Variable speed of light

A variable speed of light (VSL) is used in VSL cosmologies that "resolve the cosmological problems that are resolved by the inflationary models, along with some other cosmological problems."[1] A changing speed of light and our current view of relativity are not compatible; they are not both true. VSL cosmologies usually have to re-derive relativistic equations with "hard" or "soft" breaks to the basic relativity principle of Lorentz invariance [2] but a recent paper shows that c can vary without violating special or general relativity. [3] VSL theories often distinguish between the speed of light in vacuum and the value of "c" in gravity but consider the ratio of the two important. VSL cosmologies usually investigate a decreasing speed of c.

Some researchers have argued that investigating a change in the speed of light ("c") is not as important or direct as studying a change in the fine-structure constant (alpha) because c has dimensions (m/s). They believe only dimensionless constants should be measured and studied for understanding fundamental concepts, but others disagree, "demonstrating a framework in which time dependence of dimensional constants becomes a well defined concept" [4]. The speed of light's units of length/time may be viewed as unitless (but not dimensionless) because the theory of relativity indicates length and time are equivalent concepts in space-time, although in different dimensions. This allows c to be viewed as a constant, man-made conversion factor between seconds and meters. This viewpoint is used in our current definition of a meter (the length light travels in one second) which prevents c from ever changing by definition.

Can the speed of light change?

In 1983 the meter was defined as the distance light travels in vacuum during a time interval of 1/299,792,458 of a second. This defines the speed of light (referred to as "c" in this article) in a simple vacuum to be exactly 299,792,458 m/s so that it is a constant by definition. A definition of the meter based on time is completely compatible with (if not required by) our current view of relativity. If the speed of light is somehow half as fast tomorrow based (going against our current view of relativity), then our old rulers will be twice as long as our new definition of distance. A simple example of a problem relativity has with a change in the speed of light is that if the conservation of energy and relativity hold through the change, then E=mc^2 would require the mass of all objects to change.

How can a change in c be detected?

There are geological (nuclear decay rates) and cosmological observations that indicate c has not changed a measurable amount, but changes in c have wide-ranging effects that may cause the methods of observation to disguise any change in c. Atomic clock readings over the last few decades provide a very direct method of observation and may someday detect a change, but the readings depend on the hyperfine structure which depends on the value of c, so it may not be possible to use atomic clocks to measure a change in c. A 1973 article [5] shows that c could not have changed by more than 0.5% in the past 300 years based on the observations of eclispes of Jupiter's satellite Io. The analysis assumed gravity was not affected by any change in c. For these reasons, unitless natural constants are believed to be more useful in determing if the unit-based constants (like c, h, and G) are changing (see Does the speed of light change in time by Vladimir Dzuba [6])

What if c changes?

In relativity, c defines the relationship between meters and seconds, so every measurement that contains units of meters or seconds has the possibility of being affected. Planck units shows the interconnectedness of units and constants. If c changes (outside of the already known variations allowed in quantum theory), then there would be at least a few profound changes to other constants, equations, or ideas. Here are some possibilites:

the energy and/or mass of all particles would have to change: $E=m*c^{2}$
in photons, energy and/or Planck's constant would have to change: $E=h*c/wavelength$ (see energy of a photon)
Hubble's constant would require adjustment (redshift increases with a decreasing c) so that the inflation model of the universe would be drastically altered
the gravitational constant G, mass of particles, and/or the Schwarzschild radius R that determines acceleration in a gravitational field would have to change: $R=2mG/c^{2}$
in quantum physics, alpha, proton charge, and/or planck's constant would have to change, as explained in the next section.

Although the statements above imply a changing c "causes" the changes, the changes are just the manifestion that something "greater" than just a change in c has occurred if a change in c is detected. A change in c is just the easiest parameter to understand and therefore gain the most media attention. The equations above have such a potential for interconnectedeness because they all refer to units of meters and seconds. This (and avoiding historical definitions) is the reason for studying unitless physical constants. If a particular unitless physical constant changes, we can more directly understand how physical ideas and constants with units are affected. In studying a changing c, the unitless alpha is frequently considered (see below). The media did not pay much attention when it was reported that alpha may have changed, but when it was pointed out that c may have changed as a result of an alpha change, the media took great interest.

History and current research

In the 1930's, 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 10^11 per year of G (in the force of gravity) but Richard Feynman showed in his famous 1961 lectures (vol 1, chapter 7) that geological evidence indicates 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 the observations themselves may depend on assumptions about the constant not changing other constants).

Interestingly, creation theorists investigated the idea of a changing c in 1987 ( [7] ) and it was mentioned by Marilyn vos Savant in May 22 1988 Parade magazine. Of recent (2001) renewed interest is the possibility that the speed of light is decreasing.

The Australian Centre for Astrobiology [8] renewed interest in the constancy of the speed of light after taking measurements that showed the unitless fine-structure constant (alpha) is one millionth larger today than when light left a distant quasar. Paul Davies of the Centre subsequently published that the possible increase in alpha could be due to a decrease in c since $\alpha ={\frac {e^{2}}{\hbar c}}$ in electrostatic cgs units where e is the charge of a proton. If alpha has increased (which is still being debated) then it could be because c has decreased. If alpha has not changed, then c could decrease and $\hbar$ could increase so that alpha remained constant (this was the 1987 creationists viewpoint). A change in the proton charge could have a similar counter-effect. Davies published an argument that the proton charge has not changed, but others published saying it can't be ruled out. A June 2004 article [9] indicates the issue of an alpha change is still up in the air. The Oklo natural nuclear reactors in South Africa has been used both to support and reject the possibility of a significantly changing alpha. Lamoreaux and Torgerson report alpha may have decreased by more than 4.5 parts in 10^8 (Physical Review D, vol 69, p121701) after 2 billion years (which corresponds to a 13 m/s change in c).

If alpha is not changing, other considerations and cosmological observations may prove $\hbar$ and proton charge are not changing above some detectable limit which would limit the possible change in c. João Magueijo has published on the subject and wrote "Faster Than the Speed of Light" which has been said to be lacking in explaining the details and too much of a child-like rant aganist the physics establishment.

Experiments that modify c

Photons move at a speed less than c, unless they are travelling in vacuum. This slow-down is considerable in some circumstances (see Light-slowing experiments). On the other hand, there are also some observations of things moving faster than the speed of light; as long as no information is transmitted, this is not in contradiction with the relativity theory.

Varying c in quantum theory

Light can have any value within the limits of the uncertainty principle as demonstrated in any Feynman diagram that draws a photon at any angle other than 45 degrees. 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." - Chapter 3, page 89 of Richard Feynman's book "QED".