Quantum mechanics has irked physicists ever since its conception more than 100 years ago. While some of the misgivings, such as it being unintuitive, are merely aesthetic, quantum mechanics has one serious shortcoming: it lacks a physical description of the measurement process. This ``measurement problem'' indicates that quantum mechanics is at least an incomplete theory -- good as far as it goes, but missing a piece -- or, more radically, is in need of complete overhaul. Here we describe an approach which may provide this sought-for completion or replacement: Superdeterminism. A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent nonlocality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way.
Quantum mechanics has irked physicists ever since its conception more than 100 years ago. While some of the misgivings, such as it being unintuitive, are merely aesthetic, quantum mechanics has one serious shortcoming: it lacks a physical description of the measurement process. This ``measurement problem'' indicates that quantum mechanics is at least an incomplete theory -- good as far as it goes, but missing a piece -- or, more radically, is in need of complete overhaul. Here we describe an approach which may provide this sought-for completion or replacement: Superdeterminism. A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent nonlocality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way.
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 violation of Bell inequalities seems to establish an important fact about the world: that it is non-local. However, this result relies on the assumption of the statistical independence of the measurement settings with respect to potential past events that might have determined them. Superdeterminism refers to the view that a local, and determinist, account of Bell inequalities violations is possible, by rejecting this assumption of statistical independence. We examine and clarify various problems with superdeterminism, looking in particular at its consequences on the nature of scientific laws and scientific reasoning. We argue that the view requires a neo-Humean account of at least some laws, and creates a significant problem for the use of statistical independence in other parts of physics and science more generally.
The violation of Bell inequalities seems to establish an important fact about the world: that it is non-local. However, this result relies on the assumption of the statistical independence of the measurement settings with respect to potential past events that might have determined them. Superdeterminism refers to the view that a local, and determinist, account of Bell inequalities violations is possible, by rejecting this assumption of statistical independence. We examine and clarify various problems with superdeterminism, looking in particular at its consequences on the nature of scientific laws and scientific reasoning. We argue that the view requires a neo-Humean account of at least some laws, and creates a significant problem for the use of statistical independence in other parts of physics and science more generally.
A recent proposal for a superdeterministic account of quantum mechanics, named Invariant-set theory, appears to bring ideas from several diverse fields like chaos theory, number theory and dynamical systems to quantum foundations. However, a clear cut hidden-variable model has not been developed, which makes it difficult to assess the Proposal from a quantum foundational perspective. In this article, we first build a hidden-variable model based on the Proposal, and then critically analyse several aspects of the Proposal using the model. We show that several arguments related to counter-factual measurements, nonlocality, non-commutativity of quantum observables, measurement independence etcetera that appear to work in the Proposal fail when considered in our model. We further show that our model is not only superdeterministic but also nonlocal, with an ontic quantum state. We argue that the bit string defined in the model is a hidden variable and that it contains redundant information. Lastly, we apply the analysis developed in a previous work (Sen I, Valentini A, 2020 Proc. R. Soc. A , 476 , 20200214) to illustrate the issue of superdeterministic conspiracy in the model. Our results lend further support to the view that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.
Abstract Bell’s theorem demonstrates that any physical theory that is consistent with the predictions of quantum mechanics, and which satisfies some apparently innocuous assumptions, must violate the principle of local causality . It may therefore be possible to maintain local causality by rejecting one of these other assumptions instead. One possibility that has recently received significant attention involves rejecting the principle of statistical independence (SI). In this paper, we consider the frequency interpretation of SI, which states that ρ(λ)≈ρ(λ∣Z) , where ρ(λ) is the relative frequency of an element of an ensemble being in the state λ , and Z is a label that separates the ensemble into apparently randomly selected sub-ensembles. SI is violated when the sub-ensemble frequency ρ(λ∣Z) fails to be representative of the ensemble frequency ρ(λ) . We argue that physical theories that systematically violate SI should all be understood as superdeterministic . This perspective on SI sheds light on a number of issues that are being debated in the superdeterminism literature, especially concerning its scope and philosophical consequences. Regarding scope, we argue that superdeterministic theories fall into three categories, deterministic theories with fine-tuned initial conditions, fluke theories, and nomic exclusion theories. We also argue that retrocausal and invariant set theories need not violate SI, which is contrary to how they are normally presented. Regarding philosophical implications, we argue that superdeterminism is incompatible with free will according to some prominent compatibilist accounts. We also argue that although superdeterminism is conspiratorial, it is not unscientific, but pre-scientific.
Tests of Bell's theorem rule out local hidden variables theories. But any theorem is only as good as the assumptions that go into it, and one of these assumptions is that the experimenter can freely choose the detector settings. Without this assumption, one enters the realm of superdeterministic hidden variables theories and can no longer use Bell's theorem as a criterion. One can like or not like such superdeterministic hidden variables theories and their inevitable nonlocality, the real question is how one can test them. Here, we propose a possible experiment that could reveal superdeterminism.