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When we usually talk about elementary particles such as electrons neutrinos etc... we mention their rest mass or their four vector mass which is invariant However how can we associate the "relativistic or inertial" mass that increase with velocity into the rest mass of a particle. Even if a particle is in his inertial frame and he will measure his own rest mass, he should still see a change in his mass if he is going faster because his kinetic energy is increasing as given by the equation

m(rest mass)=Etotal/c^2

So are not relativistic (inertial) mass and rest mass actually two sides of the same coin that we should include in our calculations (the increase of velocity being part of the rest mass too)?

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The mass of a system is its energy ($/c^2$) in its rest frame, so $E_0 = mc^2$. The rest frame is the frame in which the systems momentum is zero. For a photon this only exists in a limiting sense. In any other frame than the rest frame the energy $E^2 = m^2c^4 + p^2c^2$. The concept of relativistic mass has been abandoned as it only creates confusion.

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