Title: Fractal-Flows and Time's Arrow Authors: Leonard Susskind

This is the written version of a lecture at the KITP workshop on Bits, Branes, and Black Holes. In it I describe work with D. Harlow, S. Shenker, D. Stanford which explains how the tree-like structure of eternal inflation, together with the existence of terminal vacua, leads to an arrow-of-time. Conformal symmetry of the dS/CFT type is inconsistent with an arrow-of-time and must be broken. The presence in the landscape of terminal vacua leads to a new kind of attractor called a fractal-flow, which both breaks conformal symmetry, and creates a directional time-asymmetry. This can be seen from both the local or causal-patch viewpoint, and also from the global or multiversal viewpoint. The resulting picture is consistent with the view recently expressed by Bousso. In the last part of the lecture I illustrate how the tree-model can be useful in explaining the value of the cosmological constant and the cosmic coincidence problem. The mechanisms are not new but the description is.

Quantum gravity, the initial low entropy state of the Universe, and the problem of time are interlocking puzzles. In this article, we address the origin of the arrow of time from a cosmological perspective motivated by a novel approach to quantum gravitation. Our proposal is based on a quantum counterpart of the equivalence principle, a general covariance of the dynamical phase space. We discuss how the nonlinear dynamics of such a system provides a natural description for cosmological evolution in the early Universe. We also underscore connections between the proposed non-perturbative quantum gravity model and fundamental questions in non-equilibrium statistical physics.

It controls the rhythm of our lives like a Metronome ticking away and measuring the pace and tempo of our existence. Time is an enduring mystery. And, along with time's arrow we are taking an inexorable voyage into an unknown future. Read more

Ed ~ The arrow of time is likely caused by the time-asymmetric boundary conditions of the universe. The thermodynamic arrow is linked to the cosmological arrow of time, because it is ultimately about the boundary conditions of the universe (aka Wheeler-Feynman absorber theory).

The Wheeler-Feynman absorber theory (also called the Wheeler-Feynman Time-Symmetric theory) is an interpretation of electrodynamics that starts from the idea that a solution to the electromagnetic field equations has to be symmetric with respect to time-inversion, as are the field equations themselves. The motivation for such choice is mainly due to the importance that time symmetry has in physics. Read more

Title: The Universal Arrow of Time III: Gravitation theory Authors: Oleg Kupervasser

The paper is dealing with the analysis of general relativity theory (theory of gravitation) from the point of view of thermodynamic time arrow. Within this framework "informational paradox" for black holes and "paradox with the grandfather" for time travel "wormholes" are resolved.

Title: Arrows of Time in the Bouncing Universes of the No-boundary Quantum State Authors: James Hartle, Thomas Hertog

We derive the arrows of time of our universe that follow from the no-boundary theory of its quantum state (NBWF) in a minisuperspace model. Arrows of time are viewed four-dimensionally as properties of the four-dimensional Lorentzian histories of the universe. Probabilities for these histories are predicted by the NBWF. For histories with a regular `bounce' at a minimum radius we find that fluctuations are small at the bounce and grow in the direction of expansion on either side. For recollapsing classical histories with big bang and big crunch singularities we find that the fluctuations are small near one singularity and grow through the expansion and recontraction to the other singularity. The arrow of time defined by the growth in fluctuations thus points in one direction over the whole of a recollapsing spacetime but is bidirectional in a bouncing spacetime. We argue that the electromagnetic, thermodynamic, and psychological arrows of time are aligned with the fluctuation arrow. The implications of a bidirectional arrow of time for causality are discussed.

Ed ~ The arrow of time is caused by the time-asymmetric boundary conditions of the universe. The thermodynamic arrow is linked to the cosmological arrow of time, because it is ultimately about the boundary conditions of the universe.