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| '''Variable speed of light (VSL)''' is a hypothesis that states that the [[speed of light]], usually denoted by ''c'', may be a function of space and time. Variable speed of light occurs in some situations of classical physics, as equivalent formulation of accepted theories, but also in various alternative theories of gravitation and cosmology, many of them non-mainstream. In classical physics, the [[refractive index]] describes how light slows down when traveling through a [[condensed matter physics|medium]]. The speed of light in vacuum instead is considered a [[Physical constant|constant]], and defined by the [[SI]] as 299792458 m/s. Alternative theories therefore usually modify the definitions of [[meter]] and [[second]]s. VSL should not be confused with [[faster than light]] theories. Notable VSL attempts have been done by [[Albert Einstein|Einstein]] in 1911, by [[Robert Dicke]] in 1957, and by several researchers starting from the late 1980s. Since some of them contradict established concepts, VSL theories are a matter of debate.
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| ==Einstein's VSL attempt in 1911==
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| While Einstein's first mentioned a variable speed of light in 1907,<ref>{{cite journal | author = Albert Einstein | journal = Jahrbuch für Radioaktivität und Elektronik | year = 1907 | volume = 4 | pages = 411–462 }}</ref> he reconsidered the idea more thoroughly in 1911.<ref>{{cite journal|author=A. Einstein|title = Uber den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes| journal = Annalen der Physik|year = 1911|volume = 35|pages = 898–906 |url=http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1911_35_898-908.pdf|doi=10.1002/andp.19113401005}}</ref> In analogy to the situation in media, where a shorter wavelength <math> \lambda </math>, by means of <math> c = \nu \lambda </math>, leads to a lower speed of light, Einstein assumed that clocks in a gravitational field run slower, whereby the corresponding frequencies <math> \nu </math> are influenced by the gravitational potential (eq.2, p. 903):
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| : <math> \nu_1 = \nu_2 \left(1+\frac{GM}{r c^2}\right). </math> | | Often times these clients offer a user friendly interface and have many more features than regular Yahoo Chat. Aspects like their favorite movies, likes and dislikes and lots more. You can't ever prove what was really agreed upon if one should go back on their deal. I was able to see these psychics through my computer and I was shocked at how they really meditated and took my reading seriously. If you said for example: "What does it feel like to be the most beautiful girl in this room?" She may reply by being all bashful and not really give you a proper reply, but what then if you follow up by looking around the bar or street where you are, and actually challenge her to point out better looking women! To cruise the bar and club scene in search of a prospective man for the evening is either not so appealing or involves too much time.<br><br>First we'll see how this one turns out, and then consider another project." Fortunately, the service will usually bill you discreetly so that no one knows you have signed up to a phone dating service. Because it is possible to see or contact the products within the World wide web, outlets should head to a little more effort to supply you with technical specifications, which will allow you to compare everything you're obtaining in your funds throughout various internet sites. Obviously this type of interaction can be over done and feel robotic if it is over used, but common responses such as "give me a second and I will look up your record" can be efficiently stored as text and inserted into chat. We need to set an example not just tell them not do this or that.<br><br>In order to know more about their personal background, special abilities, areas of expertise and authenticity, and legal licenses, people can visit the websites of psychic reading companies for proof and verification. The results of a love calculator gives the reason to trust your online date and to possibly invest in the online dating relationship with no limitation whatsoever. Ryan Fitzgerald, an unemployed 20-year-old who lives with his father, had a little bit of free time on his hands. Your dear ones may be across seas but you can hear them, talk to them and see them if you have the gadgets ready.<br><br>Not only can you use JiveTalk and iPhone for personal conversations but it works well as a business tool as well. Since posting his number on Friday, Fitzgerald received more than 5,000 phone calls and text messages from people from around the world. Do You Use Free [http://vitskavali.in/alumni/groups/free-phone-chat-lines-movie-theaters-in-macon-ga/ Phone Chat] Lines For Positive Singles? Text Chat Smileys Smiley Face Symbols Meaning :) Smiling, Happy Face, Cheshire Cat Smile (Indicates that you are not to be taken seriously. Choosing the best live chat software for a small business web site can be confusing, based on the wide range of options and prices for such products. Your Xbox Live account will be featured on your Windows Phone 7 mobile phone and you'll be able to chat with friends, earn achievements, and play games on your mobile phone.<br><br>No one has to know what you are doing and you can make money without having to leave your home. Find one that will assist you in every way in running and promoting your business. For some singles, bars are where it is at. The first words are the hardest! You are able to record your voice to ensure that other can listen to it later or you are able to use the live chat to interact with them.