On Wednesday, April 27, 2022 at 2:55:37 PM UTC+3 johnk...@gmail.com wrote: > It's not perfect, no analogy is, but classical thermodynamics can provide > a pretty good analogy.[...] but that world is *VASTLY* outnumbered by > worlds in which other things happen. >
You mean, statistical mechanics. Counting worlds, then? I remember as a young student, the "equal probabilities" argument based on sheer ignorance of the microstate made me depressed. A much better explanation is based on the sort of agument known by the name "arbitrary functions", started by Jules Henri Poincaré. Here is an example of mine. Whatever the microstate is (among those compatible with what we know), let us focus on the box in which the gas is contained. It has been constructed with some procedure, of which we can obtain (with good approximation) probability density functions of errors. For example, if we aim to make the height to be 4 meters exactly, then we know that the method of construction will give us 4 meters plus some error of known distribution. Therefore the dimensions of the box are random variables -- even if we assume for the time that the surfaces are perfectly flat and it is perfectly orthogonal. Every time a gas molecule hits a wall, its future trajectory becomes randomised, as well as that of every other molecule it bounces with. Soon a probabilistic description of the gas-in-the-box is all we can do, but these probabilities are well grounded on the errors in the construction of the box. (If, instead of errors of construction, you prefer to deal with errors of measurement, we shall be mired by the controversy in the foundation of statistics. Therefore I suggest that we just consider construction.) George K. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/e07d6e23-f92b-46e5-a141-7abcd9d9363bn%40googlegroups.com.
