Skeptical Notes on a Physics of Passage

TL;DR

This paper critically examines the mathematical representation of time in physics, questioning whether the current real-number framework can accommodate a concept of passage and analyzing the viability of causal set theory as a physics of passage.

Contribution

It provides a philosophical and mathematical critique of the idea that physics should incorporate a notion of passage of time, and evaluates causal set theory in this context.

Findings

Current mathematical framework resists incorporating passage of time.

Arguments for passage based on experience are challenged.

Causal set theory does not convincingly provide a physics of passage.

Abstract

This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question of the paper is whether the existing representation of time is adequate, or whether it can or should be supplemented: especially, do we need a physics incorporating some kind of `dynamical passage' of time? The paper argues that the existing mathematical framework is resistant to such changes, and might have to be rejected by anyone seeking a physics of passage. Then it rebuts two common arguments for incorporating passage into physics, especially the claim that it is an element of experience. Finally the paper investigates whether, as has been claimed, `causal set theory' provides a physics of passage.