Indeterminism in Physics and Intuitionistic Mathematics

TL;DR

This paper explores how intuitionistic mathematics could provide a mathematical framework that naturally incorporates indeterminism and the passage of time, potentially resolving issues like the measurement problem in quantum mechanics.

Contribution

It proposes intuitionistic mathematics as an alternative to classical mathematics for modeling indeterminism and temporal evolution in physical theories.

Findings

Intuitionistic mathematics can model indeterminism.

Classical mathematics may limit understanding of temporal passage.

Potential to address quantum measurement problem.

Abstract

Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to "speak" of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We argue that intuitionistic mathematics provides such a language and we illustrate it in simple terms.