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Physical Review Letters

Realism and quantum flux tunneling

L. E. Ballentine

Published Oct 5, 1987• 45 citations
Publisher

Abstract

Leggett and Garg have argued that the phenomenon of quantum flux tunneling oscillations will, according to the predictions of quantum mechanics, contradict the pair of assumptions ``macroscopic realism'' and ``noninvasive measurability.'' It is argued here that there can be no contradiction of realism in such a case, and that the contradiction is between quantum mechanics and noninvasive measurability.

DOI
10.1103/physrevlett.59.1493

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Leggett and Garg have argued that the phenomenon of quantum flux tunneling oscillations will, according to the predictions of quantum mechanics, contradict the pair of assumptions macroscopic realism'' and noninvasive measurability.'' It is argued here that there can be no contradiction of realism in such a case, and that the contradiction is between quantum mechanics and noninvasive measurability.
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.
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.
Macroscopic realism is the thesis that macroscopically observable properties must always have definite values. The idea was introduced by Leggett and Garg (1985), who wished to show a conflict with the predictions of quantum theory, by using it to derive an inequality that quantum theory violates. However, Leggett and Garg's analysis required not just the assumption of macroscopic realism per se, but also that the observable properties could be measured non-invasively. In recent years there has been increasing interest in experimental tests of the violation of the Leggett-Garg inequality, but it has remained a matter of controversy whether this second assumption is a reasonable requirement for a macroscopic realist view of quantum theory. In a recent critical assessment Maroney and Timpson (2014) identified three different categories of macroscopic realism, and argued that only the simplest category could be ruled out by Leggett-Garg inequality violations. Allen, Maroney, and Gogioso (2016) then showed that the second of these approaches was also incompatible with quantum theory in Hilbert spaces of dimension 4 or higher. However, we show that the distinction introduced by Maroney and Timpson between the second and third approaches is not noise tolerant, so unfortunately Allen's result, as given, is not directly empirically testable. In this paper we replace Maroney and Timpson's three categories with a parameterization of macroscopic realist models, which can be related to experimental observations in a noise tolerant way, and recover the original definitions in the noise-free limit. We show how this parameterization can be used to experimentally rule out classes of macroscopic realism in Hilbert spaces of dimension 3 or higher, without any use of the non-invasive measurability assumption. Even for relatively low precision experiments, this will rule out the original category of macroscopic realism, that is tested by the Leggett-Garg inequality, while as the precision of the experiments increases, all cases of the second category and many cases of the third category, will become experimentally ruled out.
In a recent paper, I have analysed and criticised Leggett and Garg’s argument to the effect that macroscopic realism contradicts quantum mechanics, by contrasting their assumptions to the example of Bell’s stochastic pilot-wave theories, and have applied Dzhafarov and Kujala’s analysis of contextuality in the presence of signalling to the case of the Leggett–Garg inequalities. In this chapter, I discuss more in general the motivations for macroscopic realism, taking a cue from Einstein’s criticism of the Bohm theory, then go on to summarise my previous results, with a few additional comments on other recent work on Leggett and Garg. [To appear in: E. Dzhafarov (ed.), Contextuality from Quantum Physics to Psychology (Singapore: World Scientific).]
In 1985, Leggett and Garg put forward the concept of macroscopic realism (macrorealism) and, in analogy to Bell's theorem, derived a necessary condition in terms of inequalities, which are now known as the Leggett-Garg inequalities. In this paper, we discuss another necessary condition called no-signaling in time. It solely bases on comparing the probability distribution for a macrovariable at some time for the cases where previously a measurement has or has not been performed. Although the concept is analogous to the no-signaling condition in the case of Bell tests, it can be violated according to quantum mechanical predictions even in situations where no violation of Leggett-Garg inequalities is possible.