On Saturday, July 3, 2021 at 1:10:43 AM UTC+2 Brent wrote: > > On 7/2/2021 2:43 PM, Tomas Pales wrote: > > > > On Friday, July 2, 2021 at 2:54:19 PM UTC+2 Lawrence Crowell wrote: > >> The GRW interpretation states there is with any quantum wave a >> fundamental phenomenon of collapse. The collapse occurs fundamentally by a >> stochastic rule. > > > Fundamental, irreducible probability seems like an incompletely baked > concept. Mathematically/structurally, probability can be defined in terms > of pure sets, like any other mathematical/structural concept. Pure sets > (combinations of combinations of combinations etc. founded on the empty > combination) are the fundamental concept from which it is possible, in > principle, to build up any structure. MWI attempts to define the quantum > probability in terms of sets, whose most straightforward interpretation > seems to be worlds. But the problem is that there seem to be infinitely > many worlds in MWI and a system of infinitely many objects may have > different probability measures that give different results, so it seems > that the Schrodinger equation is not sufficient to calculate probabilities > even in MWI and MWI also needs a probability measure as an additional > property of the quantum multiverse, namely such that it results in the Born > rule. There have been some claims that such a measure is the only possible > one > > There's only one consistent measure on a Hilbert space and that's the Born > rule, as proven by Gleason's theorem. > If it is obvious that the Born rule is the only consistent probability measure in QM, why is there not a generally accepted proof of it? What is so controversial about proving that 1 = 1?
Wikipedia mentions several attempts to derive the Born rule from more basic principles: https://en.wikipedia.org/wiki/Born_rule#Derivation_from_more_basic_principles and one of the referenced articles concludes at the end: "The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle." https://www.math.ru.nl/~landsman/Born.pdf Everett noted that every observer gets entangled with the result and then > exists in a superposition of different observed values. He claimed this > meant that any observer would observe the Born rule probablity. But this > depended on considering the observer in one special basis of the Hilbert > space (the pointer states) and then zeroing out cross terms in the density > matrix. By what mechanism the observer or instrument gets into this state > is unclear. Isn't it the mechanism of decoherence that is contained in Schrodinger equation? -- 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/3e4c3f4c-b61c-4be1-89bf-a1da041d1292n%40googlegroups.com.
