Comment on “Bell’s Theorem Versus Local Realism in a Quaternionic Model of Physical Space”

Richard D Gill

doi:10.1109/access.2021.3127572

Abstract

I point out critical errors in the paper "Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space" by J. Christian, published in IEEE Access. Christian's paper in fact contains several conflicting models. None of them form counterexamples to Bell's theorem. Most of Christian's paper is devoted to a model based on the detection loophole due to Pearle (1970).

Highlights

Bell’s 1964 theorem [1] states that the conventional framework of quantum mechanics is incompatible with a physical principle called local realism
Christian (2019) [4] claims in IEEE Access that the usual proof of this inequality depends on an incorrect physical assumption
CHRISTIAN’S ARGUMENT CONTRA BELL The physical assumptions of local realism lead to a mathematical model for a Bell-CHSH type experiment where Alice and Bob each toss a coin to select a measurement setting on a measurement apparatus, and go on to observe a binary outcome, of the following form

Summary

INTRODUCTION

Bell’s 1964 theorem [1] states that the conventional framework of quantum mechanics is incompatible with a physical principle called local realism. CHRISTIAN’S ARGUMENT CONTRA BELL The physical assumptions of local realism lead to a mathematical model for a Bell-CHSH type experiment where Alice and Bob each toss a coin to select a measurement setting on a measurement apparatus, and go on to observe a binary outcome, of the following form. For very sound reasons (in experiments one does not observe perfect anti-correlation at equal settings; at best, only approximate anti-correlation) Bell and the whole community rapidly adopted the CHSH inequality and allowed for further randomness at the measurement locations Given these assumptions, let us take a look at the following expression Z := X1Y1 − X1Y2 − X2Y1 − X2Y2. It turned out that experiments could be done which violated consequences of the initial assumptions

CHRISTIAN’S FIRST MODEL

CHRISTIAN’S SECOND MODEL

CONCLUSION