Mass and Energy

A symbol of the twentieth century is the famous Einstein relation between mass and energy. Here are four possible equations: (1) E₀ = mc² (2) E = mc² (3) E₀ = m₀c² (4) E = m₀c². In the equations c is the velocity of light, E is the total energy of a free body, E₀ its rest energy, m₀ its rest mass, and m its mass.

Which of these equations expresses one of the main consequences of the STR? Which equation was first written by Einstein and was considered by him a consequence of STR?

Answer

The answer to both questions is equation 1, although the majority of physicists seem to prefer equations 2 or 3! Their choices probably are caused by the confusing terminology widely used in the physics literature that says that a body at rest has a “proper mass”  or “rest mass” m0, and a body in motion has a “relativistic mass” m = .

There is only one mass in physics, m, which does not depend on the reference frame. This mass m is the relativistic invariant quantity in E² – p²c² = m²c⁴, whereas the energy is different in different reference systems. There is no need to place the index 0 with the mass. However, the total energy E needs the 0 index if the particle has no momentum in that reference frame that is, E₀ = mc².

For a complete and stimulating discussion of these ideas and their history see the L. V. Okun reference below.