Is the energy of a macroscopic body in special relativity still given by: $E=\gamma m c^2$? If so why do we not need to consider the motion of the individual particles that make it up? Is this because the rest mass $m$ includes this motion? If this is the case and the rest mass includes all the energies of the particles that it is made up from then why is the rest mass invariant? Since the individual energies of these particles are not invariant, so why taken as a whole why do they become invariant? (any formulas of how to get from energies of particles to the rest mass of the whole macroscopic body would be appreciated)
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Assuming the body is rigid (i.e. the constituent particles don't move relative to each other - a good approximation when an everyday object is travelling at relativistic speeds), then $\gamma$ will be the same for all particles. Thus:
$E = \gamma m_1c^2 + \gamma m_2c^2 = \gamma(m_1+m_2)c^2 = \gamma mc^2$.
Kieran Hunt
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