[math-fun] Black hole paradox
OK, I read S.Hawking's http://arxiv.org/pdf/hep-th/0507171v2.pdf Phys.Rev.D72 (2005) 084013 but do not understand it. It supposedly shows "information is not lost during black hole formation+evaporation." This also was supposedly shown by J.Maldecena's "AdS-CFT correspondence" which I do understand (for a very poor value of "understand" -- I understand his top level argument plan). Neither tells me the answer to this: "Is Joe's lepton number preserved when he falls into a black hole and it later evaporates?" Neither convinces me they're right, either. In fact, if that exact verbatim paper had been written by me, not Hawking, I feel 100% confident Physical Review D would not have published it -- i.e. this is yet another example of the failure of the refereeing process in Science. Now here's a little thought experiment that suggests Hawking is wrong. Consider the big bang that created our universe. Did it generate lots of information from {little or none}? If so, we would seem to have a counterexample to Hawking's "physics is information-preserving (unitary)" claim. Another: the correct theory of quantum gravity is not known. If it is possible to create two such theories, both self-consistent, but one features black hole info loss, other doesn't, then I would conclude that the power of pure thought simply cannot tell us whether "info loss" happens. And I think that is the situation we are in, or anyhow neither Maldecena nor Hawking has ruled that out. Instead they each have worked within one partial quantum theory of gravity, and since not the same theory, evidently they disagree.
From: Warren Smith <warren.wds@gmail.com>
To: math-fun@mailman.xmission.com Sent: Sunday, May 27, 2012 5:00 PM Subject: [math-fun] Black hole paradox
"Is Joe's lepton number preserved when he falls into a black hole and it later evaporates?"
No, baryon number and lepton number are not preserved under processing through a black hole. Hawking radiation peaks at a wavelength on the order of the size of the black hole, and exponentially dies off at shorter wavelength, like the Planck black body spectrum. If baryon number is to be preserved, then the black hole must emit baryons as part of the Hawking radiation. But the lowest mass baryon has a mass of 1 GeV, so baryons cannot begin to be emitted until the black hole has shrunk to about 1 fm in size. But the mass of a black hole is proportional to its radius, and 1 fm / 10 km = 1e-19. So by the time a black hole is ready to emit baryons, its remaining mass is about 1e-18 solar masses, and it's too late to conserve baryon number. Applying the same reasoning to each of the three lepton numbers (e, μ, τ), the lowest mass lepton is the neutrino. Even with a neutrino mass of 1 μeV, the black hole size must shrink to 1 m. It is possible that lepton number fails to be conserved in the first place. In the old days when neutrinos were massless, the spin of a neutrino was always antiparallel to its momentum, and always parallel for an antineutrino, or maybe the other way around, I can never remember which. Now that neutrinos have mass, you can go fast enough to overtake a neutrino, reverse the direction of its momentum, and thus reverse its helicity. You now have one of two possibilities. (1) The neutrino is still a neutrino, but has the "wrong" helicity. Its interaction via the weak force is vastly much weaker. Or, (2) the neutrino has become an antineutrino. In this case, lepton number is not conserved. In the first case, the neutrino is said to be a Dirac particle, in the second case a Majorana particle. It is not known which case is true. There exist even-even nuclei that are more stable than the two adjacent even-odd isobars (equal mass nuclei). These cannot beta decay the ordinary way. But if there is a more stable isobar two steps away, a double beta decay is possible, with the emission of two electrons and two neutrinos. Measured double beta decay half lives range from 7.0e18 years for Mo-100 to 3.5e24 years for Te-128 ( http://www.nndc.bnl.gov/bbdecay/list.html ). Experiments have been underway for a long time to search for neutrinoless double beta decay, the confirmation of which would demonstrate that neutrinos are Majorana particles. -- Gene
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