<br><br>It'll Only Be on Cool Phones Microsoft is not going to let its cool Windows Phone 7 hardware and features to be taken through the dumps with out-dated and underequipped mobile phones. I forgot what I was thinking of in the first place. 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As technology bridges the world, making even the most distant continents feel closer together, so too are people coming together who otherwise might not have had the chance to meet.<br><br>Then I can upload the video or save it as an animated screen saver. Since I was already having difficulty forcing myself to get on the phone again after the first time, this was not a hard decision. That special somebody is not so far away from you now. But these charges are many times lower than the regular phone calls. Youth today believe they need fast love and like to meet new people.<br><br>There is no reason to wait. So which is the best I hear you ask? If you have always wanted to start your own business and be your own boss, this is your chance to do it right. My dad is in India, but in another state. It is also important to read (or listen to) all the terms and conditions of a service before signing up.<br><br>So how exactly do they work? Mixed reviews, so far. Be sure to sort out the differences between phone sex and local and live chat lines. However, we also cautioned her to take care.<br><br>It is a good place for these not yet adults individuals to learn that one gets accepted by others for the quality of thought. I have come across people who have married after chatting with someone on a chat line. Plenty housewives now don't whine to their spouses for not going to shopping with them or not bringing their pals party on stays, No more quarrels. I prefer not to phone chat as it takes up too much valuable time, but when I do, I charge for the call using my hourly rates and then I plug the details into pre-typed contract templates that I have on my hard drive and send it over for their signature. As usual the adult industry leads the way in introducing you new ways to interact with people and you'll find there a few video chat services already being used.<br><br> |
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| Einstein commented:
| | If you are the type of person who can come over with confidence and without embarrassment, try these: "I'm new in town and can't find my way around; er, could I have directions to your place?" Laugh, be cool and this sort of thing can work well. Revamping your social life has never been easier. This just led me to delve deeper into the matter, and I soon realized how out of touch I was. This also constitutes keyboard shortcuts, push emails, Myspace notifications, Facebook and Ebay notifications. |
| {{Block quote| "Aus dem . . ., dass die Lichtgeschwindigkeit im Schwerefelde eine Funktion des Ortes ist, lasst sich leicht mittels des Huygensschen Prinzipes schliessen, dass quer zum Schwerefeld sich fortpflanzende Lichtstrahlen eine Krummung erfahren mussen."
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| ("Given ... that the speed of light is a function of position, it is easily deduced from Huygens's principle that light rays propagating at right angles to the gravity field must undergo deflection.") }}
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| In a subsequent paper in 1912 <ref>{{cite journal|author=A. Einstein|title = Lichtgeschwindigkeit und Statik des Gravitationsfeldes| journal = Annalen der Physik|year = 1912|volume = 38|pages = 355–369 |url=http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1912_38_355-369.pdf}}</ref>
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| he concluded that
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| {{block quote| “Das Prinzip der Konstanz der Lichtgeschwindigkeit kann nur insofern aufrechterhalten werden, als man sich auf für Raum-Zeitliche-Gebiete mit konstantem Gravitationspotential beschränkt.“ (“The principle of the constancy of the speed of light can be kept only when one restricts oneself to space-time regions of constant gravitational potential.”)}}
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| However, Einstein deduced a light deflection at the sun of “almost one arcsecond” which is just one-half of the [[Tests of general relativity|correct value]] later derived by his theory of [[general relativity]]. While the correct value was later measured by [[Arthur Eddington|Eddington]] in 1919, Einstein gave up his VSL theory for other reasons. Notably, in 1911 he had considered variable time only, while in general relativity, albeit in another theoretical context, both space and time measurements are influenced by nearby masses.
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| ==Dicke's 1957 attempt and Mach's principle==
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| [[Robert Dicke]], in 1957, developed a related VSL theory of gravity.<ref name="Dicke">{{cite journal|author=R. Dicke|title=Gravitation without a Principle of Equivalence|doi=10.1103/RevModPhys.29.363|journal= Reviews of Modern Physics|year=1957|volume = 29|pages=363–376|bibcode=1957RvMP...29..363D}}</ref> In contrast to Einstein, Dicke assumed not only the frequencies to vary, but also the wavelengths. Since <math> c = \nu \lambda </math>, this resulted in a relative change of ''c'' twice as much as considered by Einstein. Dicke assumed a refractive index <math> n= \frac{c}{c_0} = 1+\frac{2 GM}{r c^2} </math> (eqn.5) and proved it to be consistent with the observed value for light deflection. In a comment related to [[Mach's principle]], Dicke suggested that, while the right part of the term in eq. 5 is small, the left part, 1, could have “its origin in the remainder of the matter in the universe”.
