Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
Mass–energy equivalence the velocity is small, the relativistic mass and the rest mass are almost exactly the same. Also Einstein (following Hendrik Lorentz and Max Abraham) used velocity- and direction-dependent mass concepts () in his 1905 electrodynamics paper and in another paper in 1906. However, in his first paper on (1905), he treated as what would now be called the "rest mass". Some claim that (in later years) he did not like the idea of "relativistic mass". When modern physicists say "mass", they are usually talking about rest mass, since if they meant "relativistic mass", they would just say "energy". Considerable debate