The Meter

From the length of the King’s foot under the Ancien Régime to the notion of a quarter meridian adopted during the French Revolution, to the speed of light in a vacuum... the definition of the meter has undoubtedly seen more changes than that of any other unit of measurement. The meter was also the first unit in the International System of Units (SI) that was explicitly established on the basis of a constant in nature. That paved the way to redefining other base units through the use of physical constants.

Profile of the meter

Official definition (1983, 17th CGPM)

Symbol: m

Quantity: length

Units derived from the meter: square meter, cubic meter, meters per second, etc.

The meter is the ultimate unit of measurement, because its name derives from the Latin word “metrum” and the Greek “metron,” which mean measurement. Moreover, it was the meter that gave its name to the diplomatic treaty that formally established the decimal metric system: the Metre Convention, signed on May 20, 1875, by 17 nations, which served as the basis for today’s International System of Units (SI).

Since the very first General Conference on Weights and Measures (CGPM) in 1889, which approved the International Prototype Metre made from platinum-iridium as the standard unit of length, the meter has been defined in a variety of ways. The 11th CGPM, held in 1960, ushered in a significant change by defining the meter using an atomic wavelength: that of the resonance transition between certain levels of energy of the krypton 86 atom. As a result, the meter was the first unit in the SI whose definition was drawn from quantum physics.

At the same time the meter was being redefined, the second acquired a quantum-based definition as well in 1968 that used the cesium atomic clock, which at the time had a relative accuracy approaching 10^{-13}. In the late 1970s, American researchers measured the propagation speed c of light in vacuum with unmatched precision, hampered only by the realization of the meter’s definition (limited at that time to a scale of 10^{-9}). Consequently, the meter became directly contingent on the second at the 17th CGPM in 1983, where the following definition of the meter was adopted:

Definition of the meter

The metre is the length of the path travelled by light

in vacuum during a time interval of 1/299,792,458 of a second.

That definition established the numerical value for the speed c of light in a vacuum as 299,792,458 meters per second.

For measuring very large distances, one way to apply the definition of the meter directly would be by measuring the period of time it takes a short light pulse to travel the distance in question. Currently, the measurement of distances from the earth to the moon yields the least uncertainty (approximately one to two centimeters).

Measuring distances of less than a kilometer, by contrast, requires a different approach. In general, optical interferometry is used. That method consists of comparing the length to be measured to the wavelength λ of a monochromatic ray of light whose frequency f (connected to λ by the single, known constant c) can be determined with extreme accuracy. Accordingly, the reference used is the wavelength of the ray generated by a laser stabilized on an atomic line.

To conduct measurements in air, the differences in propagation speed between air and vacuum need to be offset. Refractometers can be used to determine the air optical index and improve routine measurements of length. Thanks to scientific and technological advances over the past few decades, uncertainties of measurements in air of about 10^{-9} are within reach in practice.

By defining the meter on the basis of a fundamental physical constant – the speed of light in vacuum – we can directly ensure the traceability of even the most extreme measurements of length. With regard to the infinitely large, researchers have identified gravitational waves by measuring variations in length to the order of 10^{-18} meters using a giant interferometer.

At the other extreme lie nanosystems (approximately 10^{-9} meter in size), a promising field in which the LNE has invested heavily through its Nanotech Institute devoted to nanomaterials.

The study of nanomaterials, which involves characterizing nano-objects, analyzing their behavior, developing and comparing instrumental methods for measuring their properties, brings us to the very frontiers of measurement. The current task is to clearly define the quantities measured, develop robust methods that can be transposed from one tool to another and ensure the metrological traceability of the results. When it comes to nano-dimensions, the meter’s role is emerging through atomic force microscopy – an area where France is a leader.