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.
Being the size of a flea, she was quite visible. Her width was one sixtieth of a fingerwidth bone unit and her volume was that of a cube one sixtieth of a bone wide. This is about as wide as the line made by one of those ball point pens offices get in bulk. If you prefer metric terms, she was three tenths of a millimeter wide. Against a white background like the Founding Father's wig she looked not unlike a period printed on white paper. And her density was pretty ordinary—a millionth of an ounce in a volume which was 5 millionths of a cubic bone. You get the idea: she had the Planck mass.
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 light—so that all the energy comprising her went into a single quantum—the photon would have had wavelength (the radian version, not cyclelength!) equal to the Planck length. Indeed she would have become like one of those primordial photons at the Big Bang and would have vibrated with the primordial Planck frequency. Fleas feel about this the way we do about your greatygreats arriving on the Mayflower and Holly was enormously proud of her Compton wavelength.
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 nuclear particles—13 quintillion—were in the atoms that made up her flea-sized body and made up most of her body's weight. Anyway the point, according to Holly's way of thinking, was to have a classy wavelength like that of 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 grants to explore conditions at "Planck scale." They complained that their models of gravity and matter broke down at Planck scale and they wanted Accelerators from Congress so they could fix 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 localized—it's one of those uncertainty things: my quantum wave has Planck unit 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 two models 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 Guard and had the them locked up. They were ahead of their time and it often goes hard with such people.
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Copyright © 2002 Leonard Cottrell. All rights reserved.
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