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I was trying to illustrate intuitively (rather than rigorously) the equivalence of negative energy solutions moving backward in time to be equal to a particle of opposite sign a la Feynman. I begin with a quote from the maestro

himself

"A backwards-moving electron when viewed with time moving

forwards appears the same as an ordinary electron, except

it’s attracted to normal electrons - we say it has positive

charge. For this reason it’s called a ‘positron’. The

positron is a sister to the electron, and it is an example

of an ‘anti-particle’. This phenomenon is quite general.

Every particle in Nature has an amplitude to move backwards

in time, and therefore has an anti-particle. (Feynman,1985):98 "

I picked a super simple 1 dimensional gedanken example of of placing a test charge (particle 1) a fixed distance (x) away from an origin with another oppositely charged particle (A) fixed at the origin. Thus if the test charge began from rest, it would gain speed whilst approaching the origin. If the y axis were time therefore and the x axis the distance I would expect a curve coming into the origin (so as time gets less-> backward propagation, the particle gains momentum whilst approaching A) and the charged particle would ultimately arrive at the origin with some final momentum p oriented into the origin. Now if I were to view this (as Feynman says) with time moving forward, I would see particle 1 with p opposite in orientation, at A, moving away until it got to the position where particle 1 was at rest, tracing the trajectory this particle would also be at rest at that point. However according to Feynman's statement, I should see it continue to accelerate (if indeed it is being repelled!) So what am I doing wrong ?

Many thanks for any input ! Simple arguments please !

BlueHopoe