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.
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
where represents the vacuum as a variable medium.[5]
^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.
^S. N. Manida (1999). "Fock-Lorentz transformations and time-varying speed of light". arXiv:gr-qc/9905046.
^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.
^J. W. Moffat (2001). "A Model of Varying Fine Structure Constant and Varying Speed of Light". arXiv:astro-ph/0109350.
Further readingedit
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. ISBN978-3-540-25263-4. 40th Winter School on Theoretical Physics
April 13, 2024
fock, lorentz, symmetry, lorentz, invariance, follows, from, independent, postulates, principle, relativity, principle, constancy, speed, light, dropping, latter, while, keeping, former, leads, invariance, known, projective, lorentz, transformation, general, s. 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 c 1e0m0 displaystyle c frac 1 sqrt varepsilon 0 mu 0 where e0 and m0 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 1x x displaystyle c x frac 1 sqrt chi x where x x displaystyle chi x represents the vacuum as a variable medium 5 See also editDoubly special relativity Orders of magnitude length Planck scale Planck units Quantum gravity Planck epochReferences edit Joao 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 S N Manida 1999 Fock Lorentz transformations and time varying speed of light arXiv gr qc 9905046 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 Vladimir Aleksandrovich Fock 1964 The theory of space time and gravitation 2 ed Macmillan ISBN 978 0 08 010061 6 J W Moffat 2001 A Model of Varying Fine Structure Constant and Varying Speed of Light arXiv astro ph 0109350 Further reading editGiovanni 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 Joao 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 Retrieved from https en wikipedia org w index php title Fock Lorentz symmetry amp oldid 1187974198, wikipedia, wiki, book, books, library,
