Planckian Fables, by Leonard Cottrell
The universe has a set of special quantities (technically known as Planck quantities) which serve as natural scales of measurement: a top speed, a main force, a core frequency, a full power, and so on. We can attune our own quantity-senses to the natural units by using familiar-sized, power-of-ten scaled versions of them — a set of human-scale Planck units.
These fables, and the preceding set called Planckian Fables, are intended to illustrate mainstream physics ideas and to suggest some advantages of human-scale versions of the Planck units. In terms of such units many of the fundamental constants of nature take on values which are powers of ten. Which powers of ten depend to some extent on choice. We use a particular choice of human-scale Planck system here which is arranged so that the the powers of ten have exponents which are multiples of five. It simplifies things because there is less variation in the exponents. The units are called the "ton-pace-minute" or TPM units.
Five of what are probably among the most intuitively accessible fundamental constants take on a fairly simple series of values in this system. The values of the gravitational constant, the speed of light, the frequency coefficient of temperature, the voltage coefficient of frequency, and the elementary charge turn out, respectively, to be 1, 1010, 1015, 10-20, and 10-20.
That is to say that G, c, kB/h-bar, h-bar/e, and e have the values 1, 1010, 1015, 10-20, and 10-20.
The names of the TPM units are fairly self-explanatory because the ton is a ton-sized force (some 20 percent stronger than the metric ton-force but still in the ballpark), the pace is pace-sized (right around five feet), and the minute is 90 percent of a conventional minute. I won't go into the temperature and electrical units belonging to this system except to say that the basic temperature step is very large and it is hundredths of this step (called a "grade") which are roughly degree-sized.
G—universal gravitational constant—1 pace4 per
minute4 per ton
c—speed of light in vacuum—1010 pace per minute
k/h-bar—ratio of characteristic radiant frequency to
temperature—1015 per minute per grade.
k—Boltzmann's temperature coefficient—10-25 tonpace
per grade
h-bar—Planck's constant (angular frequency format)—10-40
tonpace minute.
In these fables the TPM unit speed (which is one pace per minute and equal to 10-10 of the speed of light), is sometimes called a DIME of speed. The unit power, which is delivered by pushing with unit force (ton) at unit speed (dime) is sometimes called a TONDIME of power. It is about half a horsepower or 360 watts).
A million times the Planck mass happens to be OUNCE-size, and we use this ounce as a convenient auxilliary unit of mass. It works out to about 22 conventional grams or roughly 3/4 of a conventional avoirdupois ounce, well within the range of variation for ounces (of which there have been quite a variety over the course of time.) So, in one of the fables, a rabbit is 100 ounces and a frog is 10 ounces—their inertias influence how rapidly they can accelerate and do so in a definite way.
Proceed to An Orbit Dream.
Copyright © 1999, 2001 by Leonard Cottrell. All rights reserved.