16 June 2004

Threepenny Planet: the Planck units

The present writing is a collection of essays concerned with how Planck quantities are perceived. Certain features of the quantities will be emphasized. One feature is their involvement in everyday experience. Another is the opportunity they provide for a fresh look at physical laws and data. Another is their concreteness: One of the power-of-ten multiples of the Planck length happens to be about a mile and another is the thickness of a penny--if there is a penny in your pocket you have with you a decimal Planck cousin. Their concrete reality can be emphasized in the way we handle the quantities: decimal multiples (such as a penny's thickness) will be identified and used descriptively. Other aspects will be discussed later, after the quantities have been introduced. Much of what I have to say is apt to be familiar to anyone with a background in general physics, though some ramifications may have escaped notice. In any case, the focus here is not on the latest theories and discoveries, but on something which is considerably more modest and which runs in a contrary direction. The concern is with more thorough assimilation of what is long-standing and well known--and with broader awareness of the fundamental proportions in nature.

The Planck quantities form a coherent set including one constant of each physical type: one length, one interval of time, one speed, and so on. Members are interrelated in simple, direct ways and play fundamental roles. The Planck speed, for instance, simply consists of traveling the Planck length during the Planck interval of time--and it is the speed of light.

Just when you'd got used to the metric system, the evil physicists are proposing a different set. Actually, the metric system is almost as abstruse as the Planck quantities. The metre, for instance is defined as:

The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

The historical definition was French (and therefore probably encourages the terrorists):

The origins of the meter go back to at least the 18th century. At that time, there were two competing approaches to the definition of a standard unit of length. Some suggested defining the meter as the length of a pendulum having a half-period of one second; others suggested defining the meter as one ten-millionth of the length of the earth's meridian along a quadrant (one fourth the circumference of the earth). In 1791, soon after the French Revolution, the French Academy of Sciences chose the meridian definition over the pendulum definition because the force of gravity varies slightly over the surface of the earth, affecting the period of the pendulum.

Jefferson proposed a different metric system, but was pipped at the post by the perfidious French.

Jefferson's system actually resembles the metric system in many ways. Its biggest shortcoming is that Jefferson didn't hit on the idea of using prefixes to create names for multiples of units. Consequently, his system was burdened with a long list of names. For example, he divided his basic distance unit, the foot (it was slightly shorter than the traditional foot) into 10 inches. Each inch was divided into 10 lines, and each line into 10 points. For larger distances, 10 feet equalled a decade, 100 feet was a rood, 1000 feet a furlong, and there were 10 000 feet in a mile (making the Jeffersonian mile about twice as long as the traditional mile). His basic volume unit was the cubic foot, which he proposed to call a bushel (it was about 3/4 the size of a traditional bushel). The basic weight unit was the ounce, defined so that a bushel of water weighed 1000 ounces. (This is very similar to the metric system, in which a liter of water weighs 1000 grams).

Just for completeness, Talleyrand (who starred with Fouch� in the corruption leaning on the arm of vice crack), advocated a pendulum-based measure.

My bet is that Planck will win out of sheer contrariety in a century or so. Until then we are stuck with the light shining in darkness.

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