Time, the arrow of time, and Quantum Mechanics

TL;DR

The paper argues that any viable physical theory must include a notion of time with an arrow, and explores this concept within a deterministic cellular automaton interpretation of quantum mechanics.

Contribution

It introduces the idea that time is fundamental in physical theories and discusses the arrow of time within a cellular automaton interpretation of quantum mechanics.

Findings

Time is essential in physical theories; theories without it do not exist.

The arrow of time can be uniquely defined even locally.

The cellular automaton interpretation offers insights into the nature of time and reversibility.

Abstract

It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost by definition, time has an arrow. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. We explain these statements in terms of the author's favoured deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as `vector space analysis', and expand on these ideas.