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Vladimir_Nesov comments on Open Thread: February 2010 - Less Wrong
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In time-reversible deterministic world, information is gained from observation of stuff that wasn't in contact with you in the past, and logical information is also gained (new knowledge about facts following from the premises -- there is no logical transparency). Analogously, an action can be seen as "splitting", where you part with a prepared action, and action parts with you, so that you lose knowledge of that action. If you let info split away in this manner, you may never get it back.
You're a little over my head -- though I mostly follow.
My question was actually simpler. Is the world time-reversible? Do we know anything about that?
I'll contribute my thoughts on whether the world is time-reversible...
By time-reversible, I mean that information doesn't get "lost" as you move forward in time; that with unlimited information about the universe at time t you could deduce everything about the state of the universe at time t-ε.
Classical mechanics is reversible. If you have the velocity and positions of 3 billiard balls, you can deduce if and when they collided and what their original velocities were.
I think what we know about quantum mechanics is inconclusive; we don't know how to trace the wave-function backwards in a unique/deterministic way, but we don't know how to follow it forwards, either.
If you many-worlds, then all possible past universes make up the past universe, so you seem to have reversibility -- a reversibility that is no less determined and unique in the past direction as the future direction.
Being agnostic about many worlds, I would give a higher probability for reversibility over non-reversibility, just because of the reversibility of classical mechanics. However, 51% in favor of reversibility for a hand-waving intuition is pretty much just a random guess and I wonder if anyone has a tighter probability estimate, or other reasons?
In Many Worlds Quantum Mechanics, the wave function is fundamental, and the many worlds are a derived consequence. The wave function is time reversable. Running it backwards, you would see worlds merge together, not the world we currently experience splitting into possible precursors. This assymetry is due to simple boundry conditions at the beginning of time.