Four-momentum | Wikipedia audio article
Channel: wikipedia tts
Date: 24/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Four-momentum


00:00:20 1 Minkowski norm
00:01:39 2 Relation to four-velocity
00:01:47 3 Derivation
00:01:57 4 Conservation of four-momentum
00:04:27 5 Canonical momentum in the presence of an electromagnetic potential
00:06:12 6 See also
00:06:28 7 References
00:07:36 ct, x1
00:07:46 y, x3
00:07:58 −x0, x1
00:08:10 x2, x3
00:11:32 0, (δxμ)t1
00:16:54 Conservation of four-momentum
00:18:21 pAμ + pBμ, while the mass M of the heavier particle is given by −PC ⋅ PC
00:20:51 Canonical momentum in the presence of an electromagnetic potential
00:22:31 See also



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SUMMARY
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In special relativity, four-momentum 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 E and three-momentum p = (px, py, pz) = γmv, where v is the particle's three-velocity and γ the Lorentz factor, is

  
    
      
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    {\displaystyle p=(p^{0},p^{1},p^{2},p^{3})=\left({E \over c},p_{x},p_{y},p_{z}\right).}
  The quantity mv of above is ordinary non-relativistic momentum of the particle and m 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.
The above definition applies under the coordinate convention that x0 = ct. Some authors use the convention x0 = t, which yields a modified definition with p0 = E/c2. It is also possible to define covariant four-momentum pμ where the sign of the energy is reversed.