Right. And frequentist interpretation is in fact applied in testing
probabilistic theories like QM because in fact we can only have finite
experimental results.
Brent
On 12/5/2022 11:36 AM, Jesse Mazer wrote:
There are a number of variants of frequentism, would you include
hypothetical frequentism with a time-ordering? Namely, the idea that
probability should be understood in terms of a hypothetical scenario
where we could do an unending number of trials, such that if the
frequency of some outcome in the first N trials is f_N (with 'first N'
defined in terms of the time they occurred, not some other ordering),
then the probability of that outcome would be defined as the limit of
f_N as N approaches infinity. In this case I don't see why an infinite
set of possible outcomes should be a problem--if each outcome has some
finite probability, that means the number of trials with that specific
outcome approaches infinity in the limit as the total number of trials
approaches infinity, and the relative frequencies of any given pair of
outcomes should approach the ratio of their probabilities according to
QM laws.
On Sun, Dec 4, 2022 at 11:24 PM Alan Grayson <[email protected]>
wrote:
How can the frequentist theory of probability be applied to a
system, such as the H atom, which has an infiniteset of possible
outcomes for all energy level transitions? AG
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