Longitudinal corollary to the transverse mass–energy relation of special relativity

Ivesʹ identity which links the different gamma factors of special relativity can be used to show that Einsteinʹs famous E=mc2 law is the quadratic (transverse) special case of a more general first-order longitudinal law E=mcv/2. The latter allows the conversion of energy into both positive and negative mass increments. It arises as an implication of both the equivalence principle and quantum mechanics in a gravitational potential.