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In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.
So relativistic energy and momentum significantly increase with speed, thus the speed of light cannot be reached by massive particles. In some relativity textbooks, the so-called "relativistic mass" = is used as well. However, this concept is considered disadvantageous by many authors, instead the expressions of relativistic energy and momentum ...
In particle physics, a relativistic particle is an elementary particle with kinetic energy greater than or equal to its rest-mass energy given by Einstein's relation, =, or specifically, of which the velocity is comparable to the speed of light. [1]
If the energy–momentum tensor T μν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor = (+) is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory): + = (+).
To derive the equations of special relativity, one must start with two other The laws of physics are invariant under transformations between inertial frames. In other words, the laws of physics will be the same whether you are testing them in a frame 'at rest', or a frame moving with a constant velocity relative to the 'rest' frame.
In its basic form, it is the sum of the 'opposing' centrifugal potential energy with the potential energy of a dynamical system. It may be used to determine the orbits of planets (both Newtonian and relativistic) and to perform semi-classical atomic calculations, and often allows problems to be reduced to fewer dimensions.
The sources of any gravitational field (matter and energy) is represented in relativity by a type (0, 2) symmetric tensor called the energy–momentum tensor. It is closely related to the Ricci tensor. Being a second rank tensor in four dimensions, the energy–momentum tensor may be viewed as a 4 by 4 matrix.
The total energy can also be approximated as = where = is the Lorentz invariant momentum. This can result from holding the mass fixed and increasing the kinetic energy to very large values or by holding the energy E fixed and shrinking the mass m to very small values which also imply a very large γ {\displaystyle \gamma } .