User:Brews ohare/Speed of light (Example)

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.  It is an exact value, set by definition.


 * 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.