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A variable speed of light (VSL) is the idea that the speed of light, usually denoted by c, may not be constant, for some reason. In most situations in condensed matter physics when light is travelling 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 speculative and controversial theories in cosmology, the speed of light also varies by changing the postulates of special relativity.
Varying c in condensed matter physics Photons move at a speed less than c, unless they are travelling in vacuum. This leads to several important effects, such as dispersion (see also refractive index). The slow-down in condensed matter, such as gases, liquids and solids, can be considerable. It results from the delay between the time an electron absorbs a photon, and re-emits it. The group velocity of light can be lowered to arbitrary speeds, though only for an arbitrarily slow (low bandwidth) signal (see Slow light). In certain highly unusual circumstances, it is also possible to prepare experiments in which the group or phase velocity of light exceeds c. Since these velocities are mathematical constructs, these faster than light observations do not indicate any contradiction with causality or special relativity, as no information or energy travels faster than c. Varying c in classical physics 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.• 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. Varying c in quantum theory 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."• 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 interpreted not as a physical picture of what is actually taking place, but rather as a convenient calculational tool (which, in some cases, happen to involve faster-than-light velocity vectors). Varying c in time 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• 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: "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 ''mP'' you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged." 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.• 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, and their possible variation has been extensively studied One group, studying distant quasars, has claimed to detect a variation of the fine structure constant • Some Young Earth Creationists have investigated the idea of a changing c in 1987 as an explanation for the discrepancy between the biblical and measured ages of the universe. This idea was mentioned by Marilyn vos Savant in Parade magazine. This idea has been refuted. The varying speed of light cosmology A variable speed of light cosmology has been proposed independently by John Moffat and the two-man team of Andreas Albrecht and João Magueijo to explain the horizon problem of cosmology.•• However, it has been pointed out by Ellis and Uzan• that the VSL cosmology is an ad hoc modification of various equations of physics without a consistent underlying scheme, such as a Lagrangian from which the equations of motion can be derived. It has been suggested out that a modification of the Einstein-Maxwell action can cause light to propagate at a speed faster than the speed of light defined by the metric, but this necessarily causes problems with causality and quantum mechanics.• | ||||||||
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