I am wondering how probability is intended in classical physics. I have read a number of articles where it is said that probability in classical physics is generally intended in subjectivist terms as bayesian probability. But I am not sure if there is accordance among physicists' community and the philosophical one about this and if there are other relevant ways to intend probability in classical physics.
There is definitely not complete concordance among Physicists. Some insist on Bayesian interpretations of probability and others prefer the frequentist interpretation.
One definition of "subjectivist probability" is: "In probability, a subjectivist stand is the belief that probabilities are simply degrees-of-belief by rational agents in a certain proposition, and which have no objective reality in and of themselves."
I do not believe that many physicists condone this view of probability. A fair coin is a coin that, if flipped, has a 50/50 chance of coming down heads or tails. That is an actual physical description of the coin, independent of anyone's views. One can measure a coin's symmetries and determine how appropriate the word "fair" is as a description of a coin. This probability is an objective assessment of the coin.
1The "50/50 chance" does depend on subjective lack of information about precise initial conditions and applied force, typical for humans, but subjective nonetheless. Someone with that information, like Laplace's demon, can give a 100% accurate prediction of how the coin will land, whether it is fair or loaded. Many physicists are determinists when it comes to classical mechanics, in which case any "chance" involved would have to be subjective in some way.– ConifoldAug 24, 2020 at 21:07
I interpret the 50/50 chance to mean: "There are lots of ways to flip a coin, many with only miniscule differences from each other. Of that entire set, about half of them will yield heads and the rest will yield tails." There is no lack of knowledge conveyed by that statement. Sep 18, 2020 at 22:27
How do you propose to determine "half" of those lots of ways? There are infinitely many of them, presumably. "Miniscule differences" seems like a reference to human perceptions of size, and the ways are human ways too. There are lots more ways Laplace's demon can do it that humans wouldn't be capable of. What this really amounts to is this: there are lots of ways humans tend to flip coins and of those heads and tails come up about half of the time because relevant differences are neither perceptible to them, nor controllable. Limited perception and control result in lack of knowledge.– ConifoldSep 18, 2020 at 22:50
There are an (uncountably) infinite number of points inside a circle, yet I think no one would question the statement that 1/4 of them are within radius/2 of the center. We extend that to: If an unskilled person throws a dart at a circular dartboard, many of the darts will miss, but of those that do hit, about 1/4 will hit within 1/2 the radius from the center. This is not a statement of uncertainty, but a statement about the vector space of dart throws. Sep 28, 2020 at 19:25
More to the point, the question was specifically: what do classical physicists mean by the word "probability." You may disagree with the frequentist definition, but that is, by and large, what most physicists mean. Sep 28, 2020 at 19:27