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 in special relativity Mass in special relativity Mass in special relativity incorporates the general understandings from the laws of motion of special relativity along with its concept of mass–energy equivalence. The word "mass" is given two meanings in special relativity: one ("rest" or "invariant mass", and its equivalent "rest energy") is an invariant quantity which is the same for all observers in all reference frames; the other ("relativistic mass" or the equivalent "total energy" of the body) is dependent on the velocity of the observer. The term "relativistic mass" tends not to be used in particle and nuclear physics and is often avoided