Fock–Lorentz symmetry

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

${\displaystyle c={\frac {1}{\sqrt {\varepsilon _{0}\mu _{0}}}},}$

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

${\displaystyle c(x)={\frac {1}{\sqrt {\chi (x)}}},}$

where ${\displaystyle \chi (x)}$ represents the vacuum as a variable medium.^[5]

See also

• Doubly special relativity
• Orders of magnitude (length)
• Planck scale
• Planck units
• Quantum gravity
• Planck epoch

References

1. João Magueijo (2000). "Covariant and locally Lorentz-invariant varying speed of light theories". Phys. Rev. D. 62 (10): 103521. arXiv:gr-qc/0007036. Bibcode:2000PhRvD..62j3521M. doi:10.1103/PhysRevD.62.103521. S2CID 56377853.
2. S. N. Manida (1999). "Fock-Lorentz transformations and time-varying speed of light". arXiv:gr-qc/9905046.
3. Sergey S. Stepanov (1999). "A time-space varying speed of light and the Hubble Law in static Universe". Phys. Rev. D. 62 (2): 023507. arXiv:astro-ph/9909311. Bibcode:2000PhRvD..62b3507S. doi:10.1103/PhysRevD.62.023507. S2CID 102341932.
4. Vladimir Aleksandrovich Fock (1964). The theory of space, time and gravitation (2 ed.). Macmillan. ISBN 978-0-08-010061-6.
5. J. W. Moffat (2001). "A Model of Varying Fine Structure Constant and Varying Speed of Light". arXiv:astro-ph/0109350.

Further reading

• Giovanni Amelino-Camelia; Jerzy Kowalski-Glikman; Gianluca Mandanici; Andrea Procaccini (2005). "Phenomenology of Doubly Special Relativity". Int. J. Mod. Phys. A. 20 (26): 6007. arXiv:gr-qc/0312124. Bibcode:2005IJMPA..20.6007A. doi:10.1142/S0217751X05028569. S2CID 119340651.
• João Magueijo; Lee Smolin (2002). "Lorentz invariance with an invariant energy scale". Phys. Rev. Lett. 88 (19): 190403. arXiv:hep-th/0112090. Bibcode:2002PhRvL..88s0403M. doi:10.1103/PhysRevLett.88.190403. PMID 12005620. S2CID 14468105.
• J Kowalski-Glikman (2004). "Introduction to doubly special relativity". In Giovanni Amelino-Camelia; Jerzy Kowalski-Glikman (eds.). Planck Scale Effects in Astrophysics and Cosmology. Springer. pp. 131ff. ISBN 978-3-540-25263-4. 40th Winter School on Theoretical Physics