Leggett-Garg Inequalities, Pilot Waves and Contextuality

TL;DR

This paper critically examines the assumptions behind Leggett-Garg inequalities, arguing that violations do not necessarily refute macrorealism, and explores contextuality using pilot-wave theories and signaling analysis.

Contribution

It clarifies the assumptions in Leggett-Garg arguments and applies contextuality analysis to challenge their implications for macrorealism.

Findings

Violations of Leggett-Garg inequalities do not definitively refute macrorealism.

Bell's pilot-wave theories serve as counterexamples to non-invasive measurability.

Contextuality analysis reveals surprising insights into quantum measurements.

Abstract

In this paper we first analyse Leggett and Garg's argument to the effect that macroscopic realism contradicts quantum mechanics. After making explicit all the assumptions in Leggett and Garg's reasoning, we argue against the plausibility of their auxiliary assumption of non-invasive measurability, using Bell's construction of stochastic pilot-wave theories as a counterexample. Violations of the Leggett-Garg inequality thus do not provide a good argument against macrorealism per se. We then apply Dzhafarov and Kujala's analysis of contextuality in the presence of signalling to the case of the Leggett-Garg inequalities, with rather surprising results. An analogy with pilot-wave theory again helps to clarify the situation.