Variable speed of light

Scientific Theory
Name	Variable speed of light
Type	Family of theories in which c is not a universal constant
Author(s)	Einstein (1911); John W. Moffat (1992); Andreas Albrecht and Jo Magueijo (1998); and many independent researchers
Keywords	Light, speed of light, c, Relativity, Aether, Emission Theory, Redshift, one-way light speed, Cosmology
Year	1911 (Einstein); 1992– (modern VSL cosmology)

Variable speed of light (VSL) is the proposition that the speed of light c is not a universal constant — that it may differ with position, with epoch, with the gravitational potential, with the medium, with direction of travel, or with the motion of the source.

The proposition matters more than it may appear. The constancy of c is the second postulate of special relativity and the foundation on which the Lorentz transformation, time dilation, length contraction and the relativity of simultaneity all rest. If c varies, that structure requires reworking. It is for this reason that VSL is among the most frequently revisited subjects on this wiki, and also why it attracts researchers with otherwise incompatible positions.

VSL is not one theory but several. The label covers proposals that differ profoundly in what they claim, in how respectable they are considered, and in what would count as evidence for them. Distinguishing them is the first task of this article, because arguments against one variety are routinely presented as though they told against all of them.

Why the question is subtle

Two features of the problem make it harder than it looks, and both are worth stating before the varieties are set out.

The metre is defined by c. Since 1983 the metre has been defined as the distance light travels in 1/299,792,458 of a second. The speed of light in vacuum is therefore fixed by definition at exactly 299,792,458 m/s, and can no longer be measured — a measurement that appeared to show a different value would be interpreted as a change in the length of the metre, not in c. Critics on this wiki regard this as making the constancy of c unfalsifiable by construction. Physicists working on VSL in the mainstream accept the point and respond that the meaningful question concerns dimensionless quantities, above all the fine structure constant α = e²/(4πε₀ℏc), whose variation would be observable without reference to any unit.

Only the two-way speed has been measured. Every terrestrial determination of c — Fizeau's wheel, Michelson's mirrors, modern interferometry — sends light out and back along the same path and divides by the round trip. Measuring the one-way speed requires two clocks at separate places already synchronized, and synchronizing them requires assuming the very thing to be measured. Einstein recognized this and settled it by convention rather than by experiment. Several researchers here argue that the isotropy of c is therefore a stipulation, and that anisotropic one-way speeds are consistent with all existing measurements.

Varieties of the claim

Einstein's 1911 gravitational VSL

The first variable-c theory was Einstein's own. In his 1911 paper on the influence of gravitation on the propagation of light, he treated gravity not as spacetime curvature but as a position-dependence of c: light slows in a gravitational potential, and rays bend accordingly, exactly as they would in a medium of varying refractive index. Within a few years he had replaced this picture with the metric formalism of general relativity, and the earlier approach was set aside.

Alexander Unzicker has made the recovery of this line his central project, arguing in Einstein's Lost Key (2015) that spacetime curvature can be mimicked by a speed of light c(r) depending on the distribution of masses, that the two descriptions are far closer than textbook history suggests, and that the variable-c version retains a physical transparency the geometrical version loses. He connects it to Mach's principle: a c set by the distant masses of the universe would explain the origin of inertia and gravitation together.

Cosmological VSL

The best-established variety, and the only one with a substantial mainstream literature, holds that c was very much larger in the early universe than it is now.

John W Moffat (University of Toronto, Perimeter Institute) proposed this in 1992, and Jo Magueijo (Imperial College London) developed it with Andreas Albrecht in 1998. Their motivation was to replace cosmic inflation: a very high early c would let distant regions of the universe come into causal contact, solving the horizon problem, and would bear on the flatness and cosmological-constant problems as well — without postulating a period of exponential expansion driven by an unobserved inflaton field. Magueijo set the story out for a general readership in Faster Than the Speed of Light.

