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Has anyone ever seen a proof that lorentz transforms are the only transforms for maxwells equations to remain invariant between two reference frames moving at a uniform velocity with respect to each other?
Has anyone ever seen a proof that lorentz transforms are the only transforms for maxwells equations to remain invariant between two reference frames moving at a uniform velocity with respect to each other?
The proof is simple.
Max's equations contain the constant c.
This leads to the speed of light being c in any coordinate system.
The LT is the only transformation between two frames moving at a uniform velocity with respect to each other that preserves the speed c.
The proof is simple.
Max's equations contain the constant c.
This leads to the speed of light being c in any coordinate system.
The LT is the only transformation between two frames moving at a uniform velocity with respect to each other that preserves the speed c.
The addition of any charged object changes the permittivity (from a constant that produces the speed of light to a tensor producing dispersion and a different group velocity)
The full set of transformations that leave Maxwell's equations form-invariant is the Poincare group, which is larger than the group of Lorentz boosts.
... that the form of Maxwell's equations are invariant under not only the ten dimensional Poincare group (generated by boosts, rotatations, and translations) but also under the E^{1,3} conformal group, which happens to be SO(2,4), a fifteen dimensional Lie group. The extra generators of the Lie algebra can be given as a scaling transformation and certain "toral rolls" (higher dimensional generalizations of certain Moebius transformations); the corresponding transformations are conformal but do not preserve the Minkowski interval.
The addition of any charged object changes the permittivity (from a constant that produces the speed of light to a tensor producing dispersion and a different group velocity)
Is this generally accepted?? Never knew about it if accurate...
The presence of a medium provides a preferred system, the rest system of the medium, so the Lorentz transformation does not have the same meaning as it does in vacuum.That's an interesting proof, but it only applies to a pure vacuum. The addition of any charged object changes the permittivity (from a constant that produces the speed of light to a tensor producing dispersion and a different group velocity)
The presence of a medium provides a preferred system, the rest system of the medium, so the Lorentz transformation does not have the same meaning as it does in vacuum.