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An account of the arrow of time when scale is surplus

Sean Gryb, Simon Friederich

TL;DR

The paper tackles the cosmological arrow of time by proposing a third path that neither relies on time-asymmetric fundamental laws nor on a Past Hypothesis. By treating the cosmic scale factor as surplus structure and elevating the Hubble parameter as the empirically accessible quantity, the authors formulate a JA (Janus–Attractor) scenario in which attractors and Janus points create a locally emergent arrow of time within a time-reversal-invariant framework. They develop the theory using dynamical similarity as a gauge symmetry, advocate a contact-space formulation with drag-like dynamics, and illustrate the mechanism with two concrete models: a flat FLRW cosmology and a scale-free Newtonian N-body system. The results show how early smoothness and rapid red-shift can arise from JA dynamics, offering a unified explanation that avoids prior objections to generalism and particularism and suggesting fruitful directions for quantum treatment and further model-realizations.

Abstract

Existing accounts of the cosmological arrow of time face a dilemma: generalist approaches that posit time-asymmetric laws lack independent motivation, while particularist approaches that invoke a Past Hypothesis face serious conceptual and explanatory problems. We propose a novel account that dispenses with the need for both time-asymmetric laws and a Past Hypothesis. Instead, it is centred around a symmetry argument that reveals attractors and so-called 'Janus points'. The main idea is that the global spatial scale of the Universe is not empirically accessible, and should therefore be treated as surplus structure. By contrast, the Hubble parameter, which encodes the relative rate of change of scale, is empirically accessible. Once the scale redundancy is eliminated, the empirically meaningful description of cosmic dynamics involves a drag-like variable that transforms in a way that preserves time-reversal invariance. The resulting space of dynamical possibilities possesses universal attractors and Janus points, giving rise to particular states in which observers experience a cosmological arrow of time akin to our own. We illustrate the proposal by applying it to cosmological and gravitational N-body models, showing how it accounts, respectively, for the rapid cooling of the early universe and its relative smoothness.

An account of the arrow of time when scale is surplus

TL;DR

The paper tackles the cosmological arrow of time by proposing a third path that neither relies on time-asymmetric fundamental laws nor on a Past Hypothesis. By treating the cosmic scale factor as surplus structure and elevating the Hubble parameter as the empirically accessible quantity, the authors formulate a JA (Janus–Attractor) scenario in which attractors and Janus points create a locally emergent arrow of time within a time-reversal-invariant framework. They develop the theory using dynamical similarity as a gauge symmetry, advocate a contact-space formulation with drag-like dynamics, and illustrate the mechanism with two concrete models: a flat FLRW cosmology and a scale-free Newtonian N-body system. The results show how early smoothness and rapid red-shift can arise from JA dynamics, offering a unified explanation that avoids prior objections to generalism and particularism and suggesting fruitful directions for quantum treatment and further model-realizations.

Abstract

Existing accounts of the cosmological arrow of time face a dilemma: generalist approaches that posit time-asymmetric laws lack independent motivation, while particularist approaches that invoke a Past Hypothesis face serious conceptual and explanatory problems. We propose a novel account that dispenses with the need for both time-asymmetric laws and a Past Hypothesis. Instead, it is centred around a symmetry argument that reveals attractors and so-called 'Janus points'. The main idea is that the global spatial scale of the Universe is not empirically accessible, and should therefore be treated as surplus structure. By contrast, the Hubble parameter, which encodes the relative rate of change of scale, is empirically accessible. Once the scale redundancy is eliminated, the empirically meaningful description of cosmic dynamics involves a drag-like variable that transforms in a way that preserves time-reversal invariance. The resulting space of dynamical possibilities possesses universal attractors and Janus points, giving rise to particular states in which observers experience a cosmological arrow of time akin to our own. We illustrate the proposal by applying it to cosmological and gravitational N-body models, showing how it accounts, respectively, for the rapid cooling of the early universe and its relative smoothness.

Paper Structure

This paper contains 28 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Motivation
  3. Roadmap
  4. Price's taxonomy
  5. The dilemma
  6. Objections to generalism
  7. Objections to particularism
  8. Reconsidering "typical" states of the Universe
  9. Dynamical similarity
  10. Dynamical similarity and physical identity
  11. Treating dynamical similarity as gauge
  12. The Janus-Attractor scenario as a third way
  13. Intermezzo: a clue from the Boltzmann--Schütz hypothesis
  14. Attractors
  15. Janus points
  16. ...and 13 more sections

Figures (1)

  • Figure 1: The Janus-Attractor scenario obtained by removing scale. Observers in states near an attractor experience an Arrow of Time pointing from the Janus point to the nearby attractor. In a time-reversal invariant theory, the arrow experienced by an observer in the forward flow is balanced by an oppositely oriented arrow experienced by an observer near the attractor in the backward flow.