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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 .
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.
In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum mechanics and thermodynamics , it places a heavy emphasis on the commonalities between the topics covered.
The Abraham–Minkowski controversy is a physics debate concerning electromagnetic momentum within dielectric media. [1] [2] Two equations were first suggested by Hermann Minkowski (1908) [3] and Max Abraham (1909) [4] [5] for this momentum. They predict different values, from which the name of the controversy derives. [6]
If the energy–momentum tensor T μν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting T μν = 0 in the trace-reversed field equations , the vacuum field equations, also known as 'Einstein vacuum equations' (EVE), can be written as R μ ν = 0 . {\displaystyle R ...
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 }} .
Who arranges it: In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating any object's rest (intrinsic) mass, total energy, and momentum:... holds for a system, such as a particle or macroscopic body, having intrinsic rest mass m0, total energy E, and a momentum of magnitude p,
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 ...