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Let, we have an object with mass (previously called rest mass) m. It starts moving with a velocity v, and its relativistic mass (not a preferred term nowadays) or total energy becomes $m_{\mathrm{Rel}} = \gamma m$. This is the mass we get if we measure it on a scale. Now if we collide this object with another object having the same relativistic mass, assuming that no energy escapes, the combined rest mass of the new object would be $M = 2 \gamma m$ (Resnick/Special Relativity). Should we assume that the increase in mass is because of the temperature increase of the new body, meaning it is solely due to the kinetic energy of its particles? I guess the answer is no, some of the energy should be used as binding energy or other forms. How does special relativity explain those other energies, like binding energies? I mean, they simply have mass even though nothing is 'moving'.

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  • $\begingroup$ Where the mass precisely comes from depends on the details of the system. Kinematics cannot tell you something like this. I also don't think $\gamma m$ is what a scale would see. $\endgroup$ Nov 8, 2021 at 6:36

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Suppose there is a binding energy. Maybe a proton and an electron collide to make a Hydrogen atom.

This means that these two objects decreased in potential energy by being bound together, and therefore there is surplus kinetic energy in the system. This kinetic energy of the constituents manifests as extra rest mass of the whole. So the mass is larger?

Well, sort of. Obviously, this energy was contained in the field, in this case the electromagnetic field. In fact, the Poynting vector of that Liénard-Wiechert potential must have been pointing forwards, so the field is apparently containing forward-flowing energy and one might expect this to not only be a mass term but even to be measurable—change the trajectory of the charged particle, and in addition to a wave propagated to infinity, any new field energy and momentum must have been transferred to the field by your process of changing that trajectory. So it seems very likely that this energy was already there, and was part of the measurement, but is now somewhat invisible?

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