Determinism and Quantum Mechanics with time Bell inequalities

TL;DR

This paper introduces a new definition of determinism encompassing the environment, derives time Bell inequalities under these assumptions, and demonstrates their violation by quantum mechanics, exemplified through spin 1/2 particle measurements.

Contribution

It presents a novel formulation of determinism including environmental factors and derives time Bell inequalities that are violated by quantum mechanics.

Findings

Time Bell inequalities are violated by quantum mechanics.

Determinism can be extended to include the environment.

Quantum measurements on spin 1/2 particles violate these inequalities.

Abstract

We propose a definition of determinism for a physical system that includes, besides the measurement device, the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial conditions that play the role of hidden variables for the experiment. These assumptions, which are different from realism, allow us to derive a type of time Bell inequalities, which are violated by Quantum Mechanics. In order to illustrate this violation, we discuss the particular case of measurements on a spin 1/2 particle.