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.
The Existence of TimeInternational Journal of Geometric Methods in Modern Physics
Citation InformationSpencer, J. A. and Wheeler, James T., The existence of time, International Journal of Geometric Methods in Modern Physics, Vol. 8 No. 2 (2011) 273-301.