Is time reversal symmetry true on the microscopic level? I often hear that on the microscopic level, time-reversal symmetry is true for all physical processes. However, I can easily come up with counterexamples that seem to disprove this:


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*Two particles of opposite charge being attracted by each other and accelerating towards one other as a result.


Furthermore, even barely observed on a microscopic level, the gravitational force surely defies time-reversal symmetry. A movie of an apple accelerating away from the ground is immediately recognizable as the reversed version of the true process. This is a macroscopic example, but you get the point.
So where am I wrong?
 A: 
Furthermore, even barely observed on a microscopic level, the gravitational force surely defies time-reversal symmetry. A movie of an apple accelerating away from the ground is immediately recognizable as the reversed version of the true process. 

No. When an apple falls from a tree, it starts motionless at a high point, then gains more and more speed as it moves lower. The time reverse of this occurs when you throw an apple up. It starts with high speed at the bottom, then ends up motionless at a high point. In both cases the acceleration is toward the ground.
More mathematically, suppose the position of the falling apple is $y(t)$. Then the acceleration must be $-g$. When you time reverse the trajectory to get $y(-t)$, you get two minus signs when differentiating from the chain rule, so the acceleration is still $-g$. So if $y(t)$ is a legal path, so is $y(-t)$.
You might say the time reversed process is impossible, because obviously an apple can't jump up from the ground and back into the tree. But that's the entire point of the paradox. Microscopically, Newton's laws allow both processes; it's only thermodynamics that forbids one.
