On 7/30/2018 4:11 PM, John Clark wrote:
On Mon, Jul 30, 2018 at 4:27 PM, Brent Meeker <[email protected] <mailto:[email protected]>>wrote:>> Many, perhaps most, physicists do exactly that because they believe in the "Shut Up And Calculate" quantum interpretation and are only interested in predicting how far to the right a indicator needle on a meter moves in a particular experiment. But for some of us that feels unsatisfying and would like to have a deeper understanding about what's going on at the quantum level and wonder why there is nothing in themathematics that says anything about a wave collapsing./ > That's not true. "The mathematics" originally included the Born rule as part of the axiomatic structure of QM. /A axiom is supposed to be simple and self evidently true, the Born rule is neither; and it wasn't derived from first principles
?? You think matix mechanics was "derived from first principles"?? What "first principles"? Have you gone platonic on us?
it was picked for reasons that were were empirical and practical, for some strange reason the damn thing works.
Well, maybe it works because the Born rule is the only consistent way to put a probability measure on Hilbert space. Born just inuitited the rule (and actually got it wrong and corrected it in a footnote); but Gleason proved it in 1957. So the Born rule comes a lot closer to being "derived from first principles" than does Schroedinger's equation or matrix mechanics.
The catch is that Born had assume a probability interpretation; which nobody liked at the time because they could only think of probability as ignorance about ensembles and there were no ensembles...until Dewitt.
Also, the square of the absolute value of the complex wave produces a probability which collapses into a certainty when a observation is made, but the mathematics can't say when that happens because it doesn't say what a observation is.
Mathematics never includes the interpretation that allows you to apply it. Brent -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
