I was surprised by the subtitle of Susskind’s Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. I would have expected that information loss would violate classical mechanics (“God does not play dice”, Einstein 1926), not quantum mechanics (“The future is unpredictable”, Feynman 1965). Susskind himself says on page 91: “If we do look [at a photon] the conservation of information fails.” I asked him about this and he replied:
“Ok, you have put your finger on an important issue that I felt was just too technical to completely spell out for the layman, but maybe I should have. In quantum mechanics the conservation of information is defined for isolated systems during the time when they are prepared and when they are observed.
“During this interval we assume the system was completely isolated from the environment which includes observers, apparatuses etc. Technically this means that the system remains in a pure state unentangled (in the technical sense) with anything else. In that case information is conserved.
“In the case of a black hole the experiment (?) consists of preparing a system of particles in some pure state—allowing it to collapse to a black hole and evaporate—and only at the end, measure the radiation. Any observation or interaction with the environment during the interval would ruin the experiment.
“To confirm that information is conserved one needs to replicate the experiment many times and observe mutually incompatible observables in different instances of the experiment. For example the system could be a particle prepared in a pure wave-packet state. It could pass through slits and hit s florescent screen. To confirm the non-loss of information would mean to detect an interference pattern but that would take many particles.
“What Hawking was saying is that even in the most ideal case of a perfectly isolated system, black holes would not be subject to the usual rules—in other words decoherence would take place without interaction with any environment.”
That leaves me with several questions, since raised with Professor Susskind, but he has not replied:
Why is quantum determinism, in Susskind’s view, more in need of preservation than classical determinism?
How is it that information loss in black holes threatens quantum determinism, but information loss in quantum mechanics does not? In his book, Susskind says “Quantum Mechanics, despite its unpredictability, nevertheless respects the conservation of information.” Isn’t this self-contradictory?
Hawking talks about throwing computers and encyclopaedias into black holes – classical objects losing classical information. What has that got to do with a pure quantum state decohering “without any interaction with any environment”? Is Susskind talking about virtual particles converting to the real particles of Hawking radiation? Doesn’t the gravitational pull at the event horizon count as an environment?