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| Given that in a universe with an increasing horizon more and more masses contribute to the above refractive index, Dicke considered a cosmology where ''c'' decreased in time, providing an alternative explanation to the [[Hubble's law|cosmological redshift]] <ref name="Dicke"/> (p. 374). Dicke's theory does not contradict the [[International System of Units|SI]] definition of c= 299792458 m/s, since the time and length units [[second]] and [[meter]] can vary accordingly (p. 366).
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| ==Other VSL attempts related to Einstein and Dicke==
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| Though Dicke's attempt presented an alternative to [[general relativity]], the notion of a spatial variation of the speed of light as such does not contradict general relativity. Rather it is implicitly present in general relativity, occurring in the coordinate space description, as it is mentioned in several textbooks, e.g. Will,<ref>{{cite book|author=C.M. Will |title=Theory and Experiment in Gravitational Physics|publisher=Cambridge University Press|year=1995|page=144}}</ref> eqs. 6.14, 6.15, or Weinberg,<ref>{{cite book|author=S. Weinberg |title=Gravitation and Cosmology|publisher=Wiley| year=1972|location=London |page=222}}</ref> eq. 9.2.5 (<math> \phi </math> denoting the gravitational potential −''GM''/''r''):
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| "note that the photon speed is ... <math> |u| = 1+2 \phi +O(v^3)</math>."
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| Based on this, variable speed of light models have been developed which agree with all known tests of general relativity,<ref>{{cite journal|author=J. Broekaert |title =A Spatially-VSL Gravity Model with 1-PN Limit of GRT|journal=Foundations of Physics|year = 2008| volume = 38| pages=409–435|arxiv=gr-qc/0405015|doi=10.1007/s10701-008-9210-8}}</ref> but some distinguish for higher-order tests.<ref>{{cite journal|author=K. Krogh |title=Gravitation Without Curved Space-time|year = 1999| arxiv=astro-ph/9910325}}</ref> Other models claim to shed light on the equivalence principle<ref>{{cite journal|author=M. Arminjon |title = Space Isotropy and Weak Equivalence Principle in a Scalar Theory of Gravity| journal = Brazilian Journal of Physics |arxiv=gr-qc/0412085|year = 2006|volume = 36|pages = 177–189| doi = 10.1590/S0103-97332006000200010}}</ref> or make a link to Dirac's [[Dirac large numbers hypothesis|Large Numbers Hypothesis]].<ref>{{cite journal|author=A. Unzicker |title=A look at the abandoned contributions to cosmology of Dirac, Sciama, and Dicke|journal=Annalen der Physik| year = 2009|volume=521|pages=57–70| arxiv=0708.3518|doi=10.1002/andp.200810335}}</ref>
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| ==Modern VSL theories as an alternative to cosmic inflation ==
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| The varying speed of light cosmology has been proposed independently by [[Jean-Pierre Petit]] in 1988,<ref>
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| {{cite journal |title= An interpretation of cosmological model with variable light velocity |author= J.P. Petit |journal= Mod. Phys. Lett. A |volume= 3 |issue= 16 |year= 1988 |pages= 1527–1532 |doi= 10.1142/S0217732388001823 |bibcode = 1988MPLA....3.1527P |url=http://www.bigravitytheory.com/pdf/modern_physics_letters_a1.pdf}}</ref><ref>
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| {{Cite journal |title= Cosmological model with variable light velocity: the interpretation of red shifts |author= J.P. Petit |journal= Mod. Phys. Lett. A |volume= 3 |issue= 18 |year= 1988 |pages= 1733–1744 |doi= 10.1142/S0217732388002099 |bibcode = 1988MPLA....3.1733P |url=http://www.bigravitytheory.com/pdf/modern_physics_letters_a2.pdf}}</ref><ref>
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| {{cite journal |title= Gauge cosmological model with variable light velocity. Comparizon with QSO observational data |author= J.P. Petit, M. Viton |journal= Mod. Phys. Lett. A |volume= 4 |issue= 23 |year= 1989 |pages= 2201–2210 |doi= 10.1142/S0217732389002471 |bibcode = 1989MPLA....4.2201P |url=http://www.bigravitytheory.com/pdf/modern_physics_letters_a3.pdf}}</ref><ref>
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| {{cite journal |title= Scale invariant cosmology |author= P. Midy, J.P. Petit |journal= Int. J. Mod. Phys. D |issue= 8 |year= 1989 |pages= 271–280|url=http://www.bigravitytheory.com/pdf/scale_inv.pdf}}</ref> [[John Moffat (physicist)|John Moffat]] in 1992,<ref>
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| {{cite journal | title= Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology | author= J. Moffat | journal= Int. J. Mod. Phys. D |volume= 2 |issue= 3 |year=1993 | pages=351–366 | doi= 10.1142/S0218271893000246 |arxiv = gr-qc/9211020 |bibcode = 1993IJMPD...2..351M }}</ref>
