The Bell experiment and the Limitations of Actors

TL;DR

This paper examines the limitations of actors' reasoning in Bell experiments, showing that their mental constraints prevent them from fully applying the CHSH inequality for decision-making.

Contribution

It introduces a framework where actors' limited Hilbert spaces restrict their ability to derive the CHSH inequality in Bell experiments.

Findings

Actors with limited Hilbert spaces cannot derive the CHSH inequality.

No rational decision-maker can be convinced by the CHSH argument in Bell experiments.

Quantum theory reconstruction applies to decision processes under cognitive limitations.

Abstract

The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up certain background themes before I enter a discussion of Alice's analysis of the situation. An important point is that her mind is limited by the fact that her Hilbert space in this context is two-dimensional. General statements about a mind's limitation during a decision process are derived from recent results on the reconstruction of quantum theory from conceptual variables. These results apply to any decision situation. Let all the data from the Bell experiment be handed over to a new actor Charlie, who performs a data analysis. But his mind is also limited: He has a four-dimensional Hilbert space in the context determined by the experiment. I show that this implies that neither Alice nor Charlie can have the argument leading to the CHSH inequality as a background for making decisions related to the experiment. Charlie may be any data analyst, and he may communicate with any person. It is argued that no rational person can be convinced by the CHSH argument when making empirical decisions on the Bell situation.