Fock–Lorentz symmetry

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Lorentz invariance follows from two independent postulates: the principle of relativity and the principle of constancy of the speed of light. Dropping the latter while keeping the former leads to a new invariance, known as Fock–Lorentz symmetry[1] or the projective Lorentz transformation.[2][3] The general study of such theories began with Fock,[4] who was motivated by the search for the general symmetry group preserving relativity without assuming the constancy of c.

This invariance does not distinguish between inertial frames (and therefore satisfies the principle of relativity) but it allows for a varying speed of light in space, c; indeed it allows for a non-invariant c. According to Maxwell's equations, the speed of light satisfies

where ε0 and μ0 are the electric constant and the magnetic constant. If the speed of light depends upon the space–time coordinates of the medium, say x, then

where represents the vacuum as a variable medium.[5]

See also[edit]


  1. ^ João Magueijo (2000). "Covariant and locally Lorentz-invariant varying speed of light theories". Phys Rev D. 62 (10). arXiv:gr-qc/0007036Freely accessible. Bibcode:2000PhRvD..62j3521M. doi:10.1103/PhysRevD.62.103521. 
  2. ^ S.N.Manida (1999). "Fock-Lorentz transformations and time-varying speed of light". arXiv:gr-qc/9905046Freely accessible. 
  3. ^ Sergey S. Stepanov (1999). "A time-space varying speed of light and the Hubble Law in static Universe". Phys Rev. D62 (2). arXiv:astro-ph/9909311Freely accessible. Bibcode:2000PhRvD..62b3507S. doi:10.1103/PhysRevD.62.023507. 
  4. ^ Vladimir Aleksandrovich Fock (1964). The theory of space, time and gravitation (2 ed.). Macmillan. ISBN 0-08-010061-9. 
  5. ^ J. W. Moffat (2001). "A Model of Varying Fine Structure Constant and Varying Speed of Light". arXiv:astro-ph/0109350Freely accessible. 

Further reading[edit]