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In "Does the inertia of a body depend upon its energy content?," http://fourmilab.ch/etexts/einstein/E_mc2/www/ , Einstein says:
My interpretation of this is that these energies contain both potential and kinetic terms. A potential energy U is only defined up to an additive constant. If, for example, U depends on the distance r between particles, and the distance undergoes a Lorentz contraction, there is no reason to imagine that the constant will stay the same. In nonrelativistic physics, a particular expression for U(r) would give the same result in either frame, so although we would still be free to pick a different C when starting a problem over in a different frame, there would be less physical motivation for doing so.
Am I interpreting this correctly?
At first I thought that the C might refer to the energy equivalent of the rest mass, but Einstein later explicitly states that C has to stay the same before and after emission of the light waves. The rest mass of the emitting body, however, changes.
Thus it is clear that the difference H-E can differ from the kinetic energy K of the body, with respect to the other system [itex](\xi,\eta,\zeta)[/itex], only by an additive constant C, which depends on the choice of the arbitrary additive constants of the energies H and E.
My interpretation of this is that these energies contain both potential and kinetic terms. A potential energy U is only defined up to an additive constant. If, for example, U depends on the distance r between particles, and the distance undergoes a Lorentz contraction, there is no reason to imagine that the constant will stay the same. In nonrelativistic physics, a particular expression for U(r) would give the same result in either frame, so although we would still be free to pick a different C when starting a problem over in a different frame, there would be less physical motivation for doing so.
Am I interpreting this correctly?
At first I thought that the C might refer to the energy equivalent of the rest mass, but Einstein later explicitly states that C has to stay the same before and after emission of the light waves. The rest mass of the emitting body, however, changes.