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Logical positivism is often invoked to explain why external observers can't talk about black hole interiors, or why we can't talk about what happens outside our causal patch in inflationary models. But just exactly how justified is this questionable philosophy of logical positivism? According to another philosophical tradition, scientific realism, it is meaningful to ask about what happens inside a black hole, or beyond our causal patch.

Just because we can't measure something in principle doesn't mean it doesn't exist!

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Positivism isn't questionable, it is obvious. The arguments against is are very weak. – Ron Maimon Aug 12 '11 at 14:22

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That's a good question. These issues have an important philosophical core. But science is ultimately not about philosophy. The robust propositions made by science are about calculations and proofs obtained from empirically validated theories.

So it is appropriate to view your question as a scientific one. Then there may actually be a pretty good reason, besides the philosophical stance you mention, why exterior observers shouldn't talk about the detailed microscopic events in the black black hole interior. If the black hole complementarity is right, then $$ [\phi(x,t)_{\rm out},\phi(x',t')_{\rm in}] \neq 0.$$ If you take two points $x,t$ and $x',t'$ outside and inside a black hole that are space-like separated, according to classical geometry, the corresponding fields in effective field theory should commute with each other. But it's very likely that in the exact quantum gravity, they don't. The non-vanishing of the commutator seems to be necessary to get rid of the strict locality and strict causality. The strict locality and strict causality are bad because they are the key assumptions that allow one to prove the demonstrably wrong proposition that the information is being lost during black hole evaporation.

The hypothetical - and likely - situation is called black hole complementarity. If that's so, the fields in the interior are complicated functions of the fields and their derivatives outside the black hole. So observables inside the black hole are actually encoded in some subtle correlations of physical features of the region outside the black hole.

Much like in the uncertainty principle you can't talk about the exact values of $x,p$ at the same moment because they don't commute with each other, you can't talk about physical observations inside and outside at the same moment because they don't commute with each other. So the question "what actually happened inside the black hole" may really be ill-defined for the observers outside. Not only they have no way to find out; but even in principle, the answer may fail to exist. The infalling observers do see some outcomes; but their perspective may be fundamentally incompatible with the observers who stay outside.

The expanding cosmological case is probably analogous, with the region behind the cosmic horizon following the same rules as the black hole interior. None of the propositions above has been rigorously proved. After all, our functioning theory of quantum gravity isn't really a local field theory with negligible refinements; it is fundamentally formulated in a nonlocal way which becomes particular manifest in extreme environments such as those with the event horizons. However, if one formulates questions about the "interior", it's clear that we're using concepts of some effective field theory - the most general description of quantum gravity may refuse to separate the spacetime (and its degrees of freedom) into such simple regions, and when we do talk about the effective fields, it seems inevitable that the rules have to be modified relatively to the flat space if there are event horizons.

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"the demonstrably wrong proposition that the information is being lost during black hole evaporation." When exactly has this been demonstrated? I didn't think we'd managed to observe enough evaporating black holes to really ensure no information was lost. – wnoise Jul 27 '11 at 18:17

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