Antimatter is just matter that is traveling backwards in time

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Feynman proposed that antimatter is just matter that is traveling backwards in time.

If you had jar of antimatter gas in some thermodynamic state what would happen to the entropy of the antimatter over time?

In my understanding matter and antimatter can interact with each other without pair annihilation via radiation.
 
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you have missinterpreted the "backward in time" issue
 


I think if you invert both the direction and time flow of the particles they would behave very much like particles that weren't inverted.

Philosophically my question is like "If all particle reactions are reversible how do you know which direction time flows in?"
 


{~} said:
I think if you invert both the direction and time flow of the particles they would behave very much like particles that weren't inverted.
except those particles traveling backward in time would have a negative energy. The condition of positive energy is what makes the time flow in the right direction, and imposes the antiparticle interpretation.

In the standard framework, antiparticles fall in a gravitational field for instance. Backwards in time, those particles would fly away, which is also self(in)consistent with having a negative energy.