Abstract
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.
Highlights
It is well known that a locally causal hidden-variable theory of quantum physics need not be constrained by the Bell inequalities if this theory violates the measurement independence condition ρ(λ|a, b) = ρ(λ|a, b ), (1.1)2015 The Authors
We have presented a new approach to formulating a locally causal hidden-variable theory of quantum physics, in which the measurement independence condition is partially violated without conspiracy, superdeterminism, retrocausality, fine-tuning and without denying experimenter free will
The key ingredient in this approach is the global invariant set; the notion that globally defined invariant subsets of state space define the notion of physical reality
Summary
We consider the temporal correlation between the size of the black hole at t0, as determined by the radius of its event horizon H +(t0), and the (supposed) hidden variable of the radioactive atom at t1 The existence of such a correlation, even when t0 t1, is easy to understand (without conspiracy or retrocausality) if we take into account the fact that H + is a globally defined invariant subset of space–time. To avoid requiring some implausible conspiracy, the physicist may conclude that there may be a retrocausal effect by which information, associated with the decay of the radioactive atom, propagates back in time causing the black hole event horizon to expand at earlier times In this case, there is a simple explanation for the correlation which requires neither conspiracy nor retrocausality.
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