Undergrad Time Reversal Operator: Physics Explained

[Silviu]

Hello! I am a bit confused about the physical meaning of time reversal operator (both in classical and quantum/QFT physics). Classically if we drop a ball, I can easily see why this is invariant under the translation operator, but I am not sure I understand how does it work with the time reversal. We would see a ball increasing its velocity upwards, despite having a force acting on it downwards? How does this work?

 

[Dale]

We would see a ball increasing its velocity upwards, despite having a force acting on it downwards

No, we would not see that. The path of a ball is given by $y(t)=-\frac{g}{2}t^2+v_0 t +y_0$

What do you get if you map $t \to -T$