Observed Spacetime Dimensionality from Fundamental Principles

TL;DR

This paper argues that the observed 3+1 spacetime dimensionality naturally arises from fundamental principles like causality and gauge invariance, and it explains the compactification of extra dimensions in higher theories.

Contribution

It provides a simple, principle-based explanation for the dimensionality of spacetime and the compactification of extra dimensions in string theory.

Findings

Spacetime dimensionality fixed at 3+1 by fundamental principles

Extra dimensions must be compactified for consistency

Approach offers internal consistency criteria for higher-dimensional theories

Abstract

It is shown by very simple arguments that the observed 3+1 dimensionality of spacetime may be understood on the basis of four fundamental principles of physics namely, Causality, General Covariance, Gauge Invariance and Renormalizability. This approach not therefore only fixes the spacetime dimensionality at 3+1, but also imposes the compactification of extra dimensions in higher dimensional theories based on these principles such as string theory as an internal consistency requirement rather than an external imposition.