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Consider a matter and antimatter pair having the same mass and one of the two has been accelerated by an external force or supplied with some initial kinetic energy (After big bang least one of the many formed matter and antimatter pairs may have different kinetic energies). According to relativity (relativistic) mass varies with speed even if the variation may is minute there will definitely be a mass variation for two objects having same rest mass and moving with different velocities. So the mass of antimatter and matter are different. Or does the rest mass of the two have to be the same?

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According to relativity mass varies with speed even

No, according to relativity, relativistic mass varies with speed.

Rest mass does not vary with speed, which is why we call it rest mass.

Or does the rest mass of the two have to be the same?

Bingo! That's what we refer to when you talk about "the mass of a particle".

It's perfectly fine for the two to have different relativistic mass.

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    $\begingroup$ Relativistic mass is an extremely outdated concept and should not be discussed anymore. Mass always means rest mass. $\endgroup$
    – Prahar
    Mar 20, 2018 at 16:59
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It should be cited that, for two equal-mass particles, even if you accelerate one to some (constant) speed, there will always be a frame of reference, called the center-of-mass frame, where the two particles will have equal momenta and energies. So if you're worried about unequal relativistic masses in a particle collision causing some sort of imbalance, you can always transform to the center of mass frame, calculate the results of the annihilation, and then convert back to your original frame.

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    $\begingroup$ and yes, "relativistic mass" isn't something that should be used anymore. $\endgroup$ Mar 20, 2018 at 17:08

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