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.
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.
[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.
[7]: 374 Variable speed of light models, including Dicke's, have been developed which agree with all known tests of general relativity.
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).
However, Richard Feynman showed[18] 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 G varying in isolation.
[20][21][22] The natural nuclear reactor of Oklo has been used to check whether the atomic fine-structure constant α might have changed over the past 2 billion years.
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.
[29] 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.