If I could turn back time

Newton's law states F=mr¨(t)F = m\ddot{r}(t). Solving this equation for a given force field yields a curve r(t)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)r(t) is a permissible motion, r(t)r(-t) is as well.

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

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


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

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