Variable speed of light

Source: Wikipedia, the free encyclopedia.

A variable speed of light (VSL) is a feature of a family of hypotheses stating that the

gravitation and cosmology
, many of them non-mainstream, incorporate variations in the local speed of light.

Attempts to incorporate a variable speed of light into physics were made by

Robert Dicke
in 1957, and by several researchers starting from the late 1980s.

VSL should not be confused with

faster than light theories, its dependence on a medium's refractive index or its measurement in a remote observer's frame of reference in a gravitational potential. In this context, the "speed of light" refers to the limiting speed c of the theory rather than to the velocity of propagation of photons
.

Historical proposals

Background

Einstein's equivalence principle, on which general relativity is founded, requires that in any local, freely falling reference frame, the speed of light is always the same.[1][2] This leaves open the possibility, however, that an inertial observer inferring the apparent speed of light in a distant region might calculate a different value. Spatial variation of the speed of light in a gravitational potential as measured against a distant observer's time reference is implicitly present in general relativity.[3] The apparent speed of light will change in a gravity field and, in particular, go to zero at an event horizon as viewed by a distant observer.[4] In deriving the gravitational redshift due to a spherically symmetric massive body, a radial speed of light dr/dt can be defined in Schwarzschild coordinates, with t being the time recorded on a stationary clock at infinity. The result is

where m is MG/c2 and where natural units are used such that c0 is equal to one.[5][6]

Dicke's proposal (1957)

Robert Dicke, in 1957, developed a VSL theory of gravity, a theory in which (unlike general relativity) the speed of light measured locally by a free-falling observer could vary.[7]
Dicke assumed that both frequencies and wavelengths could vary, which since resulted in a relative change of c. Dicke assumed a refractive index (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".

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 cosmological redshift.[7]: 374 

Subsequent proposals

Variable speed of light models, including Dicke's, have been developed which agree with all known tests of general relativity.[8]

Other models make a link to Dirac's large numbers hypothesis.[9][why?]

Several hypotheses for varying speed of light, seemingly in contradiction to general relativity theory, have been published, including those of Giere and Tan (1986)[10] and Sanejouand (2009).[11] In 2003, Magueijo gave a review of such hypotheses.[12]

Cosmological models with varying speeds of light

cosmic inflation
.

Relation to other constants and their variation

Further information: Time-variation of fundamental constants

Gravitational constant G

See also: Dirac large numbers hypothesis

In 1937,

fundamental forces. This has become known as the Dirac large numbers hypothesis
.

However,

strong equivalence principle
.)

Fine-structure constant α

See also: Fine-structure_constant § Potential_time-variation

One group, studying distant quasars, has claimed to detect a variation of the fine-structure constant[19] at the level in one part in 105. Other authors dispute these results. Other groups studying quasars claim no detectable variation at much higher sensitivities.[20][21][22]

The

149
Sm
 captures a neutron to become 150
Sm
, and since the rate of neutron capture depends on the value of α, the ratio of the two samarium isotopes in samples from Oklo can be used to calculate the value of α from 2 billion years ago. Several studies have analysed the relative concentrations of radioactive isotopes left behind at Oklo, and most have concluded that nuclear reactions then were much the same as they are today, which implies α was the same too.[23][24]

Planck's constant, and the speed of light) of which the fine-structure constant is composed is responsible for the variation.[25] However, this has been disputed by others and is not generally accepted.[26][27]

Criticisms of various VSL concepts

Dimensionless and dimensionful quantities

To clarify 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 Barrow
wrote:

"[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
Planck mass mP] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged."[28]

Any equation of

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, ε0), notably the fine-structure constant or the proton-to-electron mass ratio, could in principle have meaningful variance and their possible variation continues to be studied.[29]

General critique of varying c cosmologies

From a very general point of view,

G. F. R. Ellis and Jean-Philippe Uzan 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.[30][31] 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
; and (5) must be done consistently with respect to all other physical theories. VSL cosmologies remain out of mainstream physics.

References

  1. ISBN 978-1-108-57749-6
    .
  2. ISBN 978-1-4008-8909-9
    .
  3. ISBN 9780471925675
    .
  4. ISBN 978-0-486-27378-5
    .
  5. Tolman, Richard
    (1958). Relativity Cosmology and Thermodynamics (1st reprint from 1934 ed.). Oxford UK: Oxford. p. 212.
  6. OCLC 1202475208
    .
  7. ^
    doi:10.1103/RevModPhys.29.363
    .
  8. S2CID 8955243
    .
  9. S2CID 11248780
    .
  10. ^ Giere, A. C.; Tan, A. (1986). "A Derivation of Hubble". Chinese Journal of Physics. 24 (3): 217–219.
  11. S2CID 121784053
    .
  12. S2CID 15716718
    .
  13. ^ Barrow, J. D. (1998). "Cosmologies with varying light-speed". Physical Review D. 59 (4): 043515.
    S2CID 119374406
    .
  14. ^ Petit, Jean-Pierre (1988). "An interpretation of cosmological model with variable light velocity" (PDF). Mod. Phys. Lett. A. 3 (16): 1527–1532.
    doi:10.1142/S0217732388001823
    .
  15. ^ Moffat, John (1993). "Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology". International Journal of Modern Physics D. 2 (3): 351–366.
    S2CID 17978194
    .
  16. S2CID 56138144
    .
  17. S2CID 121069801
    .
  18. ISBN 0-8053-9045-6
    .
  19. S2CID 40461557
    .
  20. S2CID 17863903
    .
  21. S2CID 29581666
    .
  22. S2CID 119351573
    .
  23. S2CID 118272311
    .
  24. S2CID 119227720
    .
  25. S2CID 1400235
    .
  26. arXiv:hep-th/0208093
    .
  27. S2CID 209814835
    .
  28. ISBN 0-375-42221-8
    .
  29. ^
    S2CID 118684485
    .
  30. S2CID 119393303
    .
  31. S2CID 119530637
    .

External links
Retrieved from "https://en.wikipedia.org/w/index.php?title=Variable_speed_of_light&oldid=1189987972"