… 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

• A gentle rant about reality and the pointlessness of trying to make it mean something not anchored in what we experience.
• A description of the mutual gravitational orbit of two massive bodies far from any others; and a related account of how flying by a planet can help a space-craft on its journey.
• statistical physics – in which I find temperature meaningful for a system of only one particle – and initial ruminations on thermodynamics.
• A brief explanation of what energy is.
• Some thoughts on what we can infer from our own existence.
• Comments on area-element fields, i.e. second rank antisymmetric covariant tensors.
• A rough sketch of Hawking radiation from black holes.
• How greenhouse gasses work or, to be more specific, why some claims I read about them are wrong.
• When does it make sense to integrate which quantities in physical theories ?
• A minimal mention of Murray Gell-Mann's famous totalitarian principle.
• Thoughts prompted by Erik Verlinde's work on gravity as an emergent effect from information-theoretic considerations.
• I sometimes find time to catch up with some of NASA's astronomy picture of the day and have collected together a page of links to my favourites in their archive.
• what constant accelleration means for special relativity.
• on Planck's units, dimensional analysis, Poisson Brackets.
• on SI's virtuous simplicity.
• a rough guide to the scale of various quantities.

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.

Preliminary notes and old doodles

Sometimes I jot something down for later study and don't immediately get round to actually doing anything with it. They may lie around for years, so be aware that these pages probably don't say much of interest. None the less, here they are, if only so that I can find them and this mention of them might poke me into exploring them in more detail.

• The Lorenz Model, a very simple nonlinear dynamical system that exhibits chaotic behaviour.
• A note on alchymical thinking.
• A note on calendars.
• A doodle about a cunning contrivance I once heard a flat-earther use to hand-wave away how folk far away can see the sun when I can't.
• A beginning of thoughts on how the greenhouse effect works.
• A ramble about the interplay of discrete and continuum in our models and understanding of what we observe.
• The beginings of an examination of the Sagnac effect.
• The beginnings of some thoughts about the implications of a smooth continuum in physics.
• I mostly deliberately chose to nerd-snipe myself by attempting to solve a problem posed in XKCD.
• The start of an account of transforming descriptions of systems.

There are also some older pages that could do with clean-up or upgrades to their notation (as could some of those mentioned above):

• The Lagrangian and Hamiltonian Formalisms for describing dynamical systems.
• A rough analysis of what happens when two bodies collide.
• A doodle about scientific deduction.

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:

• Phill Platt's Bad Astronomy blog takes on everything from astrologers to the moon landing deniers.
• Peter Woit's blog, Not Even Wrong, takes a critical view of some of the flights of fancy that have been popular among theoretical physicists for the last several decades.
• Sarah Kavassalis blogs about bogus theories and poor terminology.
• Sean Carroll offers a respectability check-list for alternative science (linked from Ten signs a claimed mathematical break-through is wrong).
• Gerard 't Hooft's gude to how to become a good theoretical physicist

Further reading

There's plenty of physics out there on the Web – after all, it was the physicists who got the Web going – so here are a few links to places to get started, followed by links of general interest:

• the FAQs of the news groups, such as the relativity FAQ, which points you to various others (UK mirror);
• the physics forums
• Eric's Treasure Trove.
• The many open access journals in physics.
• what looked like a reasonable account of orthodox general relativity at Modern Relativity, 'though I haven't looked into it in detail
• John Baez does a weekly survey of interesting mathematical physics work on the web, e.g. one from the summer of 2007
• Greg Egan's pages provide not only neat accounts of some of modern physics, but some good science fiction stories to go with them.
• Classical mechanics without determinism
• someone's trying to describe the Universe as a braid
• Haidinger's brush is cool ;^)
• Florence gives an interesting perspective on the safety record of stars.
• Holographic movies are now possible :-)
• Constructivist or intuitionist mathematics, rejecting the law of the excluded middle, lets Gisin capture the passage of time in ways that the traditional pointilist model of the reals never can.

… and viewing

• Richard Feynman explains quantum electrodynamics (and a little about the strong and weak forces) in four lectures (glued together as a single video), each an hour and a half long. It's a bit hand-wavy, but illuminating in his unique style.
• Sabine Hossenfelder points out that the limitations of our theories needn't be limitations of the reality we use them to describe.
• Indeed, pretty much anything by Sabine Hossenfelder (tag-line: Science without the gobbledegook) but notably (given my aim of developing the mathematics that physics needs) her treatment of Is infinity real? (no: I agree) and Do complex numbers exist? (I have a different view).
• Bob the Angry Flower says everything I consider worth saying about so-called brane theory.

Written by Eddy.