Why 3 + 1 metric rather than 4 + 0 or 2 + 2?

TL;DR

The paper explains why our universe's spacetime has a 3+1 signature rather than other configurations, using group theory to show that multiple time dimensions lead to physically unacceptable infinite-dimensional representations.

Contribution

It provides a group-theoretic explanation for the 3+1 signature of spacetime, highlighting why multiple time dimensions are physically implausible.

Findings

3+1 signature is favored due to finite-dimensional unitary representations

Higher-dimensional spaces with multiple time dimensions have infinite-dimensional representations

The approach applies to flat spaces of higher dimensions

Abstract

Why does the physical 4-dimensional space have a 3 + 1 signature rather than a 4 + 0 or a 2 + 2 for its metric? We give a simple explanation based largely on a group-theoretic argument a la Wigner. Applied to flat spaces of higher dimensions the same approach indicates that metrics with more than one time dimension are physically unacceptable because the corresponding irreducible unitary representations are infinite dimensional (besides the trivial representation).