If this seems like sort of a theoretical definition of mass, where do you think most of the mass in your body is concentrated? I have had students who, after a lifetime of body shaming answer, "In my butt?", but the right answer is of course: "In your atomic nuclei!" and the quarks that make up your atomic nuclei are moving at a healthy fraction of the speed of light, so if we didn't use the relativistic $4$-vector definition of mass to compute your mass we wouldn't come up with a number that was all that close to your mass as measured by a balance or your resistance to acceleration.Īfter atomic nuclei or molecules react, the mass of the reactants is identical to the mass of the products, and the same holds for their momentum and energy. This is emphasized the the Wikipedia section cited earlier: mass and energy don't get interconverted but rather are separately conserved. In our example, $E_1=E_2=m_ec^2$ and $\theta=180°$ so we have $m=2m_e$, so the mass didn't change nor did the energy in the reaction of $e^+e^-$ annihilation. Physicists don't typically make a distinction between rest mass $m_0$ and moving mass $m$ but rather consider mass to be the invariant of the energy-momentum $4$-vector: $mc^2=\sqrt2$$ Since this thread seems to have been bumped by a better answer is in order.
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