Metre (unit)

This article is about Metre (unit). For other uses of the term Metre, please see Metre (disambiguation).

The metre (American meter) is the basic unit of length measurement in the International System of Units (SI) commonly known as the metric system. The metre is abbreviated as m, appearing after the quantity.

Currently, the SI units define the metre in terms of the speed of light and the second, such that the metre is the length traveled by light in the reference medium of classical vacuum in the time interval of 1/299 792 458 second. The metre has been adopted as the fundamental unit of length in almost all countries of the world, with the United States being a notable exception.

An easily realized and reproducible measurement is a major goal of metrology. The practicality of adoption of a time of flight as a measure of length depends critically upon the experimental fact that the speed of light in vacuum is a universal constant to within experimental error. As a result of the present definition, aside from the error in measuring transit times, length measurements are subject only to the uncertainty in relating the medium used in a particular measurement to a reference vacuum, taken in SI units to be the classical vacuum.

The metre is also the basis of the SI units of area and volume, which are the square metre (m²) and cubic metre (m³), respectively.

Very few adult humans are as tall as 2m in height.

History

(PD) Image: John R. Brews
Measuring a length in wavelengths of light using interference.

The metre was initially adopted as a unit of measure in France in 1790, during the French Revolution.

The original definition of the metre was the length of a pendulum with a half-period of 1 second, but was changed in 1791 to be the length of a prototype bar which was supposed to be 1/10 000 000 of the length of the meridian of Paris from the north pole to the equator. Since then, the metre has been redefined a number of times.

After 1960 and before the switch to the transit-time definition in 1983, lengths were measured in terms of the number of wavelengths of light that could be fitted into them. The figure shows schematically how length was determined: the two panels show a laser source emitting a light beam split to travel two paths. The light is recombined by bouncing the two components off a pair of mirrors, and it is the distance between the mirrors that is measured as this spacing is adjusted to match the length of the object to be measured.

In the top panel the path is such that the two beams reinforce each other after reflection, leading to a strong light pattern. The bottom panel shows a path that is made a quarter wavelength longer by moving the right-hand mirror further away. The result is the two beams are in opposition to each other, and the recombined light intensity drops to zero. Thus, as the spacing between the mirrors is adjusted, the observed light intensity cycles between reinforcement and cancellation as the number of wavelengths of path difference changes, and the observed intensity alternately peaks and dims. This behavior is called interference and the machine is called an interferometer.

This methodology for length determination requires a careful specification of the wavelength of the light used. The precise definition of the metre was established in the 11th CGPM of 1960 as 1 650 763.73 wavelengths of the 2p₁₀−5d₅ line of krypton-86. The measurement also requires careful specification of the medium in which the light propagated, which had to be related to a reference medium of ideal vacuum.

This interferometer methodology had an experimental uncertainty related to determining the precise frequency of the source and the careful measuring of the interference pattern that led in 1983 (along with other considerations spelled out in the final decision) to the switch to the more exact procedure based upon the transit time of light.

Other systems of units

In systems of units where, unlike the current SI system, lengths are fundamental units (for example, the Bohr radius a₀ in atomic units, or wavelengths in the older SI units) and are not defined by times of transit, it may be noted that the comparison of lengths even in such units is more accurately made by comparing the transit time of light along the lengths, because transit times are more accurately measured than are the lengths of the paths as multiples of the fundamental length unit, at least using present techniques.

Traditional units

The foot has been defined in the United States to equal exactly 0.3048m, though an earlier definition of the survey foot was 1200/3937 m, which is different than the current definition by about one part in 500 000. The inch, being 1/12 foot, is exactly 0.0254m, or 2.54cm.

The modern Chinese chǐ (市尺), or "Chinese foot", has been defined to equal exactly one-third of a meter. The Hong Kong chek (尺) is exactly 0.371475m. The Japanese kanejaku (曲尺) was defined as 10/33m in 1891.

The Spanish vara was fixed at about 835.9mm in 1801; however, the vara was defined in California as 838.2mm (33 inches), and in Texas as 846.666...mm (33 1/3 inches).

The megalithic yard is approximately 0.83m.