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| and the two-man team of [[Andreas Albrecht]] and [[João Magueijo]] in 1998<ref>
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| {{cite journal |author= J.D. Barrow |title= Cosmologies with varying light-speed |year= 1998 |doi= 10.1103/PhysRevD.59.043515 |journal= Physical Review D |volume= 59 |issue= 4 |arxiv=astro-ph/9811022|bibcode = 1999PhRvD..59d3515B }}</ref><ref>
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| {{cite journal |title= A time varying speed of light as a solution to cosmological puzzles |author= A. Albrecht, J. Magueijo |journal= Phys. Rev. |volume= D59 |pages= 043516 |year= 1999 |arxiv=astro-ph/9811018|bibcode = 1999PhRvD..59d3516A |doi = 10.1103/PhysRevD.59.043516 }}</ref><ref name="local">
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| {{cite journal |author= J. Magueijo |title= Covariant and locally Lorentz-invariant varying speed of light theories |journal=Phys. Rev. |volume= D62 |year= 2000 |pages= 103521 |arxiv=gr-qc/0007036|bibcode = 2000PhRvD..62j3521M |doi = 10.1103/PhysRevD.62.103521 }}</ref><ref>
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| {{cite journal |author= J. Magueijo |title= Stars and black holes in varying speed of light theories |journal= Phys. Rev. |volume= D63 |year= 2001 |pages= 043502 |arxiv=astro-ph/0010591|bibcode = 2001PhRvD..63d3502M |doi = 10.1103/PhysRevD.63.043502 }}</ref><ref>
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| {{cite journal |author= J. Magueijo |title= New varying speed of light theories |journal= Rept. Prog. Phys. |volume= 66 |year= 2003 |issue= 11 |pages= 2025 |doi= 10.1088/0034-4885/66/11/R04 |arxiv = astro-ph/0305457 |bibcode = 2003RPPh...66.2025M }}</ref><ref>
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| {{cite book |title= Faster Than the Speed of Light: The Story of a Scientific Speculation |author= J. Magueijo |publisher= Perseus Books Group |location= Massachusetts |year= 2003 |isbn= 0-7382-0525-7}}</ref>
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| to explain the [[horizon problem]] of [[physical cosmology|cosmology]] and propose an alternative to [[cosmic inflation]]. An alternative VSL model has also been proposed.<ref>{{cite arXiv |author= J. Casado |title= A Simple Cosmological Model with Decreasing Light Speed |journal= |volume= |year= 2003 |pages= |doi= |eprint=astro-ph/0310178 |class= astro-ph}}</ref>
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| In Petit's VSL model, the variation of ''c'' accompanies the joint variations of all [[physical constant]]s combined to space and time [[Scale factor (Universe)|scale factors]] changes, so that all equations and measurements of these constants remain unchanged through the evolution of the universe. The [[Einstein field equations]] remain invariant through convenient joint variations of ''c'' and ''G'' in [[Einstein's constant]]. According to this model, the cosmological horizon grows like R, the space scale, which ensures the homogeneity of the primeval universe, which fits the observational data. Late-model restricts the variation of constants to the higher [[energy density]] of the early universe, at the very beginning of the [[radiation-dominated era]] where spacetime is identified to space-entropy with a [[Metric (mathematics)|metric]] [[conformally flat]].<ref>
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| {{cite conference |title= Twin matter against dark matter |author= J.P. Petit, P. Midy, F. Landsheat |conference= Int. Conf. on Astr. & Cosm |booktitle= "Where is the matter?" (See sections '''14''' and '''15''' pp. 21–26) |year= 2001 |url=http://www.bigravitytheory.com/pdf/where_is_the_matter_2001.pdf}}</ref><ref>
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| {{cite arXiv |title= Bigravity: a bimetric model of the Universe with variable constants, including VSL (variable speed of light) |author= J.P Petit, G. d'Agostini |year = 2007 |eprint=0803.1362 |class= physics.gen-ph}}</ref>
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| The idea from Moffat and the team Albrecht–Magueijo is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions of the expanding universe have had time to interact at the beginning of the universe. There is no known way to solve the horizon problem with variation of the fine-structure constant, because its variation does not change the [[causality (physics)|causal structure]] of [[spacetime]]. To do so would require modifying gravity by varying [[Newton's constant]] or redefining [[special relativity]] . Classically, varying speed of light cosmologies propose to circumvent this by varying the dimensionful quantity ''c'' by breaking the [[Lorentz invariance]] of [[Albert Einstein|Einstein]]'s [[theory of relativity|theories of general and special relativity]] in a particular way.<ref>{{cite journal |title= Dynamical Mechanism for Varying Light Velocity as a Solution to Cosmological Problems |author= M. A. Clayton, J. W. Moffat |journal= Phys. Lett. |volume= B460 |year= 1999 |pages= 263–270 |arxiv=astro-ph/9812481|bibcode = 1999PhLB..460..263C |doi = 10.1016/S0370-2693(99)00774-1 }}</ref><ref>
