Introduction

Our aim in this chapter is to extend the Bell inequality discussion in Chapter 17 to its temporal analogue, known as the Leggett–Garg (LG) inequality.

Bell inequalities involve spatial nonlocality, that is, signal observations distributed over space. It was shown by Leggett and Garg that analogous inequalities involving temporal nonlocality can be formulated (Leggett and Garg, 1985). We shall discuss one of these, known as the LG inequality.

We saw in Chapter 17 that Bell inequalities are based on certain classical mechanics (CM) assumptions about the nature of reality. Likewise, the LG inequality is based on two CM principles that are not incorporated into quantum mechanics (QM).

This principle is a foundational principle in CM but is incompatible with QM in at least two ways. First, it is vacuous, as it asserts the truth of a proposition in the absence of empirical validation: how can we define the concept of always, without introducing counterfactuality? Second, it is violated in quantum theory, for instance, in path integral calculations.

This principle in embedded in the nexus of issues explored in this book. The quantized detector network (QDN) version of it takes the form “If any SUO can be observed in any number of possible states, then it will be observed in one of them in any run.” This is a near tautology. The classical version says the same thing but makes an additional assertion about something going on in the absence of observation, which is the vacuous element that QM cannot accept.

This principle is subtle. We experience its apparent validity all the time in our ordinary lives: we look at objects and they appear not to change by those acts of observation.