The existence of time

TL;DR

This paper explores how time can be viewed as a derived property within certain gauge theories of gravity, particularly through the structures arising from biconformal gauging of conformal groups.

Contribution

It demonstrates that time emerges as a derived property in biconformal gauge theories of gravity with Euclidean or zero signature spaces, linking geometric structures to the nature of time.

Findings

Existence of conjugate, orthogonal, metric submanifolds depends on space signature.

Configuration space in Euclidean cases must be Lorentzian.

Time can be interpreted as a derived property of the geometric structures.

Abstract

Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.