Hi Doug,
Nice to re-meet you here in FQXi Contest.
Thanks for two intriguing comments/questions, here are my replies:
1) I well understand that you are playing devil's advocate as BH radiation, quantum gravity, etc. are also among your research fields. In any case, I think that an important way we can really help humanity is to improve our knowledge of the fundamental laws of nature. In my opinion, two fundamental points are that we well understand what are space and time and how must we handle quantum objects. Quantum gravity is the synthesis of these two issues. More, various researcher think that understanding quantum gravity should be also important for realizing quantum computers, which should be the future of collecting and handling information. On the other hand, I think that, without basic research in physics, we cannot have further progress in medicine, technology, nuclear power, nano-structures etc.
2)Your observations about the deviations of the usual Fermi-Dirac and Bose-Einstein distributions that I have found in BH radiance are extremely intriguing. In my opinion the key point is: do perfect black bodies exist in nature? Even cosmic background radiation shows little deviations from perfect thermality. Hawking discovery of BH radiance appeared to show that BH are perfect black bodies. On the other hand, Parikh and Wilczek showed that energy conservation generates a deviation from the strict thermality instead. More in general, do perfect thermal system exist in nature? For example, considering your example: are white dwarfs and neutron stars really held up by an EXACT Fermi degeneracy pressure? Of course, that model is an excellent approximation but, as you correctly stressed, deviations could open interesting perspectives for the search of new physics from both of the theoretical and observable points of you. As you are an expert on Hawking radiation as tunnelling, you can be interested to my rigorous derivation of equation (3) in Ann. Phys. 337, 49 (2013).
Thanks again for your comments and best luck for the Contest. I am going to read, comment and score your Essay in next days.
Cheers,
Ch.