From statistical dependence to the space of possible superdeterministic theories (2509.23047v1)

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 $\rho(\lambda) \approx \rho(\lambda | Z)$, where $\rho(\lambda)$ is the relative frequency of an element of an ensemble being in the state $\lambda$, and $Z$ is a label that separates the ensemble into apparently randomly selected sub-ensembles. SI is violated when the sub-ensemble frequency $\rho(\lambda | Z)$ fails to be representative of the ensemble frequency $\rho(\lambda)$. 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.