A Principle to Determine the Number (3 + 1) of Large Spacetime Dimensions

TL;DR

This paper proposes an entropic principle to determine the number of large spacetime dimensions, suggesting our universe naturally emerges as a (3+1)-dimensional spacetime with specific properties from highly excited string states.

Contribution

It introduces an entropic principle-based approach to explain why our universe has three large spatial dimensions, linking string theory, entropy maximization, and cosmological evolution.

Findings

Final spacetime configuration is (3+1)-dimensional with specific matter content.

The universe emerges from highly excited strings with maximum entropy.

Supports evolution into our observed universe via the Banks-Fischler scenario.

Abstract

We assume that our universe originated from highly excited and interacting strings with coupling constant g_s = {\cal O} (1). Fluctuations of spacetime geometry are large in such strings and the physics dictating the emergence of a final spacetime configuration is not known. We propose that, nevertheless, it is determined by an entropic principle that the final spacetime configuration must have maximum entropy for a given amount of energy. This principle implies, under some assumptions, that the spacetime configuration that emerges finally is a (3 + 1) -- dimensional FRW universe filled with w = 1 perfect fluid and with 6 -- dimensional compact space of size l_s; in particular, the number of large spacetime dimensions is d = 3 + 1. Such an universe may evolve subsequently into our universe, perhaps as in Banks -- Fischler scenario.