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
Electron rest mass This quantity formula_5 is frame invariant and velocity independent. However, some texts group the Lorentz factor with the mass factor to define a new quantity called the "relativistic mass", formula_7. This quantity is evidently velocity dependent, and from it arises the notion that "mass increases with speed". This construction is optional, however, and adds little insight into the dynamics of Special Relativity. Since the electron mass determines a number of observed effects in atomic physics, there are potentially many ways to determine its mass from an experiment, if the values of other physical constants are already considered known. Historically, the