If I could turn back time

Newton's law states \(F = m\ddot{r}(t)\). Solving this equation for a given force field yields a curve \(r(t)\) that governs the motion of particles in that field. The physics in a field is said to obey time-reversal symmetry if whenever \(r(t)\) is a permissible motion, \(r(-t)\) is as well.

Of the following forces, which does not obey time-reversal symmetry?

• Gravitational \(\displaystyle F = -G\frac{Mm}{r(t)^2}\hat{r}\)
• Electric \(\displaystyle F = q\vec{E}\)
• Magnetic \(\displaystyle F = q\vec{v}(t)\times\vec{B}\)

Assumptions

• Take the fields in question to be constant, and time-independent.