Randomness? What randomness?

TL;DR

This paper reviews the philosophical and technical issues of randomness in quantum mechanics, emphasizing its ambiguity, the incompatibility of deterministic interpretations with the Born rule, and the statistical nature of no-signaling principles.

Contribution

It provides a philosophical analysis of quantum randomness, critiques deterministic models, and discusses the implications of outliers and 1-randomness in quantum theory.

Findings

Deterministic interpretations conflict with the Born rule.

Outliers in measurement outcomes challenge the interpretation of no-signaling.

Quantum randomness should be understood statistically, akin to thermodynamics.

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.