A Gravitational Origin of the Arrows of Time (1310.5167v1)

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. Theparadox' 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.

• The paper proposes that time's arrows arise from gravitational dynamics and shape space structure, not special initial conditions like the past hypothesis.
• Generic solutions in the Newtonian N-body problem show complexity increasing in both temporal directions from a minimum, indicating inherent time asymmetry.
• This gravitational theory of time suggests the past hypothesis is unnecessary and could provide a unified explanation for all temporal arrows.

Overview of "A Gravitational Origin of the Arrows of Time"

The paper "A Gravitational Origin of the Arrows of Time" by Julian Barbour, Tim Koslowski, and Flavio Mercati challenges the predominant explanation for the universal directionality of time, commonly attributed to the "past hypothesis." This hypothesis posits that the Universe began in a highly ordered low-entropy state. The authors propose an alternative explanation that ascribes the emergence of time's arrows to the intrinsic properties of gravitational laws and the asymmetry of the space of the Universe's true degrees of freedom (referred to as "shape space").

Core Premise

The authors suggest that the arrows of time are a consequence of the gravitational law and arise naturally in solutions of the Newtonian $N$-body problem and potentially in General Relativity (GR). They introduce the concept of "shape space," which is invariant under translations, rotations, and dilatations, as the fundamental nature of the Universe's configuration. In this space, except for a set of measure zero, solutions exhibit a division point where complexity can only increase in both temporal directions, evidencing inherent time asymmetry without invoking special initial conditions.

Key Results

1. Newtonian $N$-Body Problem: The authors demonstrate that generic solutions (for non-negative energy) naturally evolve through a point of minimal complexity and then bifurcate, with complexity growing in both future directions. This behavior is indicative of two distinct futures emanating from a shared past, resolving the paradox of time-symmetric laws producing irreversibly entropic behavior.
2. Complexity and Information: Complexity, defined as a function on shape space, exhibits an irreversible increase. This coincides with the creation of structures that store dynamical information, implying a naturally emerging arrow of information growth.
3. General Relativity: The study suggests analogous complexity arrows could exist in GR, demonstrated through the vacuum Bianchi IX model. While concrete solutions including matter have not been established, the structural parallels with the $N$-body problem provide a foundation for further investigation.

Implications

The paper implies that the widely accepted past hypothesis may be unnecessary if time asymmetries arise inevitably from shape space topology and gravitational dynamics. Furthermore, the research opens up a pathway to unified explanations for all observed arrows of time, grounded in gravitational and configurational properties rather than anthropically contrived initial states.

Future Directions

While a solid alternative model has been proposed, the paper suggests several avenues for further research:

• Extending the complexity framework to include non-trivial solutions in GR with matter.
• Investigating the potential quantum implications of their theory, especially concerning an evolving Planck constant in a dimensionless configuration space.
• Refining the notion of growing complexity in the matter sector as the primary marker of time's arrow.

Conclusion

The authors have presented an intriguing conjecture that positions gravitational dynamics as the underlying cause of time's arrows, moving beyond the past hypothesis. The study enriches our understanding of time and challenges researchers to reconsider foundational assumptions about the Universe's evolution and the origin of time's unidirectionality. This re-conceptualization offers a fresh perspective with potential impacts on both classical and quantum theories of gravity.