Fock–Lorentz symmetry

{{Short description|Symmetry principle in physics}}

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{{cite journal |title=Covariant and locally Lorentz-invariant varying speed of light theories |year=2000 |author=João Magueijo |arxiv=gr-qc/0007036 |journal=Phys. Rev. D |volume=62 |bibcode = 2000PhRvD..62j3521M |doi = 10.1103/PhysRevD.62.103521 |issue=10 |pages=103521 |s2cid=56377853 }} or the projective Lorentz transformation.{{cite arXiv |title=Fock-Lorentz transformations and time-varying speed of light |author=S. N. Manida |eprint=gr-qc/9905046 |year=1999}}{{cite journal |arxiv=astro-ph/9909311 |year=1999 |author=Sergey S. Stepanov |journal=Phys. Rev. D |volume=62 |title=A time-space varying speed of light and the Hubble Law in static Universe |bibcode = 2000PhRvD..62b3507S |doi = 10.1103/PhysRevD.62.023507 |issue=2 |page=023507 |s2cid=102341932 }} The general study of such theories began with Fock,{{cite book |author=Vladimir Aleksandrovich Fock |author-link=Vladimir Aleksandrovich Fock |edition=2 |isbn=978-0-08-010061-6 |url=https://books.google.com/books?id=dSEvAAAAIAAJ&q=intitle:The+intitle:Theory+intitle:of+intitle:Space+intitle:Time+intitle:and+intitle:Gravitation |title=The theory of space, time and gravitation |publisher=Macmillan |year=1964}} 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

: $c\; =\; \backslash frac\{1\}\{\backslash sqrt\{\backslash varepsilon\; \_0\; \backslash mu\_0\}\},$

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

: $c(x)\; =\; \backslash frac\{1\}\{\backslash sqrt\{\backslash chi(x)\}\},$

where $\backslash chi\; (x)$ represents the vacuum as a variable medium.{{cite arXiv |eprint=astro-ph/0109350 |author=J. W. Moffat |year=2001 |title=A Model of Varying Fine Structure Constant and Varying Speed of Light}}