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The energy and momentum of an object measured in two inertial frames in energy–momentum space – the yellow frame measures E and p while the blue frame measures E ′ and p ′. The green arrow is the four-momentum P of an object with length proportional to its rest mass m 0.
In special relativity, four-momentum (also called momentum–energy or momenergy [1]) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions ; similarly four-momentum is a four-vector in spacetime .
Using the relativistic relations for energy and momentum yields = = = =. The variable v {\displaystyle \mathbf {v} } can either be interpreted as the speed of the particle or the group velocity of the corresponding matter wave—the two are the same.
The relativistic energy–momentum relationship holds even for massless particles such as photons; by setting m 0 = 0 it follows that =. In a game of relativistic "billiards", if a stationary particle is hit by a moving particle in an elastic collision, the paths formed by the two afterwards will form an acute angle.
Note that the SPI group is actually infinite-dimensional. The existence of conserved quantities is because the SPI group of "super-translations" has a preferred 4-parameter subgroup of "pure" translations, which, by Noether's theorem, generates a conserved 4-parameter energy–momentum. The norm of this 4-parameter energy–momentum is the ADM ...
Energy–momentum may refer to: Four-momentum; Stress–energy tensor; Energy–momentum relation This page was last edited on 28 December 2019, at 10:37 (UTC). Text ...
Momentum and length scales are related inversely, according to the de Broglie relation: The higher the energy or momentum scale we may reach, the lower the length scale we may probe and resolve. Therefore, the momentum-space RG practitioners sometimes claim to integrate out high momenta or high energy from their theories.
Today, the relation of mass, momentum, velocity, and all forms of energy – including electromagnetic energy – is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence. As to the cause of mass of elementary particles, the Higgs mechanism in the framework of the relativistic Standard Model is currently ...