IN PRACTICAL PLANCK UNITS THE CHIEF CONVERSION FACTORS ARE POWERS OF TEN

When expressed in terms of practical Planck units, the principal physical constants turn out to be in most cases exactly equal to powers of ten. These constants include the conversion factors which one most often uses when calculating with nature. The speed of light converts between mass and energy and between frequency and wavelength. Planck's h-bar converts between (angular) frequency and energy and likewise between wavelength and momentum. Boltzmann's k converts between temperature and quantities including energy which are consequent on temperature. The electron charge converts between microscopic and macroscopic measures of charge, energy and current. The metric system merely makes the density of water (a minor conversion factor) equal to a power of ten and leaves the major factors ungainly. Practical Planck units do the opposite—the density of water is not a power-of-ten but the major conversion factors listed here are. I will first list their values without unit-names because the values matter more than the names, and then in a second parallel tabulation show the units. Bear in mind that in a metric system version of this table, instead of these powers of thousand one would be seeing more than a dozen different numbers just as arbitrary and meaningless as 299792458.

Here is what the table looks like with unit-names inserted. The basic unit-names used here are milliminute or trice (time), centipace (length), dyne (force), grade (temperature), and quad (charge.) For conciseness, chi is used as a nickname for the unit power: erg/trice.

The Coulomb constant is alpha × 10⁹ dyne centipace² per quad². Alpha is used as a symbol for the fine structure constant, 1/137.036..., often simply written 1/137.

SENESCENCE OF THE METRIC SYSTEM

Since the French Revolution the metric units have been redefined so often that something analogous to metal fatigue has occurred. Fracturing and embrittlement in the system is shown by increasingly complicated conversion factors. Each time units are redefined, always with good reason, finicky numerical adjustments are made to save appearances. A kind of plaque of essentially meaningless numbers is accumulating at the heart of the system: numbers which are what they are purely for historical reasons but which nevertheless are essential to the system. Here are some of these plaque numbers: 299 792 458, 483 597.9, 25 812.807, 135 639 274, 6 241 509 629 152 650 000.

299 792 458: According to the 1983 redefinition, a meter is the distance light travels in vacuum in 1/299 792 458 of a second. So the speed of light is not a measureable quantity and is, by convention, exactly 299 792 458 meters per second.

483 597.9: According to the 1990 electrical standards the volt corresponds to this number of GHz in a Josephson gauge.

25 812.807: According to the 1990 electrical standards the ampere corresponds to this number of volts in a von Klitzing gauge. The combined effect is to give exact conventional values, in 1990 electrical terms, to both Planck's constant and the elementary charge.

6 241 509 629 152 650 000: According to the 1990 electrical standards the coulomb is exactly this number of elementary (or electron) charge.

135 639 274: According to the 1999 proposal of Mohr and Taylor the kilogram would be defined as corresponding to a cyclic frequency which is this number times 10⁴² Hz.

AWKWARDNESS OF METRIC SIZES IN RELATION TO NATURAL UNITS

Metric units just happen to have awkward sizes in relation to the natural units. They tend to be substantially off the mark beginning with the meter, which is either 6 times what it should be (16.16 centimeters) or else 60% of what it should be (1.616 meters) to be power-of-ten compatible with the Planck length.

In like fashion the unit speed (meter per second) is either 3 times what it should be or only 30 percent of what it should be in order to be compatible with the speed of light.

Likewise the unit mass is off the mark by a substantial factor. Less than half what it should be to fit with Planck mass. As a general rule the metric units are so far off as to make it unreasonable to suppose that the system could be trimmed and adjusted to fit the natural units. It is more likely that the metric system will have to be discarded in toto, when the accumulation of numerical trash in the system becomes intolerable.

Indeed the Planck units appear more compatible with a revised traditional system of units than with the metric system. This is particularly noticeable as regards the mile, gallon, ounce (of mass), and the traditional ton force. These are roughly power-of-ten versions of the corresponding Planck quantities. This applies as well to related measures like the pace (a thousandth of a mile), the half-foot (a tenth of a pace, used in classical times by the Greeks and others), and the fingerwidth (a hundredth of a pace, also going back to classical times.) Revised traditional units can be defined so as to make round numbers—powers of ten—of such fundamental constants as the speed of light, Planck's h-bar, Boltzmann's k, the electron charge and the gravitational constant G.

Such a postmetric system of revised traditional units would would necessarily be power-of-ten scaled versions of the Planck quantities. The units would include ones with sizes which are roughly half a foot (e.g. a thumb-to-forefinger span), a gallon (cubic span), a pace (ten span), a mile (thousand paces), a (three-quarter-size) ounce, a (twenty percent larger) vôlt, a (thirty-some percent larger) ton, a (forty percent larger than kelvin) degree, and a time duration roughly a thousandth of a minute.

Units of these sizes are implied by the requirement that the values of the principal fundamental physical constants be powers of ten. The chief difficulty with the metric system, making it awkward and out-dated, is that its units (except possibly in the case of the volt and newton) and the wrong size to be adjusted to fit the fundamental constants in this way.

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