A Gravitational Origin of the Arrows of Time

Abstract

The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the `past hypothesis': the Universe had a very special low-entropy initial state. We present the first evidence for an alternative conjecture: the arrows exist in all solutions of the gravitational law that governs the Universe and arise because the space of its true degrees of freedom (shape space) is asymmetric. We prove our conjecture for arrows of complexity and information in the Newtonian N-body problem. Except for a set of measure zero, all of its solutions for non-negative energy divide at a uniquely defined point into two halves. In each a well-defined measure of complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows. Recognition of the division is a key novelty of our approach. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of one past and one future. The `paradox' of a time-symmetric law that leads to observationally irreversible behaviour is fully resolved. General Relativity shares enough architectonic structure with the N-body problem for us to prove the existence of analogous complexity arrows in the vacuum Bianchi IX model. In the absence of non-trivial solutions with matter we cannot prove that arrows of dynamical information will arise in GR, though they have in our Universe. Finally, we indicate how the other arrows of time could arise.

44 pages + 14 pages appendices and references. 8 figures and 1 table

References in corpus (8)

• A Shape Dynamics Tutorial
• Discrete Newtonian Cosmology
• Invariant characterization of the growing and decaying density modes in LTB dust models
• Shape Dynamics. An Introduction
• Intermediate homogenization of the Universe and the problem of gravitational entropy
• Scale Anomaly as the Origin of Time
• Symmetry Doubling: Doubly General Relativity
• Observable Equivalence between General Relativity and Shape Dynamics

Cited by in corpus (14)

• Identification of a gravitational arrow of time
• A Shape Dynamics Tutorial
• Is the Hypothesis About a Low Entropy Initial State of the Universe Necessary for Explaining the Arrow of Time?
• When scale is surplus
• Time asymmetric extensions of general relativity
• Entropy and the Typicality of Universes
• Pure shape dynamics: General framework
• Cosmological signatures of time-asymmetric gravity
• A Proposal for a Metaphysics of Self-Subsisting Structures. I. Classical Physics
• Linking shape dynamics and loop quantum gravity
• Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem
• Investigating total collisions of the Newtonian N-body problem on shape space
• Janus Points and Arrows of Time
• Quantum Inflation of Classical Shapes