In this paper, I challenge the widespread view that Measurement Independence adequately represents the requirement that EPR experimenters have free will.Measurement Independence is most commonly taken as a necessary condition for free will.A number of implicit assumptions can be identified in this regard, all of which can be challenged on their own grounds.As a result, I conclude that Measurement Independence-type conditions are not to be justified by appealing to the preservation of the EPR experimenters' free will.* Some of the ideas presented in this work were developed during discussion in the context of a broader project, also on the relation between free will and No-conspiracy, in collaboration with Miklós Rédei.I thank him for his dedication and generosity.
In this paper, I challenge the widespread view that Measurement Independence adequately represents the requirement that EPR experimenters have free will.Measurement Independence is most commonly taken as a necessary condition for free will.A number of implicit assumptions can be identified in this regard, all of which can be challenged on their own grounds.As a result, I conclude that Measurement Independence-type conditions are not to be justified by appealing to the preservation of the EPR experimenters' free will.* Some of the ideas presented in this work were developed during discussion in the context of a broader project, also on the relation between free will and No-conspiracy, in collaboration with Miklós Rédei.I thank him for his dedication and generosity.
In this paper I assess the adequacy of no-conspiracy conditions present in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these can not be ruled out. I argue that an appropriate common cause explanation requires that no-conspiracy conditions are re-interpreted as mere common cause-measurement independence conditions. Violations of measurement independence thus need not entail any kind of conspiracy (nor backwards in time causation). This new reading of measurement dependence provides the grounds for an explicitly non-factorizable (in the sense of Bell’s factorizability) common cause model for EPR. 1
Physics has long lived with a schizophrenia that desires determinism for measured systems while demanding that experimenters decide what to measure on a whim. Intriguingly, such a free will assumption for experimenters has thwarted many attempts to provide a satisfactory explanation of how quantum probabilities evolve to clear-cut measurements. An overview of this quantum measurement problem is presented without equations, and the lesson is drawn that denial of experimenters' free will may be the only workable solutions. If the free will assumption is rejected, then a door is open that may ultimately reconcile quantum mechanics with the definiteness of individual experiments. A holistic view is offered for an Escher-like self-consistent space-time net of events rather than a conspiracy of initial conditions as a way forward.
Superdeterminism has received recent attention as a possible path toward a locally causal explanation of the entanglement correlations that appear in experimental tests of Bell's theorem. While the term `superdeterminism' was coined by Bell to refer to restrictions on the free will of experimenters, it was not rigorously defined until recently. It has now been defined as a property of any physical theory that produces systematic violations of statistical independence. Here we focus on formalizing the requirements that being nonsuperdeterministic places on a physical theory, and setting a standard that must be met before we can conclude that a given theory is not superdeterministic. We begin by carefully examining how a physical theory determines what outcomes we observe when performing measurements in terms of ontic states and response functions, and how this differs between superdeterministic and nonsuperdeterministic theories, in terms of the behavior of the types of vetted random sampling procedures that we use in experiments. The core result is that individual samples and measurement outcomes must be representative of the observed distributions, which is explained in detail. This also has a bearing on how measurement settings are chosen by agents, whether freely or randomly, and we argue that this standard ultimately defines what freedom/independence actually mean. We then discuss contextuality, and show that in most cases, superdeterminism is contextual. Finally, we discuss how different physical theories, with different notions of ontic states and response functions, can give rise to the same empirical data, and how the same operational contextuality may appear in different forms.
The concept of 'super-indeterminism' captures the notion that the free choice assumption of orthodox quantum mechanics necessitates only the following requirement: an agent's free-choice performance in the selection of measurement settings must not represent an exception to the rule of irreducible quantum indeterminism in the physical universe (i.e, "universal indeterminism"). Any additional metaphysical speculation, such as to whether quantum indeterminism, i.e., intrinsic randomness, implicates the reality of experimenter "freedom", "free will", or "free choice", is redundant in relation to the predictive success of orthodox quantum mechanics. Accordingly, super-indeterminism views as redundant also, from a technical standpoint, whether an affirmative or a negative answer is claimed in reference to universal indeterminism as a necessary precondition for experimenter freedom. Super-indeterminism accounts, for example, for the circular reasoning which is implicit in the free will theorem by Conway and Kochen [1,2]. The concept of super-indeterminism is of great assistance in clarifying the often misunderstood meaning of the concept of "free variables" as used by John Bell [3]. The present work argues that Bell sought an operational, effective free will theorem , one based upon the notion of "determinism without predetermination", i.e., one wherein "free variables" represent universally uncomputable variables. In conclusion, the standard interpretation of quantum theory does not answer, and does not need to answer in order to ensure the predictive success of orthodox theory, the question of whether either incompatibilism or compatibilism is valid in relation to free-will metaphysics and to the free-will phenomenology of experimenter agents in quantum mechanics.
We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula E(AB∣a,b)=∫A(a,b,λ)B(a,b,λ)ρ(λ)dλ follows from the logic of plausible reasoning (the objective Bayesian interpretation of probability theory) taken alone, without any further assumptions about realism. The space Λ, usually interpreted as some space of `hidden variables', can be constructed for an arbitrary `field of discourse' using Stone's theorem. The rejection of superdeterminism follows from logical independence -- the non-existence of information which suggest a dependence -- of the free decisions of the experimenters from everything else. To prove the Bell inequality it is, then, sufficient to reduce this to E(AB∣a,b)=∫A(a,λ)B(b,λ)ρ(λ)dλ. This follows for space-like separated measurements from Einstein causality alone. So, the consequence of the violation of Bell's inequality is that Einstein causality has been empirically falsified, without any loopholes left. We consider and reject the idea of weakening the logic of plausible reasoning could be used to create a loophole. Finally, we discuss what can be used to replace Einstein causality. While weak (signal) Einstein causality holds, it follows either from a notion of strong causality or from human inability to prepare states which violate quantum uncertainty, which makes it uninteresting for fundamental considerations. A notion of strong causality has either unacceptable causal loops or requires a hidden preferred frame. Given that a hidden preferred frame is completely compatible with modern physics, it is argued that this choice is preferable.
'In the ontological models framework [Harrigan & Spekkens 2007], it is assumed that the probability measure representing a quantum state is independent of the choice of future measurement setting.' (Leifer 2014, 140) In this recently-unearthed piece I discuss a version of the above assumption, concluding that it is 'very difficult to justify on metaphysical grounds'. I note that abandoning it has an interesting potential payoff, given its crucial role in the no-go theorems of Bell and of Kochen & Specker. There has been increased interest in this option in recent years, under the label of retrocausal models of QM (see, e.g., Price & Wharton 2015, Wharton & Argaman 2020). The present piece may be of interest to diligent historians of this approach. It was written in 1978, while I was a graduate student in Cambridge.