The variable speed of light (VSL) concept states that the speed of light in a vacuum, usually denoted by c, may not be constant in most cases. In most situations in condensed matter physics when light is traveling through a medium, it effectively has a slower speed. Virtual photons 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 is usually thought 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. However, this would require a rewrite of much of modern physics to replace the current system which depends on a constant c.[1]
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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.[2] 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. However, in quantum field theory, the photon mass is not consistent with gauge invariance or 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.[3]
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 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."[4] 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).
In 1937, Paul Dirac and others began investigating the consequences of natural constants changing with time. For example, Dirac proposed a change of only 5 parts in 1011 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. However, Richard Feynman showed in his famous lectures[5] 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.)
It is not clear 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:
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 quantities remaining. In fact, physicists often choose their units so that the physical constants c, G, h/(2π), and 4πε0 take the value one, resulting in every physical quantity being normalized against its corresponding Planck unit. As such, many physicists think that specifying the evolution of a dimensionful quantity is at best meaningless and at worst inconsistent.[7] 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, or h remain, only dimensionless quantities. Shorn of their anthropometric unit dependence, there simply is no speed of light, gravitational constant, or Planck's constant, remaining in mathematical expressions of physical reality to be subject to such hypothetical variation. For example, in the case of the gravitational constant, G, the relevant dimensionless quantities that were assumed to vary ultimately became the ratios of the Planck mass to the masses of the fundamental particles. Some key dimensionless quantities (thought to be constant) depend on the speed of light, notably the fine-structure constant, would have meaningful variance and their possible variation continues to be studied.[8]
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.
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 period of a particular caesium-133 radiation or both.
One group, studying distant quasars, has claimed to detect a variation of the fine structure constant [9] 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.[10][11][12] Moreover, even more stringent constraints, placed by study of certain isotopic abundances in the Oklo natural nuclear fission reactor, seem to indicate no variation is present.[13][14]
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.[15] However, this has been disputed by others and is not generally accepted.[16][17]
The varying speed of light cosmology has been proposed independently by Jean-Pierre Petit in 1988,[18][19][20][21] John Moffat in 1992,[22] and the two-man team of Andreas Albrecht and João Magueijo in 1998[23][24][25][26][27][28] to explain the horizon problem of cosmology and propose an alternative to cosmic inflation. An alternative VSL model has also been proposed.[29]
In Petit's VSL model, the variation of c accompanies the joint variations of all physical constants combined to space and time 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. 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 conformally flat.[30][31] However it should be noted that while this was the first VSL model to be published, and the sole to date where an evolution law is given relating the joint variations of constants through time while leaving the physics unchanged, these papers received few citations in the later VSL literature.
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 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 Einstein's theories of general and special relativity in a particular way.[32][33] More modern formulations preserve local Lorentz invariance.[25]