Salamin: No, baryon number and lepton number are not preserved under processing through a black hole.

--ah, but in the paradox I outlined, Joe "never falls in" to the hole in Mary's view (even though he falls in his own view) hence after black hole evaporation, Joe was never "processed" hence his Lepton & Baryon numbers ARE conserved. In Mary's view. So anyhow, Salamin's statement here (which last I heard was the agreed physics view too and had been stated by Hawking) encapsulates the contradiction I was speaking of.

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.

--Agreed! And I like this argument even better than other arguments I'd seen before.

Applying the same reasoning to each of the three lepton numbers (e, ?, ?), the lowest mass lepton is the neutrino.? Even with a neutrino mass of 1 ?eV, 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.

--Agreed.

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

--excellent and helpful answer, but my original Joe+Mary statement of the paradox, remains un-addressed. In Mary's view, Joe never quite falls in to the hole, hence his baryon number is preserved after hole evaporates. But in Joe's view, he fell in, hence his baryon number is not preserved. Which? Incidentally, re previous complaints Mary would effectively stop being able to see Joe since he'd become too redshifted (and also since the photons Joe emitted would arrive at Mary less and less often and become spaced too far apart in time -- a different symptom of time-distortion)... these complaints become moot after evaporation complete, since now Joe's photons can reach Mary without any redshift. --- Using Salamin's "it's too late for Baryon conservation" argument, it seems to me we can argue that even if Joe never fell in, then IF at the end of the process Joe's baryons are still there, THEN we will contradict conservation of mass-energy, since all but 10^(-18) part of the energy already was radiated away before the hole started to radiate baryons and whatever was left of Joe managed to become visible to Mary again. I.e, it is too late for Joe's baryons to be preserved because there is not enough mass-energy left.