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| {{cite journal |title= Geometrodynamics of variable-speed-of-light cosmologies |author= B.A. Bassett, S. Liberati, C. Molina-Paris, M. Visser |journal= Phys. Rev. |volume= D62 |year= 2000 |pages= 103518 |arxiv=astro-ph/0001441|bibcode = 2000PhRvD..62j3518B |doi = 10.1103/PhysRevD.62.103518 }}</ref> More modern formulations preserve local Lorentz invariance.<ref name="local"/>
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| ==Various other VSL occurrences ==
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| ===Virtual photons===
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| [[Virtual photon]]s in some calculations in [[quantum field theory]] may also travel at a different speed for short distances; however, this doesn't imply that anything can travel [[faster than light]]. While it has been claimed (see VSL criticism below) that no meaning can be ascribed to a dimensional quantity such as the speed of light varying in time (as opposed to a [[dimensionless number]] such as the [[fine structure constant]]), in some controversial theories in cosmology, the speed of light also varies by changing the postulates of [[special relativity]].{{citation needed|date=February 2013}}
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| ===Varying photon speed===
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| The [[photon]], the particle of light which mediates the [[electromagnetic force]] is believed to be massless. The so-called [[Proca action]] describes a theory of a massive photon.<ref>{{cite book |author=J. D. Jackson |title=Classical Electrodynamics |year=1998 |publisher=Wiley |edition=3rd}}</ref> Classically, it is possible to have a photon which is extremely light but nonetheless has a tiny mass, like the [[neutrino]]. These photons would propagate at less than the speed of light defined by [[special relativity]] and have three directions of [[Polarization (waves)|polarization]]. However, in [[quantum field theory]], the photon mass is not consistent with [[gauge invariance]] or [[renormalization|renormalizability]] and so is usually ignored. However, a quantum theory of the massive photon can be considered in the Wilsonian [[effective field theory]] approach to quantum field theory, where, depending on whether the photon mass is generated by a Higgs mechanism or is inserted in an ad hoc way in the Proca Lagrangian, the limits implied by various observations/experiments may be different. So therefore, the speed of light is not constant.<ref name="adel">{{cite journal|author1=Eric Adelberger|author2=Gia Dvali|author3=Andrei Gruzinov|title=Photon Mass Bound Destroyed by Vortices|doi=10.1103/PhysRevLett.98.010402|year=2007|journal=Physical Review Letters|volume=98|issue=2|arxiv=hep-ph/0306245|bibcode = 2007PhRvL..98a0402A|pmid=17358459}}</ref>
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| ===Varying ''c'' in quantum theory===
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| {{main|Propagator#Faster than light?|l1=Propagator (section "Faster than light?")}}
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| {{See also|Scharnhorst effect}}
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| In [[quantum field theory]] the [[Heisenberg uncertainty relations]] indicate that photons can travel at any speed for short periods. In the [[Feynman diagram]] interpretation of the theory, these are known as "[[virtual particle|virtual photons]]", and are distinguished by propagating off the [[mass shell]]. These photons may have any velocity, including velocities greater than the speed of light. To quote [[Richard Feynman]] "...there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, ''c''."<ref>{{cite book |author=R. Feynman |title=QED: the strange theory of light and matter |publisher=Princeton University Press |page=89 |year=1988}}</ref> These virtual photons, however, do not violate causality or special relativity, as they are not directly observable and information cannot be transmitted acausally in the theory. Feynman diagrams and virtual photons are usually interpreted not as a physical picture of what is actually taking place, but rather as a convenient calculation tool (which, in some cases, happen to involve faster-than-light velocity vectors).
