… Aristotle laid it down that a heavy object falls faster than a light one does. The important thing about this idea is not that he was wrong, but that it never occurred to Aristotle to check it.

Albert Szent-Györgyi de Nagyrápolt,
winner of the Nobel Prize in Physiology or Medicine
(c/o TV Tropes, but that page is now gone).

# Eddy's dabblings in theoretical physics

This page is a mess: it will probably remain so for some time. I'll be hanging things I write about þeoretical physics off it, except for the things separately classified as Relativity or Quantum Mechanics.

## Gabblings

Back in May 1996 I was thinking about the nature of harmonic oscillations on high-dimensional smooth manifolds: treating the manifold as a drum-skin and looking for what finite-energy patterns of oscillation arise. Given that the Universe is understood as a smooth manifold having high (but probably differing) curvatures in all but four dimensions, my aim was to see what kinds of oscillations would be stable. Whether this (entirely classical) analysis would be of any use is, of course, a matter of speculation. However, it should teach anyone investigating it plenty about the machinery of describing action on a smooth manifold, yield insights into the meaning of Einstein's field equations for gravity (which relate curvature to mass density) and provide a start-point from which to look into quantising such systems. By August 1997 I was more pre-occupied with building a mathematical toolset. More recently (2008), I've been too busy working to give much time to my research, but I've been reading some of the text-books I should have read as a student.

## Oddities

Avogadro's number tells us that there are .9963 × power(79, 2) molecules in a mole of stuff. If the stuff is an ideal gas under standard conditions, this takes up 22 and a bit litres of space, giving each a tiny volume, equal to that of a cube with 2 nanometre sides. Such a side is about 40 times the Bohr radius but in Planck lengths it's 5 times the 25th power of 10.

Divide the speed of light by a year and you get an accelleration: 9.5 metres per second, only slightly less than Earth standard gravity. By my quick calculations, that's the surface gravity one would experience at an altitude of 67 miles, above the Earth as it is; or on the surface of a similar planet whose radius is 124 miles shorter.

The inverse of the fine structure constant, 137.04, is respectably well approximated by:

• exp(π.π/2) −2 = 137.0456
• 20.power(4, γ) = 137.082039, where γ = (1+√5)/2 is the golden ratio, defined to be the positive root of γ = 1 + 1/γ
• 39 +61.γ = 137.7 = sum(: power(i,γ) ←i :[0,2,3,4,8,9])

and the ratio of the proton mass to the electron mass, when divided by 4.π, yields 146.11, which isn't all that far off; while a year is within half a percent of ten π Ms. Some people get quite misty-eyed about such coincidences. Scientists expect them.

## Hunting bogons

Unfortunately, as part of its general effect of giving wider currency to uninformed opinion, the web is home to a wild and crazy diversity of things that pass themselves off as mathematics or science but emanate from folk who plainly don't know what they're talking about. Various people with more of a clue have caught my attention in their efforts to point out the flaws in such drivel and help people to recognise when what they're reading isn't worth the time. Here are some examples: