Electromagnetism and CPT simmetry I'm having some trouble understanding the CPT theorem and in particular the time reversal part.
Let's consider for example an electron and a positron on the x axis, with the electron on the left and the positron on the right, attracting each other.
If we apply charge conjugation we swap the 2 particles and if we apply the parity we basically swap their representation back, so that the electron will be on the left and the positron on the right, even though the verse of the x axis will be inversed. And they will still attract each other.
But if we now apply time reversal, it looks to me that the charges should reject each other.
Now, all theories should be invariant by CPT symmetry, but I don't really see how/what it means.
 A: When you apply time-reversal you should take your initial conditions as your final conditions, and vice-versa, and reverse the velocities.
So let's first start with electron and positron far apart at some distance $d(0) = d_0$ and at rest, $\vec{v}_e(0) = \vec{v}_p(0) = 0$. You roll the movie, and they will attract each other. You now stop it after some time $t$ so that $d(t) = d_1 < d_0$. Their velocities will also no longer be zero, but will be towards each other, say  $\vec{v}_e(t) = - \vec{v}_p(t) = \vec{v}_1 \neq 0$.
Let us now apply time-reversal. Now we have $d(0) = d_1$, and $\vec{v}_e(0) = - \vec{v}_p(0) = -\vec{v}_1$, where we reversed the velocities. So basically, in the reversed movie the charges start closer to each other but with opposite velocities. If you now roll the movie you will see them spreading apart, but slowing down until they stop the time $t$ at a new distance $d(t) = d_0 > d_1$. Since they slowed down you must conclude that they attracted each other, so that the electrical interaction is invariant under time-reversal.
