The Meaning of Dimensions

TL;DR

This paper reviews the concept of dimensions across philosophy and physics, emphasizing their subjective yet essential nature, and discusses the implications of higher dimensions in physical theories.

Contribution

It provides a comprehensive overview of the historical and conceptual development of dimensions, highlighting the importance of careful integration of higher dimensions in physics.

Findings

Dimensions are subjective but serve as essential bookkeeping tools.

The number of dimensions increases with advances in physics.

Higher dimensions likely exist beyond the familiar four, requiring careful theoretical embedding.

Abstract

We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of book-keeping device, their number increasing as required by advances in physics. The world almost certainly has more than the four dimensions of space and time, but the introduction of the fifth and higher dimensions requires a careful approach wherein known results are embedded and new ones are couched in the most productive manner.