Natural discrete differential calculus in physics

TL;DR

This paper discusses how discrete differential calculus inherently provides additional structure needed for physical theories, unlike traditional calculus which requires extra definitions like metrics or duals.

Contribution

It demonstrates that discrete differential calculus naturally supplies the structures needed for physics without additional assumptions.

Findings

Discrete calculus offers built-in structures for physics.

Traditional calculus requires extra structures like metrics.

Discrete approach simplifies the mathematical framework for physical theories.

Abstract

We sharpen a recent observation by Tim Maudlin: differential calculus is a natural language for physics only if additional structure, like the definition of a Hodge dual or a metric, is given; but the discrete version of this calculus provides this additional structure for free.