Fourier shell correlation: Difference between revisions

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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
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while keeping the former leads to a new invariance,
known as '''Fock–Lorentz symmetry'''<ref name=Magueijo>{{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 |volume=D62 |bibcode = 2000PhRvD..62j3521M |doi = 10.1103/PhysRevD.62.103521 |issue=10 }}</ref>  or the '''Projective Lorentz Transformation'''.<ref name=Manida>{{cite journal |title=Fock-Lorentz transformations and time-varying speed of light |author=S.N.Manida |arxiv=gr-qc/9905046 |year=1999 |journal=ArXiv preprint|bibcode = 1999gr.qc.....5046M |pages=5046 }}</ref><ref name=Stepanov>{{cite journal |arxiv=astro-ph/9909311 |year=1999 |author=Sergey S. Stepanov |journal=Phys Rev |volume=D62 |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 }}</ref> The general study of such theories began with [[Vladimir Aleksandrovich Fock|Fock]],<ref name=Fock>{{cite book |author=[[Vladimir Aleksandrovich Fock]] |edition=2 |isbn=0-08-010061-9 |url=http://books.google.com/?id=dSEvAAAAIAAJ&dq=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}}</ref> 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
:<math>c = \frac{1}{\sqrt{\varepsilon _0 \mu_0} }\ , </math>
 
with ε<sub>0</sub>, μ<small>0</small> the [[electric constant]] and [[magnetic constant]]. If the speed of light depends upon the space-time coordinates of the medium, say ''x'', then:
:<math>c(x) = \frac{1}{\sqrt{\chi (x) } }\ , </math>
where χ(''x'') represents the vacuum as a variable medium.<ref name=Moffat>{{cite journal |arxiv=astro-ph/0109350 |author=J. W. Moffat |year=2001 |title=A Model of Varying Fine Structure Constant and Varying Speed of Light |journal=ArXiv preprint|bibcode = 2001astro.ph..9350M |pages=9350 }}</ref>
 
==See also==
* [[Doubly special relativity]]
* [[Orders of magnitude (length)]]
* [[Planck scale]]
* [[Planck units]]
* [[Quantum gravity]]
* [[Planck epoch]]
 
==References==
{{Reflist}}
 
==Further reading==
*{{cite journal |title=Phenomenology of Doubly Special Relativity |author=Giovanni Amelino-Camelia, Jerzy Kowalski-Glikman, Gianluca Mandanici, Andrea Procaccini |arxiv=gr-qc/0312124 |journal=Int J Mod Phys |volume=A20 |year=2005|bibcode = 2005IJMPA..20.6007A |doi = 10.1142/S0217751X05028569 |issue=26 |pages=6007 }}
*{{cite journal |title=Lorentz invariance with an invariant energy scale |author=João Magueijo & Lee Smolin |year=2002 |arxiv=hep-th/0112090 |journal=Phys Rev Lett |volume=88|bibcode = 2002PhRvL..88s0403M |doi = 10.1103/PhysRevLett.88.190403 |issue=19 }}
*{{cite book |title=Planck Scale Effects in Astrophysics and Cosmology |chapter=Introduction to doubly special relativity |author=J Kowalski-Glikman |pages=131''ff'' |url=http://books.google.com/?id=RntpN7OesBsC&pg=PA131 |isbn=3-540-25263-0 |publisher=Springer |year=2004 |editor=Giovanni Amelino-Camelia & Jerzy Kowalski-Glikman, eds.}} [http://arxiv.org/abs/hep-th/0405273v1 40th Winter School on Theoretical Physics]
 
{{DEFAULTSORT:Fock-Lorentz symmetry}}
[[Category:Special relativity]]
[[Category:Symmetry]]

Latest revision as of 12:44, 17 September 2014

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