Philosophy of Physics

The Bell inequalities can be violated by postselecting on the results of a measurement of the Bell states. If information about the original state preparation is available, we point out how the violation can be reproduced classically by postselecting on the basis of this information. We thus propose a variant of existing experiments that rules out such alternative explanations, by having the preparation and the postselection at spacelike separation. Unlike the timelike case where one can sharply distinguish Bell inequality violations based on pre- or postselection of a Bell state, in our scenario the distinction between these physical effects becomes foliation-dependent. We call this 'relativity of pre- and postselection' and conclude from it that quantum state evolution is not a fundamental process and that we should adopt an event-based Heisenbergian picture instead.

One of the key features of relativity theory is that the order in which events happen can be relative: it may depend on the frame of reference. This is the case whenever the two events are spacelike separated. To cope with this oddity, one stipulates that in such cases these events cannot have a causal effect on each other. This prevents the possibility of effects taking place before their causes (in some frame of reference). This idea is usually wrapped in the slogan "signals cannot travel faster than the speed of light".

Bell's Theorem demonstrates that quantum mechanics allows correlations between spacelike separated events. Now correlation does not imply causation and therefore there is no immediate contradiction with relativity theory. However, explaining these non-local correlations in a relativistic way is an ongoing challenge. One recurring idea is to take into account that these spacelike separated events share a common history. Usually, this includes the event where two systems were prepared jointly before being sent of to different locations. This is a form of what is called preselection.

Postselection is the idea of restricting the data of experiments to a subset. This concerns an event that lies in the common future of the two spacelike separated events and can also give rise to same non-local correlations as in the case of pre-selection. Preselection and postselection thus suggest distinct mechanisms for explaining the same non-local correlations. What we consider in this paper is a scenario where the event that correlates the two spacelike separated events is itself at spacelike separation from these two events. In this scenario, whether the correlating event acts as a preselection or a postselection thus depends on the frame of reference. We conclude that therefore there is no absolute physical distinction between preselection and postselection (at least in the context of experimental tests of Bell's Theorem).

There is a longstanding debate on the metaphysical relation between quantum states and the systems they describe. A series of relatively recent ψ-ontology theorems have been taken to show that, provided one accepts certain assumptions, "quantum states are real". In this paper I investigate the question of what that claim might be taken to mean in light of these theorems. It is argued that, even if one accepts the framework and assumptions employed by such theorems, such a conclusion is not warranted. Specifically, I argue that when a so-called ontic state is taken to describe the properties of a system, the relation between this state and some quantum state as established by ψ-ontology theorems, is not of the kind that would warrant counting the quantum state among these properties in any way.

In a series of papers Colbeck and Renner (2011, 2015a, 2015b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer (2014), Landsman (2015) and Leegwater (2016), I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.

A well known logical loophole for Bell's theorem is that it relies on setting independence: the assumption that the state of a system is independent of the settings of a measurement apparatus probing the system. In this paper the implications of rejecting this assumption are studied from an operationalist perspective. To this end a generalization of the ontic models framework is proposed that allows setting dependence. It is shown that within this framework Bell's theorem reduces to the conclusion that no-signaling requires randomness at the epistemic level even if the underlying ontology is taken to be deterministic. The ideas underlying the framework are further used to defend setting dependence against the charges of being incompatible with free will and scientific methodology. The paper ends however with the sketch of a new problem for setting dependence: a necessary gap between the ontic and the epistemic level that may prevent the formulation of a successful setting dependent theory.

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.

Recently Cator and Landsman made a comparison between Bell’s Theorem and Conway and Kochen’s Strong Free Will Theorem. Their overall conclusion was that the latter is stronger in that it uses fewer assumptions, but also that it has two shortcomings. Firstly, no experimental test of the Conway–Kochen Theorem has been performed thus far, and, secondly, because the Conway–Kochen Theorem is strongly connected to the Kochen–Specker Theorem it may be susceptible to the finite precision loophole of Meyer, Kent and Clifton. In this paper I show that the finite precision loophole does not apply to the Conway–Kochen Theorem.

In this paper I defend the tenability of the Thesis that the probability of a conditional equals the conditional probability of the consequent given the antecedent. This is done by adopting the view that the interpretation of a conditional may differ from context to context. Several triviality results are (re-)evaluated in this view as providing natural constraints on probabilities for conditionals and admissible changes in the interpretation. The context-sensitive approach is also used to re-interpret some of the intuitive rules for conditionals and probabilities such as Bayes' rule, Import-Export, and Modus Ponens. I will show that, contrary to consensus, the Thesis is in fact compatible with these re-interpreted rules.

At the 1927 Como conference Bohr spoke the famous words "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature." However, if the Copenhagen interpretation really adheres to this motto, why then is there this nagging feeling of conflict when comparing it with realist interpretations? Surely what one can say about nature should in a certain sense be interpretation independent. In this paper I take Bohr's motto seriously and develop a quantum logic that avoids assuming any form of realism as much as possible. To illustrate the non-triviality of this motto, a similar result is first derived for classical mechanics. It turns out that the logic for classical mechanics is a special case of the quantum logic thus derived. Some hints are provided as to how these logics are to be used in practical situations and finally, I discuss how some realist interpretations relate to these logics.

In this article von Neumann’s proposal that in quantum mechanics projections can be seen as propositions is followed. However, the quantum logic derived by Birkhoff and von Neumann is rejected due to the failure of the law of distributivity. The options for constructing a distributive logic while adhering to von Neumann’s proposal are investigated. This is done by rejecting the converse of the proposal, namely, that propositions can always be seen as projections. The result is a weakly Heyting algebra for describing the language of quantum mechanics.

Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To this end, we give a clear presentation of the hidden variable models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the Kochen–Specker theorem. Although we disagree with this last statement, the models do play a significant role in the discussion on the meaning of contextuality. In fact, we introduce a specific MKC-model of which we show that it is non-contextual and completely in agreement with quantum mechanical predictions. We also investigate the possibility of other definitions of non-contextuality—with an emphasis on operational definitions—and argue that any useful definition relies on the specification of a theoretical framework. It is therefore concluded that no experimental test can yield any conclusions about contextuality on a metaphysical level.