User:Brews ohare/Speed of light (1983 definition)

A change in the meaning of the term speed of light as used in the SI system of units occurred in 1983. In 1983 the 17th Conférence Générale des Poids et Mesures defined the metre to be the length of the path travelled by light in vacuum during a time interval of $1/299,792,458$ of a second. The reasons for using this definition are stated in Resolution 1.

The effect of this definition is to redefine the term speed of light in vacuum as a conversion factor with the exact value 299,792,458 m/s. The value of 299,792,458 m/s is approximately the measured value of the speed of light based upon the pre-1983 definition of the metre, and was selected in part to result in minimal dislocation of standards. According to NIST: “In all of these changes in definition, the goal was not only to improve the precision of the definition, but also to change its actual length as little as possible.” Thus, within the SI system of units, the speed of light is now a defined constant and no longer something to be measured. Improved experimental techniques do not affect the conversion factor speed of light, but do result in a better realization of the metre. Because the second is defined in terms of atomic transitions that can be measured accurately, the new definition, being a ratio of measured times, allows for a definition of the metre with greater accuracy in practical measurement than one based on a ratio of lengths determined using a fringe count of interference patterns.

Rather than measure a time-of-flight, one implementation of this definition is to use a recommended source with established frequency f, and delineate the metre in terms of the wavelength λ of this light as determined using the defined numerical value of c and the relationship. Practical realizations of the metre use recommended wavelengths of visible light in a laboratory vacuum with corrections being applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum.

The term ‘vacuum’ is used in this definition and in this article to refer to the reference state of free space. Like absolute zero, it is an idealized state that only can be approximated in the physical world. Measurements in any real-world medium, such as air or a medium perturbed by gravity must be corrected so as to relate to ‘vacuum’.

Defined speed of light and lengths as times-of-transit
The 1983 definition of the metre introduced the SI units speed of light c0 = 299 792 458 m/s as a defined (not measured) value. Setting the speed of light to a defined numerical value in the SI units means comparisons of length become equivalent to comparisons of transit times of light.

This equivalence is established by thinking of measurement as a comparison between the quantity being measured and the standard unit; it is a matter of ratios. Mathematically, comparison of two lengths ℓ1, ℓ2 with times-of-transit of light, t1, t2 may be expressed as the ratio
 * $$ \frac {\ell_1}{\ell_2} = \frac {c\ t_1}{c\ t_2} = \frac {t_1}{t_2}, $$

which is independent of the speed of light c, so long as the same speed of light is realized while measuring both times-of-transit.

As an example, if the time t2 in the above equation is selected as t2 = 1/299,792,458 s, and the measurement is done in "vacuum", then ℓ1 is determined in metres. Thus, choosing ℓ2 as one metre, the above equation is simply
 * $$ \ell_1 = \frac {t_1}{t_2} \ell_2 = \frac {\ell_2}{t_2} t_1 =   \frac {1~\mathrm{m}}{1/299,792,458~\mathrm{s}} t_1 = 299,792,458~\mathrm {m/s} \times t_1, $$

which recovers the fundamental definition of length provided by the BIPM. This result shows that the determination of ℓ1 in units of metres is determined completely by the standard time interval selected for the metre, namely  1/299,792,458 s. It also establishes that the use of a transit time of  1/299,792,458 s  to define the metre is equivalent to defining the conversion factor between time and length as 299,792,458 m/s.

Measuring the speed of light
If one wishes to measure the speed of light, not just use the SI system with its defined relationship between the metre and the speed of light, that can be done by introducing a unit of length other than the metre, for example the wavelength of an atomic transition, as was done in the earlier definition of the metre before 1983:

"On October 14, 1960 the Eleventh General Conference on Weights and Measures redefined the International Standard of Length as 1,650,763.73 vacuum wavelengths of light resulting from unperturbed atomic energy level transition 2p10 5d5 of the krypton isotope having an atomic weight of 86. The wavelength is


 * λ = 1 m / 1,650,763.73 = 0.605,780,211 µm

At different times some national laboratories used light sources other than krypton 86 as length standards. Mercury 198 and cadmium 114 were among these and they were accepted by the General Conference as secondary length standards."

Because a length such as the wavelength of an atomic transition is determined from the transit time using the relation:


 * $$ \ell  =  c\ t  \, $$

where c is the speed of light to be measured, the speed of light can be determined in units of wavelengths per second by counting interference fringes and dividing by the measured period of the transition. As with the earlier definition of the metre before 1983, this speed of light in terms of an independent length standard would be not an exactly known value, set by definition, but a measured value subject to experimental error.

Example
An example illustrates how the new metre and the conversion-factor speed of light work in practice. If c is used to denote the real physical speed of light (the distance between points divided by the time it takes for a signal to transit them) and c0 = 299 792 458 m/s, the SI-units post-1983 conversion factor (also referred to as the "speed of light" in the SI system of units), then the example shows that logically c ≠ c0, even though numerically c and c0 are nearly the same.
 * Take two points A & B. Suppose they are some fixed distance apart. (The actual distance between A & B can be measured, for example, using interferometry to determine the separation in units of wavelengths of some atomic transition). Suppose (hypothetically) measurement skills increase and the transit time of light between points A & B is measured to be a time tAB that is a slightly shorter time than previously measured with older technique.


 * In that case the real speed of light as determined from the relation real speed = (actual distance between A & B)/ tAB will be measured as larger, because points A & B have not changed position, and the time-of-transit tAB has shortened.


 * However, the SI units conversion factor c0 = 299 792 458 m/s is not affected by the new measurement technique.


 * This example shows that the real speed of light (for example, expressed in units of the number of wavelengths traveled per second) is different in principle (logically different) from the SI conversion factor of c0 = 299,792,458 m/s.


 * The distance between A & B in the SI units system is given by ℓAB = 299 792 458 m/s ·tAB, which is a smaller number of metres than previously because the time is shorter (even though the real separation has not changed). Equivalently, in SI units the metre is longer. The shorter distance in metres from A to B combined with the shorter time-of-transit results in a speed in SI units that is always the conversion factor 299 792 458 m/s, regardless of any advance in technique.


 * In both cases the measured time has shortened. In nature, the separation between A & B is fixed, so the shorter time results in a larger measured value for the real speed of light. In SI units the distance in units of metres is shorter, and the light travels at the same rate of 299,792,458 m/s. The real speed of light can change (for example, with improvement in measurement technique), but the conversion factor is fixed by definition, lies outside measurement, and is not a property of nature; rather the conversion factor c0 = 299,792,458 m/s is a property of the SI system of units.