Quantum- vs. Macro- Realism: What does the Leggett-Garg Inequality actually test?

TL;DR

This paper clarifies what the Leggett-Garg inequality tests by analyzing the concept of macroscopic realism, showing that its violation only indicates measurement disturbance, not the failure of realism itself, and distinguishes between different notions of noninvasiveness.

Contribution

It provides a model-independent analysis of the Leggett-Garg inequality, clarifies the assumptions involved, and distinguishes between operational and ontic notions of noninvasiveness in testing macroscopic realism.

Findings

Violation of LG inequality indicates measurement disturbance, not necessarily failure of realism.

Weak conditions are sufficient for deriving the inequality, which does not directly test macroscopic realism.

Different notions of noninvasiveness are distinguished, affecting the interpretation of experimental results.

Abstract

Macroscopic Realism (MR) says that a macroscopic system is always determinately in one or other of the macroscopically distinguishable states available to it. The Leggett-Garg (LG) inequality was derived to allow experimental test of whether or not this doctrine is true; it is also often thought of as a temporal version of a Bell-inequality. Despite recent interest in the inequality, controversy remains regarding what would be shown by its violation. Here we resolve this controversy, which arises due to an insufficiently general and model-independent approach to the question so far. We argue that LG's initial characterisation of MR does not pick out a particularly natural realist position, so we articulate an operationally well-defined and well-motivated position in its place. We show that much weaker conditions than LG's are sufficient to derive the inequality: in the first instance, its violation only demonstrates that certain measurements fail to be non-disturbing at the operational level. We articulate three distinct species of MR-ist position, and argue that it is only the first of these which can be refuted by LG inequality violation. This first position is an attractive one, so ruling it out remains of interest, however. A crucial role is played in LG's argument by the assumption of noninvasive measurability. We show that this notion is ambiguous between the weaker notion of disturbance at the operational level, and the stronger notion of invasiveness at the ontic level of properties of the system. Ontic noninvasiveness would be required to rule out MR per se but this property is not entailed by MR, and its presence cannot be established in a model-independent way. It follows that despite the formal parallels, Bell's and LG's inequalities are not methodologically on a par. We close with some reflections on the implications of our analysis for the pedagogy of quantum superposition.