Comment on "Multidimensional arrow of time" (arXiv:2601.14134)

TL;DR

This paper critiques a geometric origin of the arrow of time based on extra-dimensional volume growth, highlighting conflicts with gravitational constant stability and proposing a shape-dynamic alternative using Ricci flow.

Contribution

It introduces the 'shape-dynamic arrow of time' concept, resolving tensions in Kaluza-Klein models by linking geometric smoothing to time's arrow without changing volume.

Findings

Volume growth conflicts with observational bounds on G

Ricci flow smoothing preserves G stability

Shape-dynamic approach aligns with physical constraints

Abstract

In a recent preprint [arXiv:2601.14134v1], Rubin argues that the arrow of time originates from the monotonic growth of the volume of extra dimensions. While the identification of a geometric origin for time's arrow is compelling in the case of brane-world models, we point out a possible tension between the proposed volume growth and the observational stability of the effective four-dimensional Newton's gravitational constant, G, that may arise in Kaluza-Klein (KK) theory. In standard KK approaches, such volume growth induces a time-variation of G that exceeds Big Bang Nucleosynthesis (BBN) and Lunar Laser Ranging (LLR) bounds by many orders of magnitude. To resolve this tension while preserving the author's key insight in the Kaluza-Klein case, we propose an extension: the "shape-dynamic arrow of time". By utilizing the scale-invariant monotonicity of Perelman's nu-entropy under normalized Ricci flow, we demonstrate how an arrow of time can emerge from the geometric smoothing of extra dimensions at fixed volume, thereby satisfying observational constraints on fundamental constants.