Is there a physical continuum?

TL;DR

This paper explores whether the physical world necessarily involves a continuum by modeling the brain and demonstrating that some physical quantities must be continuous under natural assumptions.

Contribution

It introduces a simple brain model to argue that a continuum is essential for certain physical quantities, challenging the idea that the universe could be purely discrete.

Findings

The continuum is necessary for some physical quantities.

A simple brain model supports the existence of a continuum.

Challenges the notion of a fully discrete physical universe.

Abstract

We are used to the fact that most if not all physical theories are based on the set of real numbers (or another associative division algebra). These all have a cardinality larger than that of the natural numbers, i.e. form a continuum. It is often asked, whether there really is a continuum in the physical world, or whether a future physical theory could work with just countable infinities. The latter could for example be compatible with a quantized space-time. In this paper we formulate a simple model of the brain and show that within the presented natural assumptions, the continuum has to exist for at least some physical quantities.