The Entropy of Lost Bets

Reading John Preskill’s description of his bet with Stephen Hawking on the black hole information paradox, I began to wonder what my requirements for thinking the paradox had been solved would be. The bet Preskill and Hawking and Thorne made was

When an initial pure quantum state undergoes gravitational collapse to form a black hole, the final state at the end of black hole evaporation will always be a pure quantum state.

Well at first I thought, surely a quantum theory of gravity which showed such a preservation of purity would be sufficient? Wouldn’t it? Well, a single quantum theory of gravity might be evidence, but even if we find that theory, what makes us think it is the correct theory describing our universe? Yeah, yeah, string theorists mutter something about “the only way.” So do Taoists.
This, I guess, is the funny thing about bets made by theorists. Their criteria for satisfying the bet may have nothing to do with reality. We may resolve the paradox, say in the Euclidean theory of quantum gravity, but what if the Euclidean theory of quantum gravity doesn’t correctly describe our universe. What if Twistor theory ends up giving a valid theory of quantum gravity and entails a total overhall of quantum theory such that the paradox is resolved in the opposite direction? What if the theory of quantum gravity makes it apparent that the question doesn’t even make sense?
The only way I’ll be happy is if we go out and create a black hole. Let it evaporate. And track the information flow. Admitting this, I believe, has just caused my theoretical physicists i.d. card to spontaneously combust. Excuse me while I put out the fire in my wallet.