Hypothesis on the Nature of Time

TL;DR

This paper provides numerical evidence that particles in a quantum gravity model can exceed light speed at small scales, suggesting a scale-dependent nature of time and a possible link to dimensional reduction phenomena.

Contribution

It introduces a novel interpretation of superluminal diffusion in CDT as a scale-dependent time dilation, connecting it to spectral dimension reduction and proposing a dual description via Wick rotation.

Findings

Particles exceed light speed at small scales in CDT.

Time dilates as a function of scale, not just velocity.

A dual description involves a scale-dependent Wick rotation.

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.