Transformity: The Dependence of the Laws of Physics on Higher-Dimensional Coordinate Transformations

TL;DR

This paper explores how physical laws in higher-dimensional theories depend on coordinate choices, revealing a gauge dependence that challenges traditional views of physics and demonstrates equivalence to flat five-dimensional space.

Contribution

It introduces the concept of transformity, showing that physical laws in higher dimensions depend on coordinate transformations, with implications for the philosophy of physics.

Findings

Physical laws depend on higher-dimensional coordinate choices.

Examples include cosmological models and quantum matter waves.

Both examples are equivalent to flat five-dimensional space.

Abstract

In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in (say) five dimensions is broader than in spacetime. This kind of gauge dependence is illustrated by two examples: a cosmological model in general relativity and a matter wave in quantum theory. Surprisingly, both are equivalent by coordinate transformations to flat featureless five-dimensional space. This kind of transformity is of fundamental significance for the philosophy of physics.