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| ==Relation to other constants and their variation==
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| === Gravitational constant ''G''===
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| {{See also | Dirac large numbers hypothesis}}
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| In 1937, [[Paul Dirac]] and others began investigating the consequences of natural constants changing with time.<ref>{{cite journal|author=P.A.M. Dirac|year=1938 |title=A New Basis for Cosmology |journal=[[Proceedings of the Royal Society A]] |volume=165 |issue=921 |pages=199–208 |doi=10.1098/rspa.1938.0053 |bibcode = 1938RSPSA.165..199D }}</ref> For example, Dirac proposed a change of only 5 parts in 10<sup>11</sup> per year of [[Newton's constant]] ''G'' to explain the relative weakness of the [[gravitational force]] compared to other [[fundamental forces]]. This has become known as the [[Dirac large numbers hypothesis]].
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| However, [[Richard Feynman]] showed in his famous lectures<ref>{{cite book |author=R. P. Feynman |title=Lectures on Physics |year=1970 |publisher=Addison Wesley Longman |volume=1 |chapter=7}}</ref> that the [[gravitational constant]] most likely could not have changed this much in the past 4 billion years based on geological and solar system observations (although this may depend on assumptions about the constant not changing other constants). (See also [[strong equivalence principle]].)
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| ===Fine structure constant ''α'' ===
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| {{See also| Fine-structure constant#Is_the_fine-structure_constant_actually_constant.3F}}
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| One group, studying distant quasars, has claimed to detect a variation of the fine structure constant <ref>{{cite journal |author=J.K. Webb, M.T. Murphy, V.V. Flambaum, V.A. Dzuba, J.D. Barrow, C.W. Churchill, J.X. Prochaska and A.M. Wolfe |title=Further Evidence for Cosmological Evolution of the Fine Structure Constant |journal=Phys. Rev. Lett. |volume=87 |year=2001 |pages=091301 |doi=10.1103/PhysRevLett.87.091301 |pmid=11531558 |issue=9 |bibcode=2001PhRvL..87i1301W |arxiv = astro-ph/0012539}}</ref> at the level in one part in 10<sup>5</sup>. Other authors dispute these results. Other groups studying quasars claim no detectable variation at much higher sensitivities.<ref>{{cite journal |author=H. Chand, R. Srianand, P. Petitjean and B. Aracil |title=Probing the cosmological variation of the fine-structure constant: results based on VLT-UVES sample |journal=Astron. Astrophys. |volume=417 |year=2004 |issue=3 |pages=853 |doi=10.1051/0004-6361:20035701 |bibcode=2004A&A...417..853C |arxiv = astro-ph/0401094}}</ref><ref>{{cite journal |author=R. Srianand, H. Chand, P. Petitjean and B. Aracil |title=Limits on the time variation of the electromagnetic ne-structure constant in the low energy limit from absorption lines in the spectra of distant quasars |journal=Phys. Rev. Lett. |volume=92 |year=2004 |pages=121302 |doi=10.1103/PhysRevLett.92.121302 |pmid=15089663 |issue=12 |bibcode=2004PhRvL..92l1302S |arxiv = astro-ph/0402177}}</ref><ref>{{cite journal |author=S. A. Levshakov, M. Centurion, P. Molaro and S. D’Odorico |title=VLT/UVES constraints on the cosmological variability of the fine-structure constant |journal=Astron. Astrophys. |arxiv=astro-ph/0408188|doi = 10.1051/0004-6361:20041827 |bibcode=2005A&A...434..827L}}</ref>
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| For over three decades since the discovery of the [[Oklo]] [[natural nuclear fission reactor]] in 1972, even more stringent constraints, placed by the study of certain [[isotope|isotopic]] abundances determined to be the products of a (estimated) 2 billion year-old fission reaction, seemed to indicate no variation was present.<ref>{{cite journal |author=A. I. Shlyakhter |title=Direct test of the constancy of fundamental nuclear constants |journal=Nature |volume=264 |year=1976 |issue=5584 |pages=340 |doi=10.1038/264340a0 |bibcode = 1976Natur.264..340S }}</ref><ref>{{cite journal |author=T. Damour and F. Dyson |title=The Oklo bound on the time variation of the fine-structure constant revisited |journal=Nucl. Phys. |volume=B480 |year=1996 |issue=1–2 |pages=37 |doi=10.1016/S0550-3213(96)00467-1 |arxiv = hep-ph/9606486 |bibcode = 1996NuPhB.480...37D}}</ref> However, Lamoreaux and Torgerson of the [[Los Alamos National Laboratory]] conducted a new analysis of the data from Oklo in 2004, and concluded that ''α'' has changed in the past 2 billion years by 4.5 parts in {{val|e=8}}. They claimed that this finding was "probably accurate to within 20%." Accuracy is dependent on estimates of impurities and temperature in the natural reactor. These conclusions have yet to be verified by other researchers.<ref>
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| {{Cite journal
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| | author = S.K. Lamoreaux, J.R. Torgerson
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| | year = 2004
