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Randomness? What randomness?

Landsman, Klaas (2019) Randomness? What randomness? [Preprint]

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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 three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness (or algorithmic randomness) that in various guises was investigated by Solomonoff, Kolmogorov, Chaitin, Martin-Lo"f, Schnorr, and others, and treat Bell's (1964) Theorem and the Free Will Theorem with their implications for randomness.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Landsman, Klaaslandsman@math.ru.nl
Keywords: Quantum mechanics, Kolmogorov randomness, family resemblance
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Nicolaas P. Landsman
Date Deposited: 01 Dec 2019 22:49
Last Modified: 03 Dec 2019 03:31
Item ID: 16674
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 1 December 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16674

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