# 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:

• 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?

• Assume CPT symmetry and since CP violation is observed, T symmetry is also violated. (my limited knowledge in particle physics) – K_inverse Dec 3 '18 at 12:28
• Unless the two particles of opposite charge smash together into one, they fly towards each other, undergo Rutherford scattering, and fly apart in a way that is indistinguishable from them flying towards each other - your counterexample isn't a counterexample at all. – Jon Custer Dec 3 '18 at 13:47

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 $$y(-t)$$.