When Is Measurement Dependence Conspiratorial?

Iñaki San Pedro

Indrajit Sen, Antony Valentini

This is the first of two papers that attempt to comprehensively analyse superdeterministic hidden-variables models of Bell correlations. We first give an overview of superdeterminism and discuss various criticisms of it raised in the literature. We argue that the most common criticism, the violation of ‘free-will’, is incorrect. We take up Bell’s intuitive criticism that these models are ‘conspiratorial’. To develop this further, we introduce non-equilibrium extensions of superdeterministic models. We show that the measurement statistics of these extended models depend on the physical system used to determine the measurement settings. This suggests a fine-tuning in order to eliminate this dependence from experimental observation. We also study the signalling properties of these extended models. We show that although they generally violate the formal no-signalling constraints, this violation cannot be equated to an actual signal. We therefore suggest that the so-called no-signalling constraints be more appropriately named the marginal-independence constraints. We discuss the mechanism by which marginal-independence is violated in superdeterministic models. Lastly, we consider a hypothetical scenario where two experimenters use the apparent-signalling of a superdeterministic model to communicate with each other. This scenario suggests another conspiratorial feature peculiar to superdeterminism. These suggestions are quantitatively developed in the second paper.

Szabó, László

T. N. Palmer

A locally causal hidden-variable theory of quantum physics need not be constrained by the Bell inequalities if this theory also partially violates the measurement independence condition. However, such violation can appear unphysical, implying implausible conspiratorial correlations between the hidden variables of particles being measured and earlier determinants of instrumental settings. A novel physically plausible explanation for such correlations is proposed, based on the hypothesis that states of physical reality lie precisely on a non-computational measure-zero dynamically invariant set in the state space of the universe: the Cosmological Invariant Set Postulate. To illustrate the relevance of the concept of a global invariant set, a simple analogy is considered where a massive object is propelled into a black hole depending on the decay of a radioactive atom. It is claimed that a locally causal hidden-variable theory constrained by the Cosmological Invariant Set Postulate can violate the Clauser-Horne-Shimony-Holt inequality without being conspiratorial, superdeterministic, fine-tuned or retrocausal, and the theory readily accommodates the classical compatibilist notion of (experimenter) free will.

Indrajit Sen, Antony Valentini

We prove that superdeterministic models of quantum mechanics are conspiratorial in a mathematically well-defined sense, by further development of the ideas presented in a previous article A . We consider a Bell scenario where, in each run and at each wing, the experimenter chooses one of N devices to determine the local measurement setting. We prove, without assuming any features of quantum statistics, that superdeterministic models of this scenario must have a finely tuned distribution of hidden variables. Specifically, fine-tuning is required so that the measurement statistics depend on the measurement settings but not on the details of how the settings are chosen. We quantify this as the overhead fine-tuning F of the model, and show that F > 0 (corresponding to ‘fine-tuned’) for any N > 1. The notion of fine-tuning assumes that arbitrary (‘non-equilibrium’) hidden-variables distributions are possible in principle. We also show how to quantify superdeterministic conspiracy without using non-equilibrium. This second approach is based on the fact that superdeterministic correlations can mimic actual signalling. We argue that an analogous situation occurs in equilibrium where, for every run, the devices that the hidden variables are correlated with are coincidentally the same as the devices in fact used. This results in extremely large superdeterministic correlations, which we quantify as a drop of an appropriately defined formal entropy. Non-local and retrocausal models turn out to be non-conspiratorial according to both approaches.

Paul Busch, PEKKA J. LAHTI