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It is widely believed that special initial conditions must be imposed on any time-symmetric law if its solutions are to exhibit behavior of any kind that defines an `arrow of time'. We show that this is not so. The simplest non-trivial time-symmetric law that can be used to model a dynamically closed universe is the Newtonian N-body problem with vanishing total energy and angular momentum. Because of special properties of this system (likely to be shared by any law of the Universe), its typical solutions all divide at a uniquely defined point into two halves. In each a well-defined measure of shape complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows and act as `records'. 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 the records of one branch and deduce a unique past and future direction from inspection of the available records.
Fascinating reconstruction of common thoughts. It may be reformulated in categories terms... Is it consistent ?? yes, at the first glance. Physical ? I don't know. As a very free extension of GR, it has also implicit relations to quantum gravity. "We conclude that the origin of time's arrow is not necessarily to be sought in initial conditions but rather in the structure of the law which governs the Universe." is far of being trivial in this specific context. I hope to read a review ...
I do not understand that. Once the equations of motion are written, they imply the arrow of time, and these equations are sufficient for that. Making variable changes changes (or "explains") nothing in this respect.
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