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.
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.
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...
