We consider a Lorenz-like gauge theory with a second speed parameter that differs from the speed of light. This theory extends electrodynamics so that it has two speeds corresponding to the speeds of transverse and longitudinal waves in vacuum. The two-parameter extension of electrodynamics can be formally mapped onto the linear theory of elasticity. Because the case of equal speeds is not realized in an elastic medium, a compressible medium cannot model electromagnetism. In the Coulomb gauge electrodynamics can be formally mapped onto incompressible elasticity, which suggests that a linear-elastic incompressible medium can serve as a model of electromagnetism.
REFERENCES
1.
J. D.
Jackson
, “From Lorenz to Coulomb and other explicit gauge transformations
,” Am. J. Phys.
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(9
), 917
–928
(2002
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L. D. Landau and E. M. Lifshitz, The Theory of Elasticity (Butterworth–Heinemann, London, 1995), 3rd ed.
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© 2003 American Association of Physics Teachers.
2003
American Association of Physics Teachers
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