# Time reversal and Coulomb interaction

1. Apr 22, 2010

### krishna mohan

I have read that charge is supposed to be invariant under time reversal.

Now, if I consider two like charges placed some distance from each other, I expect them to repel and go away from each other. In a time-reversed frame, I expect them to approach each other.

Since the separation is not affected by time reversal operation, and since charge is also supposed to be time-reversal invariant, what causes the charges in the time-reversed system to attract?

2. Apr 22, 2010

### the_house

Think a little more carefully about your example. If you place two like charges at rest near each other, they will accelerate away from each other as you say. At first they will have a small relative velocity and later it will be larger.

In the time-reversed situation, the two charges are flying toward each other from far away with a large velocity, which decreases with time until they come to a stop near each other. This is still the motion of a repulsive interaction.

Or, saying it a different way, if you consider like charges at rest near each other (under no external forces) it doesn't matter whether you look forward in time or backward in time. The full scenario would have them flying toward each other, decelerating until they stop, and then continuing to accelerate outward. From the time where they are at rest, the charges will accelerate farther apart whether you look forward or backward in time.

It is not the case that the time-reverse of a repulsive acceleration is an attractive acceleration.

3. Apr 23, 2010

### krishna mohan

Thanks...I was considering only positions of the final and initial states....as you have pointed out, when I consider the velocities as well then there is no problem....

Thanks a bunch again...