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| | title = Neutron Moderation in the Oklo Natural Reactor and the Time Variation of Alpha
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| | journal = [[Physical Review D]]
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| | volume = 69 |pages=
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| | doi= 10.1103/PhysRevD.69.121701
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| | arxiv = nucl-th/0309048
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| |bibcode = 2004PhRvD..69l1701L
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| | issue = 12 }}</ref><ref>
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| {{Cite web
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| | author=E.S. Reich
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| | date=30 June 2004
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| | title=Speed of Light May Have Changed Recently
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| | url=http://www.newscientist.com/article/dn6092-speed-of-light-may-have-changed-recently.html
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| | publisher=[[New Scientist]]
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| | |
| | accessdate=30 January 2009
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| }}</ref><ref>
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| {{Cite web
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| | author=
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| | date=12 May 2005
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| | title=Scientists Discover One Of The Constants Of The Universe Might Not Be Constant
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| | url=http://www.sciencedaily.com/releases/2005/05/050512120842.htm
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| | publisher=[[ScienceDaily]]
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| | accessdate=30 January 2009
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| }}</ref>
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| [[Paul Davies]] and collaborators have suggested that it is in principle possible to disentangle which of the dimensionful constants (the [[elementary charge]], [[Planck's constant]], and the [[speed of light]]) of which the fine-structure constant is composed is responsible for the variation.<ref>{{cite journal |title = Cosmology: Black holes constrain varying constants |author=P.C.W. Davies, Tamara M. Davis, Charles H. Lineweaver |year=2002 |journal=Nature |volume=418 |pages=602–603 |doi = 10.1038/418602a |pmid = 12167848 |issue = 6898}}</ref> However, this has been disputed by others and is not generally accepted.<ref>M. J. Duff, "Comment on time-variation of fundamental constants", {{arxiv|hep-th/0208093}}.</ref><ref>{{cite journal |title=Black holes may not constrain varying constants |author=S. Carlip and S. Vaidya |year=2003 |journal=Nature |volume=421 |pages=498 |doi=10.1038/421498a |pmid=12556883 |issue=6922 |arxiv=hep-th/0209249}}</ref>
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| == Criticisms of the VSL concept ==
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| === Dimensionless and dimensionful quantities ===
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| It has to be clarified what a variation in a [[dimensionful]] quantity actually means, since any such quantity can be changed merely by changing one's choice of units. [[John D. Barrow|John Barrow]] wrote:
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| :"[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the [[fine structure constant]] and denote by α is a combination of the [[electron charge]], ''e'', the [[speed of light]], ''c'', and [[Planck's constant]], ''h''. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If ''c'', ''h'', and ''e'' were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be ''observationally indistinguishable'' from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the [[Planck mass]] ''m<sub>P</sub>''] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged."<ref>[[John D. Barrow]], ''The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe,'' Pantheon Books, New York, 2002, ISBN 0-375-42221-8.</ref>
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| Any equation of [[physical law]] can be expressed in such a manner to have all dimensional quantities normalized against like dimensioned quantities (called ''[[nondimensionalization]]'') resulting in only [[dimensionless number|dimensionless quantities]] remaining. In fact, physicists can ''choose'' their units so that the [[physical constants]] [[speed of light|''c'']], [[gravitational constant|''G'']], [[Planck constant|''ħ'' = ''h''/(2π)]], [[vacuum permittivity|4π''ε''<sub>0</sub>]], and [[Boltzmann constant|''k''<sub>B</sub>]] take the value [[one]], resulting in every physical quantity being normalized against its corresponding [[Planck unit]]. For that, it has been claimed that specifying the evolution of a dimensional quantity is meaningless and does not make sense.