On Fri, Nov 15, 2024 at 12:11:33AM -0800, Alan Grayson wrote: > FWIW, I've always thought Born's Rule refers to the Frequentist Theory of > Probabilility (FTP). Moreover, I don't recall my professors explicitly stating > this, but it was, AFAICT, the unstated assumption, likely inherited from slit > experiments and the need for a multitude of trials to establish the > interference pattern. And I've always assumed the FTP means that for a given > probability value, and some assumed tolerance (the epsilon number in the > concept of limits), there exists a certain number of trials for which there's > a > convergence to that value. But Born's Rule doesn't tell us what that number is > (which will be different for each context of probability). AG
Born's rule is a = <ψ|A|ψ>, which is basically the mean of some distribution. σ² = <ψ|A²|ψ>-<ψ|A|ψ>² is the standard deviation. The normal law of large numbers (https://en.wikipedia.org/wiki/Law_of_large_numbers) has P(|<X>-a|≥ε) ≤ σ²/(nε²) or in English, the probability the average measured value <X> over n trials differs from the Born rule prediction goes to zero as n→∞ as 1/n. So no, the Born rule is not insufficient. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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 visit https://groups.google.com/d/msgid/everything-list/ZzgIwly0oNr7pBMR%40zen.
