We know by the Feynman Stueckelberg interpretation that the Dirac solution of negative energy particles can be thought as negative energy particles going backwards in time. And considering that particles go foward in time, that solution corresponds to antiparticles with positive energy moving foward in time (the antiparticles we observe).

Additionally, Souriau pointed out in his book Structure of Dynamical Systems: "shows that time reversal It changes the sign of the energy and thus the sign of the mass (14.4

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