Postscript 1 — Clicking on the Constants

If, some lazy afternoon, you happened to put the keyword "constants" into google, before long you would find yourself at the NIST (National Institute of Standards and Technology) site, at a section called "Fundamental Physical Constants."

Under "Fundamental" there is a menu including a subsection called "Universal." If you select that you find a short list of fundamental and universal physical constant including entries like:

Planck mass

Planck time

speed of light in vacuum

In the computerese of the URLs there is a nice feeling. They refer to Planck time as "plkt" and to Planck mass as "plkm" and they contain phrases like:

Value?plkt|search_for=universal

Indeed, this NIST site understands me very well. I am searching for universals! which is for fundamental and universal things. And if you do ever go there, notice the small print which says "Click symbol for equation." The conventional symbol for Planck mass (in these fables called Mite because it is in fact the size of a barely visible flea or mite) is m_P and if you click on the symbol you get a formula showing how the Planck mass is related to other universal things — to c, and G, and h-bar.

If you are interested in how the universal quantities fit together you can figure out how to define the other ones in terms of length and mass and time. The speed of light is the length divided by the time, the Planck energy is the mass multiplied by the square of the speed, the Planck force is the energy divided by the length, the Planck volume is the cube of the length, and so on. If you have a calculator which can do power-of-ten arithmetic you may, if you choose to, calculate all the other Planck quantities from the three that NIST gives you. Or you can calculate them equally well from c, G, and h-bar.

For concise, scholarly information on the set of Planck quantities and their role in cosmology and string theory (as the fundamental scales for describing the nature of matter and the beginning of the universe) readers may wish to consult the P (for Planck) section of the glossary at NASA's Level 5 Knowledge Base for Extragalactic Astronomy and Cosmology, compiled by Dr. Barry Madore of Caltech.

For several other treatments, either at the college physics level or for a general audience, see the Center for Natural Units website.