroup$
    – user33923
    Feb 2, 2014 at 21:06

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