Mass (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations. Additionally, mass relates a body's momentum p to its linear velocity v: and the body's kinetic energy "K" to its velocity: The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass. This is most vividly demonstrated by comparing the mass of the proton in the
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