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A consistent history is a POVM set of observables corresponding to a time-ordered product of projection operators. For gauge theories, not any old operator will do, only gauge-invariant observables. In quantum gravity, there are no localized observables, meaning observables have to be defined with respect to the conformal boundary. Inside a black hole, this is none other than the black hole singularity, which is often spacelike. Spacelike singularities are enigmatic in string theory. This raises the very interesting question; can we have consistent histories inside black holes?

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sure, but afterwards you're going straight to bed, no excuses! –  Timtam Aug 14 '11 at 1:07
    
The space-time inside a black hole is space-time like any other. Given a sufficiently small region, one can define an approximately flat reference frame and do physics as is usually done in quantum mechanics. Therefore, there is no problem with consistent frames of reference inside a black hole. As to what happens in quantum gravity, , , well, until someone gets a Nobel prize for uniting the theories maybe we should leave the topic alone. –  Carl Brannen Aug 15 '11 at 1:11
    
Since you haven't gotten any answers on physics.se, you might want to try here: physicsforums.com/forumdisplay.php?f=66 –  Ben Crowell Aug 15 '11 at 2:22
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