Feynman stated that a particle travelling backwards in time traces out the same path in spacetime as an anti-particle moving forward in time.
However, a thought experiment disputes this:
Take two electrons close to each other, and let them go. They fly apart, due to electromagnetic repulsion.
When time goes backward, you have two positrons attracting each other…something violating the laws governing electromagnetic interaction.
This, however DOES describe Gravity, since mass has only “positive charge”
(Exotic matter… a theoretical substance with the quality of negative mass…has not been observed)
Does this inverse-temporal symmetry imply a deep mathematical connection between G and EM…something not found in Kaluza-Klein or M-theory?
I am not a physicist, but I believe the answer is the following:
Shoot two positrons towards each other at some initial velocities; they’ll approach each other at a decelerating pace, eventually come to momentary rest, and then depart from each other at an accelerating pace.
Play this film backwards and think of them as electrons; what does it look like? It looks like two electrons approaching each other at a decelerating pace, eventually coming to a momentary rest, and then departing from each other at an accelerating pace.
Your proposed counterexample isn’t a counterexample at all: electrons starting from momentary rest and then moving apart at an accelerating pace corresponds, in the time-reversed image, to positrons starting from velocities headed towards each other, decelerating, and then coming to a momentary rest, which is indeed what would happen if positrons started from velocities headed towards each other, to correspond with your electron scenario ending with them at velocities headed away from each other.
In other words: The rule isn’t “Like charged particles are always moving apart”. The rule is “Like charged particles are always accelerating away from each other (even though they may at some points actually have velocities approaching each other)”. And this latter rule is, in fact, symmetric with respect to time.
One way to think of it is that acceleration has units of length per time squared. Since time is squared, it doesn’t matter if it’s positive or negative; you get the same result.
That link requires a login. The URL appears to be a posting page, not one for reading a thread there?