Higher Dimensions

Abstract

The invariance group of mechanics and field theory tells us that space has three dimensions, and space-time four. Nearly all physical theory uses these numbers without consideration. There are various approaches to defining a dimension, as we discussed in Sect. 5.7, but for physics, the ordinary four space-time dimensions are anchored in the form of the field equations. We shall first answer the question of the reasons that indicate that there are just four dimensions for space [7]. Three reasons are fundamental: