Why does spin break time reversal symmetry but electric dipole moment does not break time reversal symmetry?

Question

I wasn't able to get a proper reason behind this and the only thing I could find were classical analogies for spin which (when I asked my prof) were not to be relied upon.

Answer 1

By break if you mean that spin is T odd( changes sign) when applying the time-reversal operator , then I think the classical analogy is valid here. The time reversal operator leaves the electric field the same but changes the magnetic field to it's negative. Because it leaves the electric field the same, the electric dipole moment is T-even (meaning it does not change sign under time reversal) but since spin can be thought of as magnetic moment, and since the magnetic field changes sign under the operator, the spin also changes sign.

If you are wondering why it leaves the electric field the same but changes the magnetic field to it's negative, think about a particle moving away from some electric field. Under the time reversal operator, the velocity changes sign, if you change the sign of the electric field too, they cancel each other out. To see this :

$$q(-E)=(-\frac{d^2 x}{dt^2})$$

Since it's motion should reverse direction (since charge is the same) when you "play it back" in time, the electric field should remain the same.