One result that might lend itself to a hypothetical frequentist take on QM probabilities is discussed by David Z Albert on p. 237-238 of the book The Cosmos of Science, those pages can be read at https://books.google.com/books?id=_HgF3wfADJIC&lpg=PP1&pg=PA238#v=onepage&q&f=false . He considers a scenario where a measuring device is interacting with an infinite series of identically prepared quantum systems, and creating a "pointer state" that tells you just the fraction of those systems that showed a certain result (like an electron being spin-up), and he considers what happens if we analyze this scenario without invoking the collapse postulate or the Born rule, instead just modeling the measurements as entanglement between the measuring system and the system being measured. After a finite number of trials the pointer will be in a superposition of states, but in the infinite limit, all the amplitude becomes concentrated on the eigenstate of the pointer measurement operator where the pointer shows the correct quantum-mechanical probability (for example, "1/2 of all trials showed spin-up").
This type of collapse-free derivation of something like probability in the infinite limit is also discussed in section 5 of the paper at https://www.academia.edu/6975159/Quantum_dispositions_and_the_notion_of_measurement starting on p. 12, apparently the result is known as "Mittelstaedt's theorem". I suppose this result can't really explain why we seem to see definite outcomes (as opposed to superpositions) after a finite number of trials without some additional QM interpretation, but it at least has a "flavor" reminiscent of hypothetical frequentism. On Tue, Nov 22, 2022 at 10:54 AM Lawrence Crowell < [email protected]> wrote: > There are two concepts of probability and statistics, Bayesianism and > frequentism (orthodox view), which formulate probability in somewhat > different ways. I would say that quantum mechanics might be the most > rigorous definition of probability. I would be tempted to say it is more > Bayesian than frequentist. > > LC > > On Monday, November 21, 2022 at 8:15:19 PM UTC-6 [email protected] wrote: > >> On 22-11-2022 02:47, Brent Meeker wrote: >> > On 11/21/2022 5:12 PM, smitra wrote: >> >> The problem lies with the notion of probability, he explains here that >> >> it cannot refer to anything in the physics world as an exact >> >> statement: >> >> >> >> https://www.youtube.com/watch?v=wfzSE4Hoxbc&t=1036s >> >> >> >> That's then a problem for a fundamental theory of physics as such a >> >> theory must refer to statements about nature that are exactly true. >> > >> > Who says so? Physics never makes exact measurements. Why should the >> > theory do something that the physics can't? Deutsch is like the >> > scholastics, he thinks physics is just a branch of mathematical logic. >> > >> > Brent >> >> But physics cannot implement a rigorous notion of probability. So, that >> then makes QM in the traditional formulation problematic. >> >> Saibal >> > -- > 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 [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/54ebbfed-1a27-4b4e-bcc1-0cdf1186398bn%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/54ebbfed-1a27-4b4e-bcc1-0cdf1186398bn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAPCWU3LRmP9ZCd0N7v5uWJcjxu-4NZMk2xq%3DhSCQ513Q2-V8EQ%40mail.gmail.com.
