User:Martin Hogbin/Speed of light fixed

This page contains my understanding, which I believe to be that of mainstream physicists, of the fact that since 1983 the speed of light expressed in SI units has had a fixed numerical value by virtue of the definition of the metre.

The physical concept
What is the speed of light? For the purposes of this discussion I am taking it to be the speed at which light actually travels in specified ideal conditions described below.

Free space
This a hypothetical perfect vacuum, the absence of any form of matter. In practice, such a vacuums can never be achieved. In laboratory ultra high vacuums there are still residual gases present and even in the most distant regions of outer space there is believed to be some residual gas. However, we can measure the effect of higher pressures of gas on the speed of light (they are quite small) and note the way that this effect reduces with pressure and thus calculate what we would expect the effect of the residual gas in an experimental set-up to be and then make an allowance for this. For a good laboratory vacuum the expected effect is very small, in fact less than can be detected with current techniques.

Inertial frame
For measurements of length, time and speed to have easily understood and intuitive meanings, we must do our experiments in an inertial frame. In short this means no acceleration and no gravitation. Again, real experiments are usually performed on the surface of the Earth, where there is gravity, but, as in the case of free space these effects are very small but well understood and can be allowed for.

Two-way speed
As stated in the article, the one-way speed of light cannot be measured (or used) without some kind of convention as to how clocks at the source and receiver should be synchronized. The philosophical issues are dealt with in the theory of relativity. This issue is easily circumvented my measuring (or using) the two-way speed of light, say from a source to a mirror and back again. As it happens, the techniques used to measure the speed of light (or to use light to delineate the metre) use optical interference which naturally uses the two-way transmission of light.

Classical limit
On a very small (quantum) scale everything becomes much less certain but as the scale becomes larger these effects become less important and, on the laboratory scale used for experiments concerning the speed of light, they are very small and can be allowed for if this becomes necessary.

Metrology and international standards
At present, some of the international physical standards such as the kilogram are based on arbitrary physical artifacts (in this case a specified lump of metal) but, for some time, the trend has been towards defining them in terms of fundamental physical constants.

Before 1960 the metre was defined using an arbitrary physical artifact. It was defined to be the distance between two marks on a metal rod. As the second was then defined in terms of the rotation of the Earth it was possible to measure the speed of light using these two standards. On the other hand the length of the metre could not be measured out (delineated or realized) independently; it was fixed by definition to be the length between the two marks.

In 1960 the definition of the meter was changed to be a specified number of wavelengths of a particular orange-red coloured light (spectral line) emitted by a krypton lamp (in a vacuum etc). This raised the question of what determines this wavelength. In other words, does the krypton atom emit light of a fixed wavelength or is it really of a fixed frequency (in which case the wavelength would be determined by that frequency and the speed of light). (There is a complication in cases where gravitation is strong enough to be significant. Because the meter has been defined to be a unit of proper length it turns out that to delineate the meter in such circumstances it is better to use a known wavelength of light rather than to try to measure a time of transit directly.  In fact current realizations of the metre are all performed in this way).

In 1967 the second was redefined using a specified radiation from the caesium atom.

In 1983, for a variety of reasons connected with metrology and as part of the trend towards reducing the dependence on arbitrary physical artifacts the metre was redefined as, 'the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second'. Note that there is no suggestion that the light referred to here is some formal or conventional version of light, it is just, ordinary, real, physical if you like, light.

An obvious consequence of the above definition is that the speed of light when expressed in metres per second is now exactly 299 792 458 metres per second. That is to say real light actually travels (usual conditions) at exactly 299 792 458 metres per second. It is also obvious that the speed of light can no longer be measured in SI units. The same kind of experiment can be performed but the objective is no longer to measure the speed of light but to determine (delineate or realize) the length of the metre.

Of course there are still measurement uncertainties, however these manifest themselves as as uncertainty in the realization of the metre rather than in uncertainty in the speed of light.

So in 1959 we could measure the speed of light but the length of the meter was fixed, today we can delineate the metre but the speed of light is fixed.

Practical and commercial systems
Nearly all practical and commercial systems today are based of exact SI conversions, for example one inch is defined to be exactly 25.4 mm thus the speed of light is fixed in these systems too.

Natural systems of units
It has long been common in certain branches of physics to use systems of units in which the speed of light (and sometimes other quantities) have the defined value of 1. The SI system is therefore following the general trend to use fundamental constants to define units rather than physical artifacts.

Other systems
There are special purpose units of length that do not depend on the speed of light, such as the astronomical unit. The speed of light can still be measured using these units.

What if the speed of light changes?
This is rather similar to asking what would happen if the length of the metre rod changed. The first response is that there is a very strong expectation that it will not.

If the speed of light changed due to some unexpected influence, just as the length of the rod might change due to, say, magnetic fields, then the standard would undoubtedly be modified to specify appropriate conditions.

If on the other hand, we are talking about some general and unexplained change in the speed of light, rather like a general change in the length of rods and other things, it is not clear that this would be detectable by us. Neither the speed of light not length are dimensionless quantities thus it is generally considered that we could not detect a change in them as it would be expected that everything would change together.

What if it is discovered that the speed of light varies with frequency (or some other property)?
There is good evidence that the speed of light does not vary with frequency within the current limits of uncertainty of realization of the meter, however, if it was found that the speed of light varied very slightly with frequency, the standard would undoubtedly be updated to allow for this. Some frequency of light would be specified. This might be one of the current recommended frequencies for the realization of the metre but more likely it would be an unobtainable reference frequency such as infinite frequency and measurements with real light would be corrected to allow for the frequency of light actually used.

Something similar happened with the definition of the second when it was discovered that the temperature of the caesium atoms used made a small difference. In 1997 the definition of the second was changed to include, 'This definition refers to a cesium atom at rest at a temperature of 0 K'.