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Imagine Alice falling into a black hole with a Schrodinger's cat experiment setup. after passing the event horizon towards the singularity she performs an observation to see if the cat is dead or alive. Bob floats just above the event horizon of the black hole. Will he ever know what was the result of the observation done by Alice? was this information lost? if so it contradicts basic quantum physics information conservation law and the second law of thermodynamics where entropy should always increase.

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  • $\begingroup$ In Bob’s world, Alice never crosses the horizon, so no information is lost. $\endgroup$
    – safesphere
    Sep 5, 2020 at 16:39

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The vast vast majority of physics interpretations say that the results of experiments that collapse spatially dispersed entangled states do not transmit any information, and can only be evaluated in any way by bringing the two results together and observing the correlations. The Alice and Bob in your experiment, therefore, exchange no information, and there is no contradiction with classical General Relativity.

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Information cannot reach Bob from Alice. Her information about the cat is as lost to him as she is.

Information is not destroyed simply because it becomes unavailable to Bob.

Information about Alice and the cat experiment remains in existence and contributes to the entropy of the black hole, which is proportional to the size of its event horizon.

Ultimately the black hole will evaporate. The information it contains will be transformed into Hawking radiation and carried back into the purview of Bob's descendants. Sadly, the information defining Alice and the cat will be so transformed as to be no longer recognisable.

(I play a little fast and loose here with correspondences between mass-energy, information and entropy; not all physicists agree it is that simple, but it does make my answer a lot less like a three-hour lecture)

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  • $\begingroup$ Since the outcome of Alice cat experiment was known after passing the event horizon ,it cannot be part of the information coded on the event horizon surface and it cannot be transmitted back by outer surface Hawking radiation. that is why it seems that this information will be lost assuming that one day the black hole will fully evaporate into space $\endgroup$ Sep 2, 2020 at 14:12
  • $\begingroup$ @EranSinbar You misunderstand the nature of Hawking radiation; over time the entire black hole evaporates, everything in it. You also misunderstand the distinction between losing and transforming information; in the sense you are using it, a transformation "loses" specific facts but creates new ones in their place. The net sum is not decreased, which is what physicists mean by "losing" information. $\endgroup$ Sep 2, 2020 at 14:29
  • $\begingroup$ To my best understanding , Alice knew if her cat was dead or alive before they reached the singularity . But even after the entire black hole will evaporate due to Hawking radiation the this information is lost forever and we cannot reconstruct ,even theoretically what she knew as she was falling towards the singularity. This to my understanding is a loss of information. $\endgroup$ Sep 4, 2020 at 8:52
  • $\begingroup$ @EranSinbar I am sure it is your understanding. What physicists describe it as is "transformation". $\endgroup$ Sep 4, 2020 at 16:18

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