How to understand the time reversal symmetry of position operator? How to understand the fact that position operator is symmetric under time reversal? I can visualize the momentum and magnetic field being odd under time reversal.
Got the same doubt for Electric field as well.
 A: You can easily find out which quantities are even and which
are odd upon time-reversal by considering a video showing
physical processes and then comparing it to the time-reversed
video showing the same processes backwards.
See also "T-symmetry - Effect of time reversal on some variable of
classical physics" for lists of even and odd physical quantities.
Even quantities
Obviously the spatial position $\vec{x}$ doesn't change sign
in the time-reversed video. (A body being on the right side in the
original video is still on the right side in the time-reversed video,
not on the left side.)
Also the acceleration $\vec{a}$ doesn't change sign.
(In the original video a ball thrown up and then falling down
is accelerated downwards. Viewed in the reversed video, the
ball is again accelerated downwards, not upwards.)
From Newton's $\vec{F}=m\vec{a}$ you can conclude, force
$\vec{F}$ also doesn't change sign.
And then from the definition of electric field ($\vec{F}=q\vec{E}$),
you can further conclude, the electric field $\vec{E}$ doesn't
change sign.
Odd quantities
Obviously in the reversed video time $t$ and velocity $\vec{v}$
have the opposite sign as compared to the original video.
The magnetic field $\vec{B}$ is defined by the Lorentz force
($\vec{F}=q\vec{v}\times\vec{B}$). Because force $\vec{F}$ is even
and velocity $\vec{v}$ is odd, you can conclude the magnetic field
$\vec{B}$ must be odd.
A: Position is ondependent of time. The magnetic field is even under time reversal, the electric field odd. I wouldn't know how to visualize this.
