The existence of time

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.

21 pages (Reduced to clarify and focus on central argument; some calculations condensed; typos corrected)

References in corpus (2)

• Fourth order Weyl gravity
• Quantum mechanics as a measurement theory on biconformal space

Cited by in corpus (10)

• Weyl gauge theories of gravity do not predict a second clock effect
• Nonmetricity theories and aspects of gauge symmetry
• Study of the geodesic equations of a spherical symmetric spacetime in conformal gravity
• Note on the absence of the second clock effect in Weyl gauge theories of gravity
• Time and dark matter from the conformal symmetries of Euclidean space
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• General relativity as a biconformal gauge theory
• Constructing an Explicit AdS/CFT Correspondence with Cartan Geometry
• Dynamical spacetime symmetry
• Yang-Mills sources in biconformal gravity