four-momentum
Sign in to saveAlso known as 4-momentum, four momentum, relativistic momentum, momentum 4-vector, energy-momentum 4-vector, momentum four-vector, energy-momentum four-vector, energy–momentum 4-vector
In special relativity, four-momentum (also called momentum–energy or momenergy) 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. The contravariant four-momentum of a particle with relativistic energy and three-momentum , where is the particle's three-velocity and the Lorentz factor, is p = \left(p^0 , p^1 , p^2 , p^3\right) = \left(\frac E c , p_x , p_y , p_z\right).
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Encyclopedic overview
8 sectionsContents
- Minkowski norm
- Relation to four-velocity
- Derivation
- Conservation of four-momentum
- Canonical momentum in the presence of an electromagnetic potential
- Four-momentum in curved spacetime
- See also
- References
In special relativity, four-momentum (also called momentum–energy or momenergy) 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. The contravariant four-momentum of a particle with relativistic energy and three-momentum , where is the particle's three-velocity and the Lorentz factor, is p = \left(p^0 , p^1 , p^2 , p^3\right) = \left(\frac E c , p_x , p_y , p_z\right).
The quantity of above is the ordinary non-relativistic momentum of the particle and its rest mass. The four-momentum is useful in relativistic calculations because it is a Lorentz covariant vector. This means that it is easy to keep track of how it transforms under Lorentz transformations.
Excerpted from Wikipedia’s “four-momentum” article, available under the CC BY-SA 4.0 licence.