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In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame.
The origin of charge invariance, and all relativistic invariants, is presently unclear. There may be some hints proposed by string/M-theory. It is possible the concept of charge invariance may provide a key to unlocking the mystery of unification in physics – the single theory of gravity, electromagnetism, the strong, and weak nuclear forces.
A critical requirement of the Lorentz transformations is the invariance of the speed of light, a fact used in their derivation, and contained in the transformations themselves. If in F the equation for a pulse of light along the x direction is x = ct, then in F′ the Lorentz transformations give x′ = ct′, and vice versa, for any −c < v < c.
The commutation relations of the Hamiltonian, and the Lorentz generators, guarantee that Lorentz invariance implies rotational invariance, so that any state can be rotated by 180 degrees. Since a sequence of two CPT reflections is equivalent to a 360-degree rotation, fermions change by a sign under two CPT reflections, while bosons do not.
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.
is “the rest charge density”, i.e., the charge density for a comoving observer (an observer moving at the speed u - with respect to the inertial observer O - along with the charges). Qualitatively, the change in charge density (charge per unit volume) is due to the contracted volume of charge due to Lorentz contraction .
The relativistic formulations are more symmetric and Lorentz invariant. ... The invariance of charge can be derived as a corollary of Maxwell's equations.
The corresponding result for superstring theory is again deduced demanding Lorentz invariance, but now with supersymmetry. In these theories the Poincaré algebra is replaced by a supersymmetry algebra which is a Z 2-graded Lie algebra extending the Poincaré algebra. The structure of such an algebra is to a large degree fixed by the demands of ...