<ref>J. P. Uzan, "The fundamental constants and their variation: Observational status and theoretical motivations," ''Rev. Mod. Phys.'' '''75''', 403 (2003). {{arxiv|hep-ph/0205340}}</ref> When Planck units are used and such equations of physical law are expressed in this nondimensionalized form, '''no''' dimensional physical constants such as ''c'', ''G'', ''ħ'', ''ε''<sub>0</sub>, nor ''k''<sub>B</sub> remain, only dimensionless quantities. Shorn of their [[anthropometric]] unit dependence, there simply is no [[speed of light]], [[gravitational constant]], nor [[Planck's constant]], remaining in mathematical expressions of physical reality to be subject to such hypothetical variation.{{citation needed|date=February 2013}} For example, in the case of a hypothetically varying gravitational constant, ''G'', the relevant dimensionless quantities that potentially vary ultimately become the ratios of the [[Planck mass]] to the masses of the [[fundamental particles]]. Some key dimensionless quantities (thought to be constant) that are related to the speed of light (among other dimensional quantities such as ''ħ'', ''e'', ''ε''<sub>0</sub>), notably the [[fine-structure constant]] or the [[proton-to-electron mass ratio]], does have meaningful variance and their possible variation continues to be studied.<ref>''ibid''</ref>
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| === Relation to relativity and definition of ''c'' ===
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| In relativity, space-time is 4 dimensions of the same physical property of either space or time, depending on which perspective is chosen. The conversion factor of length=i*c*time is described in Appendix 2 of Einstein's ''Relativity''. A changing ''c'' in relativity would mean the imaginary dimension of time is changing compared to the other three real-valued spacial dimensions of space-time.{{citation needed|date=February 2013}}
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| Specifically regarding VSL, if the [[SI]] [[meter]] definition was reverted to its pre-1960 definition as a length on a [[prototype]] bar (making it possible for the measure of ''c'' to change), then a conceivable change in ''c'' (the reciprocal of the amount of time taken for light to travel this prototype length) could be more fundamentally interpreted as a change in the dimensionless ratio of the meter prototype to the [[Planck length]] or as the dimensionless ratio of the SI [[second]] to the [[Planck time]] or a change in both. If the number of atoms making up the meter prototype remains unchanged (as it should for a stable prototype), then a perceived change in the value of ''c'' would be the consequence of the more fundamental change in the dimensionless ratio of the Planck length to the sizes of atoms or to the [[Bohr radius]] or, alternatively, as the dimensionless ratio of the Planck time to the [[frequency|period]] of a particular [[caesium]]-133 [[atomic clock|radiation]] or both.
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| === General critique of varying ''c'' cosmologies===
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| From a very general point of view, [[George Francis Rayner Ellis|G. Ellis]] expressed concerns that a varying ''c'' would require a rewrite of much of modern physics to replace the current system which depends on a constant c.<ref name="Ellis">{{cite journal | doi = 10.1007/s10714-007-0396-4 | title = Note on Varying Speed of Light Cosmologies | author = George F R Ellis | journal = General Relativity and Gravitation |date=April 2007 | issue = 4 | pages = 511–520 | volume = 39 | arxiv=astro-ph/0703751 |bibcode = 2007GReGr..39..511E }}</ref> Ellis claimed that any varying ''c'' theory (1) must redefine distance measurements (2) must provide an alternative expression for the metric tensor in [[general relativity]] (3) might contradict Lorentz invariance (4) must modify [[Maxwell's equations]] (5) must be done consistently with respect to all other physical theories. Whether these concerns apply to the proposals of Einstein (1911) and Dicke (1957) is a matter of debate,<ref>{{cite journal|author=A. Unzicker |title=The VSL Discussion: What Does Variable Speed of Light Mean and Should we be Allowed to Think About ? |arxiv = 0708.2927}}</ref> though VSL cosmologies remain out of mainstream physics.
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| ==References==
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| {{reflist|30em}}
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| == External links ==
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| *http://www.phys.unsw.edu.au/einsteinlight/jw/module6_constant.htm
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| [[Category:Electromagnetic radiation]]
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| [[Category:Units of velocity]]
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| [[Category:Special relativity]]
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| [[de:Physikalische Konstante#Konstanz der Naturkonstanten]]
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