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2.1.2 Special Relativity Requires Antiparticles

The above article describes a scenario where an atom A releases an electron which subsequently merges with another atom B.
A=> A+ , B=> B-.
When viewed from a different inertial frame (f) it is possible due to Heisenberg's uncertainty principle that the electron may arrive before it started. I.e the electron travels back in time and acquires negative mass?.
This being physically unacceptable we say that in frame (f) an anti-electron (positron) moves from B to A.
Again B => B- and A => A+ as before.

This is all very well as far as charge is concerned but in the first inertial frame atom B gains the mass of the electron and A loses the mass of the electron. In inertial frame (f) A gains the mass of the positron and B loses this mass.
The mass of a positron equals that of the electron so can anyone explain how this makes sense?