Is time reversible in Quantum Math?

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In a "Briefer History of Time" Hawking says what everybody else does: that the laws of physics do not indicate a preference for time running forward or backward. He says that the forward direction may be required somehow by the increase of entropy from the highly ordered state of the singularity prior to the Big Bang. That doesn't do it for me as an explanation because the degree of entropy seems like an observation of the state of things rather than a fundamental law.

Going forward, Quantum Mathematics describeRs a particle's velocity/position using a probability wave which collapses when viewed by an observer in the present moment. I think this means that an observer (at the present moment) has created an irreversible change which doesn't seem like it would work in reverse. Like the particle that decayed randomly, triggering a geiger counter click, which released the gas that killed the cat. Since Quantum events are defined by probability waves going forward, do events that have occurred revert to probabilities when time is reversed? In Quantum terms it seems like the future is undefined and the past is solidified. Does Quantum math distinguish between the past and the future?
 

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That doesn't do it for me as an explanation because the degree of entropy seems like an observation of the state of things rather than a fundamental law.
http://en.wikipedia.org/wiki/Arrow_of_time
That may have some information about why time moves one way and not the other. I don't think there is a very satisfactory answer here :(

Since Quantum events are defined by probability waves going forward, do events that have occurred revert to probabilities when time is reversed?
Yes, but if you knew those events were observed you could plug that in. (there is likely some subtleties here)

In Quantum terms it seems like the future is undefined and the past is solidified
We can't guess what happened in the past any more that we can guess what will happen in the future with QM. (see above)

Does Quantum math distinguish between the past and the future?
I don't know of any time symmetry violations, but I'm not sure.

I'm not so super good at this stuff like some of these guys here, but I took a shot at it.
 

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