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Question about time reversibility.

In considering the reversibility of a system over an interval of time, shouldn't it be put into consideration, that because all interactions were random, that if one were to somehow "go back in time" or reverse the process, that the initial state would be completely different then what the initial state was before reversing the system?

For example, we start with a system in a box, with some particles in it as some undefined locations and momenta. As time evolves through the box, we probe the environment with particles to see where things were every second or so. At the final state of the system, we have a final state that is different then the initial. Okay cool. But now lets say we were to time reverse the process. If the laws of physics are the same in reversed time, doesn't that mean that all interactions with the probes, as the system advances towards the initial state, be completely random, and thus end up with a different initial state?

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# B Time reversibility in quantum mechanics

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