This work is published in mainstream journals and is a minority but respectable position. It is nonetheless a genuine departure: a variable c contradicts the constancy assumed in special relativity, which is why it remains controversial. Magueijo has also worked, with Lee Smolin, on doubly special relativity, in which an invariant energy scale joins c as an observer-independent quantity.

Ron Forth also works on variable-speed-of-light cosmology, and the paper "Gravitational Cosmic Redshift with Variable Light Speed" applies a varying c to the interpretation of redshift — an important connection, since if c has changed over cosmic time then the redshift–distance relation, and with it the expansion of the universe, requires reinterpretation.

One-way versus two-way light speed

A distinct group accepts that the round-trip speed is invariant while denying that the one-way speed is. Joe Sorge has developed a sustained critique of Einstein synchronization and of the Lorentz transformations on exactly this ground, and papers such as "Measurement of the One-Way Speed of Light" and "Light projection velocity and not light velocity that is measured as constant" pursue the same question. Pentcho Valev has argued the case for a variable speed of light against special relativity over many years.

The significance of this variety is that it is compatible with every experiment performed to date — which its advocates present as its strength and its critics as its weakness, since a claim consistent with all observation is difficult to test.

Source-dependent c: emission theory

If light is emitted at c relative to its source, an observer measures c ± v. This is the classical emission theory of Walther Ritz, and it is a variable-speed-of-light theory in the most direct sense. Because it forms its own tradition with its own history and its own standard objections — de Sitter's binary-star argument, the Sagnac effect — it is treated separately on this wiki. Researchers include Lothar Pernes, whose Delta-Lambda effect combines emission theory with an entrained medium, and Edward Henry Dowdye, Jr., whose Extinction Shift Principle applies emission ideas to gravitation as well as to electromagnetism.

Medium-dependent c

A fifth family holds that c is a property of a physical medium and varies with the state of that medium — which is the natural position for anyone who takes an aether seriously, since wave speed in any other medium depends on the medium's properties. Papers on this wiki include "The Speed of Light varies with Magnetic Flux Density", "Time Evolution of Vacuum Parameters as the Basis for a Cosmological Model" and "Can Photon-Particle Interactions be Explained with Varying Light Speed?". Researchers working in this vicinity include Peter C M Hahn, David Tombe and Christos A. Tsolkas.

Researchers on this wiki

Alexander Unzicker — variable-c gravitation after Einstein's 1911 paper, tied to Mach's principle; Einstein's Lost Key
Jo Magueijo — VSL cosmology with Albrecht (1998) as an alternative to inflation; doubly special relativity
John W Moffat — originator of modern VSL cosmology (1992)
Ron Forth — variable speed of light cosmology
Pentcho Valev — long-running advocacy of variable c against special relativity
Joe Sorge — Einstein synchronization and the one-way speed of light
Valentin Danci, William Henry Owen, Robert J Heaston, Yi-Fang Chang, Raymond H Gallucci, Amrit Sorli — critiques bearing on the constancy of c from various directions

Selected papers on this wiki

Difficulties

An article that only made the case would not be useful. The standing objections are these.

Dimensional constants are not physically meaningful on their own. A change in c expressed in metres per second can always be absorbed into a redefinition of units. The objection applies to VSL proponents and opponents alike, and the serious response — adopted by Magueijo among others — is to frame the claim in terms of dimensionless ratios such as α. Astronomical searches for variation in α, chiefly in quasar absorption spectra, have produced contested results but no accepted detection.

The constraints are tight. The Oklo natural fission reactor, isotopic ratios in meteorites, and atomic-clock comparisons all bound any present-day variation in the relevant constants to very small values over long periods.

Consistency is not confirmation. The one-way light-speed variants are compatible with all existing measurement precisely because the convention they dispute cannot be tested without being assumed. That makes them coherent, but it also means no experiment yet proposed distinguishes them from the standard convention.

Cosmological VSL must do inflation's work. To displace inflation, a varying c must account not only for the horizon and flatness problems but for the observed spectrum of fluctuations in the cosmic microwave background, which inflation predicts in some detail. This is where the mainstream debate over VSL cosmology is actually conducted.