A force is time-symmetric if its operations do not give you a basis for determining which way the arrow of time is pointing.
In other words, it’s time-symmetric if, were you to watch things under the influence of that force unfold backwards in time, they would still appear to be under the influence of that force in the same way they appeared to be under its influence when things were going forward in time.
Gravity, for example, will still appear to be an attractive force, no matter whether things are going forward or backward in time.
Stranger and I have explained how this can be possible in the case of gravity, despite how counter-intuitive it seems. Where in our explanations did you stop following the logic?
Here’s another explanation. Imagine a sun. Lets imagine ourselves at rest relative to it. Now imagine a smaller body in deep space, hurtling nearly in the direction of the sun, but not directly at the sun. The body’s path will curve as it comes near the sun. But imagine the body is going fast enough that it’s not pulled into the sun or into orbit–it escapes the sun’s gravitational field and goes on its merry way.
So the body traces a curved path in space because of the presence of the sun. The path curves in the direction of the sun, because gravity is attractive.
Now run the tape backwards, and what do you see?
Basically the same thing–a body travelling through space, approaching a sun, its path curving as a result, and then going on its merry way. (Do you see it?) And which way is the path curved? Toward the sun.
This illustrates how gravity works the same in both time-forward and time-reversed views. In both cases, it works as an attractive force.
Here’s another way in. Think of a basketball bouncing quite high. It bounces four or five times. This involves movement both upward and downward. (And note that the upward movement is not incompatible with gravity’s being an attractive force.)
But run the tape backwards, and what do you see? Bouncing again, involving both upward and downward movement. Now there may be some mysteries about what you see (for example, why are subsequent bounces higher than previous bounces?) but here’s a question to ponder. If reversing time is supposed to make gravity repulsive, then what explains the basketball’s downward movements in the second half of each bounce in the time-reversed scenario?