On the dimensionality of spacetime

TL;DR

This paper discusses why our universe has 3+1 dimensions, arguing that other dimensionalities lack the physical properties necessary for observers and stable structures, thus explaining the observed spacetime dimensionality.

Contribution

It presents a theoretical argument that only 3+1-dimensional spacetime can support observers and stable structures, explaining the observed dimensionality among multiple string theory limits.

Findings

Higher than 3+1 dimensions lack stable structures.

Fewer than 3+1 dimensions cannot support gravity or complexity.

More or less than one time dimension impairs predictability.

Abstract

Some superstring theories have more than one effective low-energy limit, corresponding to classical spacetimes with different dimensionalities. We argue that all but the 3+1-dimensional one might correspond to ``dead worlds'', devoid of observers, in which case all such ensemble theories would actually predict that we should find ourselves inhabiting a 3+1-dimensional spacetime. With more or less than one time-dimension, the partial differential equations of nature would lack the hyperbolicity property that enables observers to make predictions. In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures. A space with less than three dimensions allows no gravitational force and may be too simple and barren to contain observers.