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Notes on the firewall paradox, complexity, and quantum theory
We investigate what it means to apply the solution, proposed to the firewall
paradox by Harlow and Hayden, to the famous quantum paradoxes of Sch\"odinger's
Cat and Wigner's Friend if ones views these as posing a thermodynamic decoding
problem (as does Hawking radiation in the firewall paradox). The implications
might point to a relevance of the firewall paradox for the axiomatic and set
theoretic foundations underlying mathematics. We reconsider in this context the
results of Benioff on the foundational challenges posed by the randomness
postulate of quantum theory. A central point in our discussion is that one can
mathematically not naturally distinguish between computational complexity (as
central to the approach of Harlow and Hayden and further developed by Susskind)
and proof theoretic complexity (since they represent the same concept on a
Turing machine), with the latter being related to a finite bound on Kolmogorov
entropy (due to Chaitin incompleteness).Comment: 31 pages; further references adde