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Choice of Units

All choices of units are completely arbitrary and are made strictly for the sake of convenience. If you were a surveyor in 18th-Century England, you would consider the chain (66 feet by our standards) an extremely natural unit of length, and the meter would seem a completely artificial and useless unit, because people were shorter then and the yard (1 yard = 3600/3937 of a meter) was a better approximation to an average person's stride. Feet and hands were even better length units in those days; and if you hadn't noticed, an inch is just about the length of the middle bone in a small person's index finger.

If you couldn't get your hands on a timepiece with a second hand, the utility of seconds would seem limited to the (non-coincidental) fact that they are about the same as a resting heartbeat period. Years and days might seem less arbitrary to us, but we would have trouble convincing our friends on Tau Ceti IV.^3.3 Remember, our perspective in Physics is universal, and in that perspective all units are arbitrary.

We choose all our measurement conventions for convenience, often with monumental short-sightedness. The decimal number system is a typical example. At least when we realize this we can feel more forgiving of the clumsiness of many established systems of measurement. After all, a totally arbitrary decision is always wrong. (Or always right.)

Physicists are fond of devising ``natural units'' of measurement; but as always, what is considered ``natural'' depends upon what is being measured. Atomic physicists are understandably fond of the Angstrom (Å), which equals 10^-10 m, which ``just happens'' to be roughly the diameter of a hydrogen atom. Astronomers measure distances in light years, the distance light travels in a year ( $365 \times 24 \times 60 \times 60 \times 2.99 \times 10^8 = 9.43 \times 10^{15}$ m), astronomical units (a.u.), which I think have something to do with the Earth's orbit about the sun, or parsecs, which I seem to recall are related to seconds of arc at some distance. [I am not biased or anything....]

Astrophysicists and particle physicists tend to use units in which the velocity of light (a fundamental constant) is dimensionless and has magnitude 1; then times and lengths are both measured in the same units. People who live near New York City have the same habit, oddly enough: if you ask them how far it is from Hartford to Boston, they will usually say, ``Oh, about three hours.'' This is perfectly sensible insofar as the velocity of turnpike travel in New England is nearly a fundamental constant. In my own work at TRIUMF, I habitually measure distances in nanoseconds (billionths of seconds: 1 ns = 10^-9 s), referring to the distance (29.9 cm) covered in that time by a particle moving at essentially the velocity of light.^3.4

In general, physicists like to make all fundamental constants dimensionless; this is indeed economical, as it reduces the number of units one must use, but it results in some oddities from the practical point of view. A nuclear physicist is content to measure distances in inverse pion masses, but this is not apt to make a tailor very happy.