George Washington and the flea
In the early days of the Republic George Washington was advised on statecraft and science policy by a flea who lived in his wig. This flea was nourished by the blood of the great Patriot, and she gave very sensible advice. From time to time, if George Washington was wearing the fine white wig where she lived, this flea (whose name was Holly) would hop down into the founding father's ear and speak to him in a determined high-pitched voice.
As for the size of the flea, she was quite visible. In metric terms she had the volume of a cube just under three tenths of a millimeter wide, which is about the width of the line made by those medium ball point pens we buy in bulk. Against a white background like that of the Founding Father's wig she looked not too different from the period at the end of a sentence. Her density was pretty ordinary and in metric terms, since her volume was some 22 millionths of a cubic centimeter her mass was some 22 millionths of a gram.
Holly had one point of vanity which was that her Compton wavelength was exactly equal to the Planck length.
This means that if she could have somehow turned herself into a flash of lightall her mass energy going into a single quantumthat photon would have had wavelength (and I mean wavelength, the radian version, not cyclelength!) equal to the Planck unit. Indeed she would be a primordial photon like those at the Big Bang and she would have been vibrating with the primordial Planck frequency. For fleas this is like your grandmother came over on the Mayflower and Holly was enormously proud of it.
A less massive thing, like a proton, would turn into a lower frequency quantum of light, and would have a longer wavelength. The proton Compton is 13 quintillion longer than Holly's because the particle is 13 quintillion less massive. This gives an idea of how many particles were in the atoms that made up her body, or at least in the nuclei that made up most of her body's weight. Anyway the point, according to Holly's way of thinking, was to have a short wavelength like the primordial light.
One day during George Washington's term the physicists had a demonstration outside the building where Congress was meeting and no one seemed to understand what they were demonstrating about. They were demanding to do research into conditions at "Planck scale." Their theories of gravity and matter broke down, they said, at Planck scale and they wanted support from Congress in fixing up their theories.
George Washington felt Holly hop into his ear and he asked "What's this ruckus about?" "It's about my black hole halfradius and my Compton," said Holly. (She tended to personalize everything.) "According to the theory of gravity, if I were compressed into a black hole my halfradius would be Planck length. So I would be localized inside an event horizon with Schwarzschild radius of two Planck lengths. According to theory I'd even be a point at the center. But according to the theory of matter my Compton wavelength imposes a limit on how much I can be localizedit's one of those uncertainty things: my quantum wave has Planck length wavelength. So if you believe matter theory, I couldn't work as a black hole because I'd be too spread out to fit the geometrical picture of one. Yours truly is the place where the theories fail to compat."
"I'm getting ready to ask Congress to impose a tax on whisky and they want me to reconcile gravity and quantum mechanics," said the Great Patriot, "clear the chambers!" But the physicists clung to the benches and refused leave, so he called the Revolutionary Guards and had the them locked up. They were ahead of their time and it often goes hard with such people.
Copyright © 2002 Leonard Cottrell. All rights reserved.
Table of contents for the New Metric Fables