Elements of Reality and the Failure of the Product Rule Measurability of Commuting Observables

TL;DR

This paper analyzes the concept of elements of reality in quantum theory, showing they fail the product rule and discussing implications for Lorentz-invariant interpretations of quantum mechanics.

Contribution

It introduces a generalized concept of elements of reality that restores Lorentz-invariance by abandoning the product rule and explores the consequences of this change.

Findings

Elements of reality do not satisfy the product rule.

Lorentz-invariance can be achieved by abandoning the product rule.

The 'and' rule must also be abandoned for consistency.

Abstract

The concept of ``elements of reality" is analyzed within the framework of quantum theory. It is shown that elements of reality fail to fulfill the product rule. This is the core of recent proofs of the impossibility of a Lorentz-invariant interpretation of quantum mechanics. A generalization and extension of the concept of elements of reality is presented. Lorentz-invariance is restored by giving up the product rule. The consequences of giving up the ``and" rule, which must be abandoned together with the product rule, are discussed.