Causal Patch Complementarity: The Inside Story for Old Black Holes

We carefully analyze the causal patches which belong to observers falling into an old black hole. We show that without a distillation-like process, the AMPS paradox cannot challenge complementarity. That is because the two ingredients for the paradox, the interior region and the early Hawking radiation, cannot be space-like separated and both low-energy within any single causal patch. Either the early quanta have Planckian wavelengths, or the interior region is exponentially smaller than the Schwarzschild size. This means that their appearances in the low-energy theory are strictly time-like separated, which nullifies the problem of double entanglement/purity or quantum cloning. This verifies that the AMPS paradox is either only a paradox in the global description like the original information paradox, or a direct consequence of the assumption that a distillation process is feasible without hidden consequences. We discuss possible relations to cosmological causal patches and the possibility to transfer energy without transferring quantum information.