Is there room for non-standard units within SI?

One of the main advantages of SI – the metric system – is that it can be used for any measurement task (from the kitchen to the science lab) – thus avoiding the need to learn a plethora of specific units for specific purposes.  However, is there a case for making certain exceptions to this rule? (Warning: this article is for the technically-minded).

The Système International (SI) has been carefully designed as a coherent system of units intended for use in all applications independent of language and national origin. At its heart is the principle that one and only one unit is used for each type of measurement. The same unit is used regardless of scale and the former traditional practice of distinct units for different ranges is supplanted by the use of a common set of prefixes based on powers of ten as an optional alternative to exponential notation also based on powers of ten.

Some measurement applications however do have key units of measurement that, by virtue of their definition, are very convenient for the purpose and if were to be incorporated into the SI would create anomalies, contrary to its principles.

In this article the discussion will focus on astronomy which has a significant number of non-SI units in common use. Readers knowledgeable in other subjects will no doubt think of examples in their own sphere.

For a very recent example consider the tables of data from the NASA/Ames Kepler mission:

http://kepler.nasa.gov/Mission/discoveries/

Note in particular the mass measurements: Solar (mass of Sun = 1), Jovian (mass of Jupiter = 1) and Earth masses which are in wide-spread use. The Astonomical Unit (AU where the mean distance from Sun to Earth = 1)  is also very common. Other common units of distance are the parsec (distance of an object from Earth such that two position measurements made over a 6 month interval yield a discrepency of 1 arc-second due to parallax) and the light year (the distance travelled by an object in a year if moving at the speed of light).

The kilogram is probably used in astro-physics for calculation involving fundamental physical laws (e.g. the gravitational constant is a key parameter in the equations of stellar structure) but the results are presented and discussed in terms of the mass ratios referred to above. This is not because the SI is being rivalled by dogmatic alternatives but, probably, for valid scientific reasons. It is likely the comparisons are significant in helping to assimilate the data and to formulate or refine theories about the formation and evolution of stars and planets.

The AU has its uses in helping to visualize the scale and structure of the Solar system which is probably more memorable than distances in metres. 1 AU is about 150 Gm so conversion to metres isn’t too bad e.g. the mean distance of Pluto at roughly 40 AU is about 6000 Gm or 6 Tm. However, its use should really be confined to circumstances where a comparison with Earth’s orbit is significant (its use in the Kepler observations may well be important).

Incidentally, when interplanetary distances are expressed in metres suitable prefixes should be used e.g. Tm not billions of km.

The light year has some usefulness for larger distance scales. For example a galaxy 2 million light years away is effectively being seen as it was 2 million years ago. It is also a significant parameter for very distant objects because a quasar say 13 billion light years away is effectively a window on the very early universe. As it happens the light year is within 6% of 10 Pm (approx 9.46 x 1015 m).

In the opinion of this author the parsec, however, is overused. It is of course sensible for the intermediate results of parallax measurements (which is necessarily limited to relatively nearby distance determination) but a poor choice as a general purpose unit due to its awkward relationship to the light year (3.24 ly) and metre. Retaining it is almost (but not quite) as bad as retaining the mile alongside the kilometre.

As a general conclusion, standard SI units should be used where it is feasible to do so and non-SI units, where justifiable, should be rationalised to avoid unnecessary proliferation and confined to appropriate circumstances.

Readers may disagree with the tolerance expressed here to some non-SI units and are invited to comment or give other examples in areas of their own knowledge and interest.

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3 Responses to Is there room for non-standard units within SI?

  1. John Steele says:

    I will argue that the BIPM, in its wisdom, has settled the argument for us. Tables 7 and 8 in the SI Brochure make room for them. If I paraphrase:
    *They are allowed, not encouraged, in the special fields where they originated.
    *In any work, they should always be defined at least once in "real" units.
    *They should not be allowed out of their niche to expand into usage in other fields.
    In short, they have surrendered, conditionally.

    Probably the test is two-fold:
    *Do they really help with calculations or understanding within the field.
    *Do they help in explanations to lay people (not in the field)

    In astronomy, I think I agree with you on the AU and light year. They at least help the public grasp the scale. As the meter itself is defined as a fraction of a light second, it is hard to argue against the light year, except for the question of "which year?" As astronomers seem to like the Julian century in equations, I assume 365.25 SI days is used. I think the AU and light year help the public understand the scale; I think the parsec is confusing and best avoided.

    In navigation, the nautical mile (and hence the knot) has a strong tie to sight reduction, celestrial navigation, and great circle sailing. It is (on an approximate spherical earth) one minute of arc as seen from the center of the earth. On a real, ellipsoidal earth, there is a range of values where one is as good as another, and 1852 m is in the range. I gave the argument in another thread and won't repeat it here. Admittedly, in GPS navigation, it is not strictly needed, in "fall-back" navigation, it is still useful.

    At the atomic level, the Angstrom strikes me as a waste. In measurement of wavelength, it has generally been replaced by the nanometer (or other suitable prefix), 1 Angstrom = 0.1 nm = 100 pm. However, it seems to remain popular in atomic structure.

    In photovoltaics and photochemistry, the electron volt (as the energy of a single quanta, either particle or photon) is extremely useful to compare to the activation energy of reactions. You will have to pry it from my cold, dead hands.

    Pressure: The bar is roughly 1 atmosphere. I can understand why mechanical engineers like it to help relate the scale of pressures and forces, but, obviously, it is 0.1 MPa. It would not be the end of the world to eliminate it. The millibar, used in weather forecasting) can be replaced by the equal hectopascal, or by scaling the numbers, kilopascal. The use of columns of mercury to measure pressure is being phased out to avoid mercury spills, the unit "mm Hg" should die with it. Water column is the poor man's pressure gauge. For high precision, it has issues with temperature and local gravity, but its use will probably persist. For measurement of low (gauge) pressures and for hydraulic head calculations, it really is quite useful, and easy to grasp the significance of the result.

    I have never used the barn and have absolutely no thoughts on it. The CGS units are an abomination and I abhor them all.

    We must not forget certain non-SI units have been used in commerce since the beginning of the metric system (table 6) but really have no stronger argument other than familiarity in their favor than the units above: liter, metric ton, are (especially hectare), and time and angular units.

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  2. Robin Paice says:

    Provided that astronomers confine their use of specialist, non-SI units to internal discussions within their own profession, and don't use them in a non-technical context, I suppose it doesn't matter too much. (This is unlike, say, aviation, where the use of knots and nautical miles in the media simply causes confusion and incomprehension to non-aviators). Nevertheless, I can't really see the point of parsecs and AU, etc. The numbers that astronomers deal with (such as distances between galaxies) are so enormous that they have to use scientific notation (i.e. a number between 1 and 10 multiplied by 10 to a power) - otherwise they would run out of zeros. A parsec is 3.0857 x 10^16 ("ten to the power of sixteen") metres. So the distance from the Earth to the Andromeda galaxy, about 7.8 x 10^5 parsecs, is about 2.4 x 10^22 metres. Isn't it just as easy to write metres as parsecs?

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  3. Anonymous says:

    I'd keep the good ol' light-year, since it is popular. We can redefine it as the 10 petameters. We do have the hectares to divvy up square kilometers into easier pieces of land. As far as the 101 kpascal-bar, a bar is really close. Normal barometric pressure varies enough that the room pressure can be more than or less than 100 kpascal (at oil slick level). The pascal is a pretty small. You'd need a pretty good vacuum pump to suck the air out of a chamber to one measly pascal. Call a bar 100 kpascal and measure weather pressure in kpascal and leave the bar and let steam plant engineers drink!

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