The Solution to the Problem of Time in Shape Dynamics

Abstract

The absence of unique time evolution in Einstein's spacetime description of gravity leads to the hitherto unresolved `problem of time' in quantum gravity. Shape Dynamics is an objectively equivalent representation of gravity that trades spacetime refoliation invariance for three-dimensional conformal invariance. Its logical completion presented here gives a dimensionless description of gravitational dynamics. We show that in this framework the classical problem of time is completely solved. Since a comparable definitive solution is impossible within the spacetime description, we believe Shape Dynamics provides a key ingredient for the creation of quantum gravity.

14 pages, no figures

References in corpus (5)

• Quantum Gravity at a Lifshitz Point
• Problem of Time in Quantum Gravity
• Einstein gravity as a 3D conformally invariant theory
• The Superspace of Geometrodynamics
• Scale Anomaly as the Origin of Time

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• Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
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• Quantum gravity in timeless configuration space
• Extracting Geometry from Quantum Spacetime: Obstacles down the road
• Measuring time in a timeless universe
• The shape dynamics description of gravity
• Relational Mechanics as a gauge theory
• Regarding the `Hole Argument' and the `Problem of Time'
• An algebraic approach to the "frozen formalism" problem of time
• Shape Dynamical Loop Gravity from a Conformal Immirzi Parameter
• An extension of cosmological dynamics with York time