Mass in special relativity what causes these particles to be termed "massless." However, even massless particles have a relativistic mass, which varies with their observed energy in various frames of reference, The invariant mass is the ratio of four-momentum (the four-dimensional generalization of classical momentum) to four-velocity: and is also the ratio of four-acceleration to four-force when the rest mass is constant. The four-dimensional form of Newton's second law is: The relativistic expressions for "E" and "p" obey the relativistic energy–momentum relation: where the m is the rest mass, or the invariant mass for systems, and "E" is the total energy. The equation is
Four-velocity are multiplied by the four-velocity, one then gets new physical four-vectors that have 4 independent components. For example: Effectively, the formula_27 factor combines with the Lorentz scalar term to make the 4th independent component Using the differential of the four-position, the magnitude of the four-velocity can be obtained: in short, the magnitude of the four-velocity for any object is always a fixed constant: The norm is also: so that: which reduces to the definition the Lorentz factor. Four-velocity In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic