Coherence (units of measurement)

The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Science Association.

The International System of Units (SI) was designed in 1960 to incorporate the principle of coherence.

Archaeologists have been able to reconstruct the units of measure in use in Mesopotamia, India, the Jewish culture and many others.

Archaeological and other evidence shows that in many civilizations, the ratios between different units for the same quantity of measure were adjusted so that they were integer numbers.

In many early cultures such as Ancient Egypt, multiples with prime factors aside from 2, 3 and 5 were sometimes used—the Egyptian royal cubit being 28 fingers or 7 hands.

[6] In 2150 BC, the Akkadian emperor Naram-Sin rationalized the Babylonian system of measure, adjusting the ratios of many units of measure to multiples of which the only prime factors were 2, 3 and 5; for example there were 6 she (barleycorns) in a shu-si (finger) and 30 shu-si in a kush (cubit).

By contrast, coherence was a design aim of the SI, resulting in only one unit of energy being defined – the joule.

[1] An additional criterion is that, for example, in a coherent system the units of force, energy and power be chosen so that the equations hold without the introduction of constant factors.

[10] Isaac Asimov wrote, "In the cgs system, a unit force is described as one that will produce an acceleration of 1 cm/sec2 on a mass of 1 gm.

Since the proportionality constant here is dimensionless and the units in any equation must balance without any numerical factor other than one, it follows that 1 lbf = 1 lb⋅ft/s2.

This conclusion appears paradoxical from the point of view of competing systems, according to which F = ma and 1 lbf = 32.174 lb⋅ft/s2.

In place of an explicit proportionality constant, this system uses conversion factors derived from the relation 1 lbf = 32.174 lb⋅ft/s2.

In numerical calculations, it is indistinguishable from the four-unit system, since what is a proportionality constant in the latter is a conversion factor in the former.

The specification of the value of any constant factor is not a part of the definition since it does not affect the ratio.

The definition, by itself, is inadequate since it only determines the ratio in one specific case; it may be thought of as exhibiting a specimen of the unit.

In order for it to become a proper definition both the quantity and the defining equation, including the value of any constant factor, must be specified.