Taking Mark's inventory 14

Date: 2009-02-08 10:10 pm (UTC)
koganbot: (Default)
From: [personal profile] koganbot
P25:
i: "it then also broke radically with tradition. Ultimately that break spread through and caused the reconstruction..."
ii: "conceived as a collection of many tiny molecules, moving rapidly about within a container, and colliding frequently" (following sentences expand on this concept)

Well, "molecules" and "container" and "colliding" are literal, not metaphoric, even if Boltzmann was conducting a thought experiment. And "many tiny molecules moving about" is what gases are considered to be, right? - but in the late nineteenth century this was not a given, that gases were made of molecules, so we might well want to consider this a "model." (Wiki: "During the 1890s Boltzmann attempted to formulate a compromise position which would allow both atomists and anti-atomists to do physics without arguing over atoms. His solution was to use Hertz's theory that atoms were 'Bilder,' that is, models or pictures.")

My guess here is that Mark is bolding "conceived" and "container" because they or similar terms reappear when we come to Planck, and "molecule" because Planck is to try to come up with something that he can treat similarly to how Boltzmann treats the molecule.

What I noted down: "Boltzmann reached the answer by a new route, from probability theory, and that route was fundamental for Planck, since whose work it has been standard." So a route to solving a problem became someone else's route for solving another problem, and since then, that route has become standard - that is, it is a... well, what's the word I'm looking for?

iii: "he mentally subdivided that energy into little cells or elements of size e... distributing the molecules at random among these cells... the last cell (energy E)... the first cell (energy 0)..."

None of the words Mark bolded inherently have anything to do with similitude or metaphor, so again I suspect that Mark is bolding them in anticipation of Boltzmann's work becoming a something-or-other for Planck and these same words therefore reappearing in Planck's work. (I guess calling subdivisions "cells" could be metaphoric (it's coincidental that Volta called something very different a "cell" in the previous example).)

P26:
What I noted down: "That way of solving the problem was invented in 1877, and twenty-three years later, at the end of 1900, Max Planck applied it to an apparently rather different problem, black-body radiation."

i: "To analyze that situation, P imagined a container or cavity filled with radiation, that is, with light, heat, radio waves, and so on. In addition, he supposed that the cavity contained a lot of what he called 'resonators' (think of them as tiny electrical tuning forks, each sensitive to radiation at one frequency, not at others)."

Except for "tiny electrical tuning forks" there's nothing metaphoric about any of these words either, but bolding them highlights that what Planck is doing is conceiving a way to make the black-body radiation problem resemble Boltzmann's problem about the entropy of gases and the velocity distribution of their molecules, since by doing so Planck therefore believes he'll have a method for solving the black-body radiation problem.

ii: "Roughly speaking, he used probability theory to find the proportion of resonators that fell in each of the various cells"

And I kept going with the sentence: "just as Boltzmann had found the proportion of the molecules.

iii: "cell size e"
iv: "an infinity of satisfactory values"

Don't know Mark's thought in including these in particular, though he's probably highlighting the reappearance of "cell size." "Infinity of satisfactory values" points out a feature of Boltzmann's derivation that Planck discovered had to be different in his own, where there could only be one cell size.
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Frank Kogan

July 2025

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