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Feynman's idea states that matter going backwards in time seems like antimatter.

But, since nature is $CPT$ symmetric, reversing time ($T$) is equivalent to $CP$ operation. So, reversing time gives parity reversed antimatter, not just antimatter.

What is happening here? Why does nobody mention this parity thing when talking about reversing time? What am I missing?

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  • $\begingroup$ You're right, never mind. $\endgroup$ Mar 20 '18 at 0:45
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Positrons have equal and opposite charge and parity to electrons. Hence when combined, they can produce a neutral gamma ray with no parity.

https://en.m.wikipedia.org/wiki/T-symmetry

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The statement that antimatter is matter going back in time is usually associated with Feynman diagrams in QED, so we're talking about electrons, and electrons have parity +1, so:

$$ CPT = C1T = CT = 1 $$

So the parity part doesn't come into play, but it is required in general.

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