Hypothesis on the Nature of Time

Abstract

We present numerical evidence that fictitious diffusing particles in the causal dynamical triangulation (CDT) approach to quantum gravity exceed the speed of light on small distance scales. We argue this superluminal behaviour is responsible for the appearance of dimensional reduction in the spectral dimension. By axiomatically enforcing a scale invariant speed of light we show that time must dilate as a function of relative scale, just as it does as a function of relative velocity. By calculating the Hausdorff dimension of CDT diffusion paths we present a seemingly equivalent dual description in terms of a scale dependent Wick rotation of the metric. Such a modification to the nature of time may also have relevance for other approaches to quantum gravity.

15 pages, 4 figures. Conforms with version to be published in PRD. Clarifications and references added

References in corpus (10)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Fractal properties of quantum spacetime
• The Nonperturbative Quantum de Sitter Universe
• Diffusion on $\kappa$-Minkowski space
• Vacuum Fluctuations and the Small Scale Structure of Spacetime
• Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term
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• Planck-scale dimensional reduction without a preferred frame
• Hausdorff dimension of a particle path in a quantum manifold

Cited by in corpus (9)

• Dimension and Dimensional Reduction in Quantum Gravity
• Imprint of quantum gravity in the dimension and fabric of spacetime
• Raychaudhuri equation with zero point length
• Quantum gravity without vacuum dispersion
• Quantum metric for null separated events and spacetime atoms
• Asymptotically Weyl-Invariant Gravity
• Renormalizing Spacetime
• Is Asymptotically Weyl-Invariant Gravity Viable?
• A Falsifiable Alternative to General Relativity