Logic and String Theory

TL;DR

This paper explores how Peircean relational logic and category theory can underpin string theory and quantum mechanics, proposing a new conceptual framework for unifying fundamental physics.

Contribution

It introduces a categorical algebra based on Peircean logic that naturally derives quantum laws and links to string theory through group structures like W_infinity.

Findings

Relational logic yields fundamental quantum laws

Categorical algebra generates W_infinity group

Connections established between logic, string theory, and quantum mechanics

Abstract

The unification of Quantum Mechanics and General Relativity remains the primary goal of Theoretical Physics, with string theory appearing as the only plausible unifying scheme. In the present work, in a search of the conceptual foundations of string theory, we analyze the relational logic developed by C. S. Peirce in the late nineteenth century. The Peircean logic has the mathematical structure of a category with the relation $R_{ij}$ among two individual terms $S_i$ and $S_j$, serving as an arrow (or morphism). We introduce a realization of the corresponding categorical algebra of compositions, which naturally gives rise to the fundamental quantum laws, thus underscoring the relational character of Quantum Mechanic. The same relational algebra generates a number of group structures, among them $W_{\infty}$. The group $W_{\infty}$ is embodied and realized by the matrix models, themselves closely linked with string theory. It is suggested that relational logic and in general category theory may provide a new paradigm, within which to develop modern physical theories.