Randomness? What randomness?
arXiv:1908.07068 · doi:10.1007/s10701-020-00318-8
Abstract
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics (like Bohmian mechanics or 't Hooft's Cellular Automaton interpretation) are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low (or even zero) probability, their very existence implies that the no-signaling principle used in proofs of randomness of outcomes of quantum-mechanical measurements (and of the safety of quantum cryptography) should be reinterpreted statistically, like the second law of thermodynamics. In appendices I discuss the Born rule and its status in both single and repeated experiments, and review the notion of 1-randomness introduced by Kolmogorov, Chaitin, Martin-Lo"f, Schnorr, and others.
arXiv comment32 pages, extended version of talk on July 11th, 2019 at the conference "From weak force to black hole thermodynamics and beyond" in Utrecht in honour of Gerard 't Hooft. v2 is significant revision with new Appendix C and various clarifications
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