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As in Wheeler's One Electron Universe idea, how do you show that electrons and positrons are time-reversed versions of each other? Do you just apply time reversal to an electron and out pops a positron? Maybe a more accurate question would be "How do you describe a particle moving backwards in time?", out of which the transformation from electron -> positron should become apparent.

Edited to add: Also, what is the difference between time reversal and moving backwards in time? Is time reversal the observer moving backwards in time (in which case we would see an electron as an electron) vs. the electron moving backwards in time (when we would see a positron)?

FatCat0
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1 Answers1

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The the easiest way to see that time reversal transforms electrons into positrons relies on the fact that PCT (parity, charge conjugation and time reversal) combined are a symmetry of every Lorentz-invant QFT. Using $P^{-1} = P$, $C^{-1} = C$, $T^{-1} = T$, i.e. a parity transformation is undone by a second parity transformation etc. you can see that $$1 = PCT = (PC)^{-1}T \Rightarrow T = PC$$ so time reversal has the same effect as a parity transformation (under which electrons stay electrons) followed by charge conjugation (which takes electrons to positrons). Therefore, time reversal turns electrons into positrons.

Neuneck
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