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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3e4c3f4c-b61c-4be1-89bf-a1da041d1292n%40googlegroups.com.
