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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 some situations, matter may indeed be converted to non-matter forms of energy (see above), but in all these situations, the matter and non-matter forms of energy still retain their original mass. For isolated systems (closed to all mass and energy exchange), mass never disappears in the center of momentum frame, because energy cannot disappear.
The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics 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.
In relativity, the COM frame exists for an isolated massive system.This is a consequence of Noether's theorem.In the COM frame the total energy of the system is the rest energy, and this quantity (when divided by the factor c 2, where c is the speed of light) gives the invariant mass of the system:
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 electromagnetic stress–energy tensor allows a compact way of writing the conservation laws of linear momentum and energy in electromagnetism. The divergence of the stress–energy tensor is: ∂ ν T μ ν + η μ ρ f ρ = 0 {\displaystyle \partial _{\nu }T^{\mu \nu }+\eta ^{\mu \rho }\,f_{\rho }=0\,} where f ρ {\displaystyle f_{\rho ...
This is not the case for the Dirac equation and its energy–momentum tensor. [ 6 ] The stress energy tensor is the set of conserved currents corresponding to the invariance of the Klein–Gordon equation under space-time translations x μ ↦ x μ + c μ {\displaystyle x^{\mu }\mapsto x^{\mu }+c^{\mu }} .
When there is no matter present, so that the energy–momentum tensor vanishes, the results are the vacuum Einstein equations, R μ ν = 0. {\displaystyle R_{\mu \nu }=0.} In general relativity, the world line of a particle free from all external, non-gravitational force is a particular type of geodesic in curved spacetime.
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