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The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields.
The energy–momentum relation goes back to Max Planck's article [5] published in 1906. It was used by Walter Gordon in 1926 and then by Paul Dirac in 1928 under the form = + +, where V is the amount of potential energy. [6] [7]
The Dyson series can be alternatively rewritten as a sum over Feynman diagrams, where at each vertex both the energy and momentum are conserved, but where the length of the energy-momentum four-vector is not necessarily equal to the mass, i.e. the intermediate particles are so-called off-shell. The Feynman diagrams are much easier to keep track ...
Matter and energy generate curvature of spacetime. This is the subject of general relativity. Curvature of spacetime affects electrodynamics. An electromagnetic field having energy and momentum also generates curvature in spacetime.
With this approach it is less clear that the energy and momentum are parts of a four-vector. The energy and the three-momentum are separately conserved quantities for isolated systems in the Lagrangian framework. Hence four-momentum is conserved as well. More on this below. More pedestrian approaches include expected behavior in electrodynamics ...
In such universes Mach's principle can be stated as the distribution of matter and field energy-momentum (and possibly other information) at a particular moment in the universe determines the inertial frame at each point in the universe (where "a particular moment in the universe" refers to a chosen Cauchy surface). [7]: 188–207
If one is only interested in the weak field limit of the theory, the dynamics of matter can be computed using special relativity methods and/or Newtonian laws of gravity and the resulting stress–energy tensor can then be plugged into the Einstein field equations. But if one requires an exact solution or a solution describing strong fields ...
With respect to classical physics, conservation laws include conservation of energy, mass (or matter), linear momentum, angular momentum, and electric charge. With respect to particle physics, particles cannot be created or destroyed except in pairs, where one is ordinary and the other is an antiparticle.