On Friday, September 13, 2019 at 3:15:47 AM UTC-5, Philip Thrift wrote: > > > > On Thursday, September 12, 2019 at 5:44:43 PM UTC-5, Lawrence Crowell > wrote: >> >> >> >> On Thursday, September 12, 2019 at 11:44:51 AM UTC-5, Philip Thrift wrote: >>> >>> >>> >>> On Thursday, September 12, 2019 at 8:45:22 AM UTC-5, Lawrence Crowell >>> wrote: >>>> >>>> On Thursday, September 12, 2019 at 4:20:46 AM UTC-5, Philip Thrift >>>> wrote: >>>>> >>>>> >>>>> >>>>> On Wednesday, September 11, 2019 at 11:45:41 PM UTC-5, Alan Grayson >>>>> wrote: >>>>>> >>>>>> >>>>>> https://www.wired.com/story/sean-carroll-thinks-we-all-exist-on-multiple-worlds/ >>>>>> >>>>> >>>>> >>>>> >>>>> Many Worlds is where people go to escape from one world of >>>>> quantum-stochastic processes. They are like vampires, but instead of >>>>> running away from sunbeams, are running away from probabilities. >>>>> >>>>> @philipthrift >>>>> >>>> >>>> This assessment is not entirely fair. Carroll and Sebens have a paper >>>> on how supposedly the Born rule can be derived from MWI I have yet to >>>> read >>>> their paper, but given the newsiness of this I might get to it. One >>>> advantage that MWI does have is that it splits the world as a sort of >>>> quantum frame dragging that is nonlocal. This nonlocal property might be >>>> useful for working with quantum gravity, >>>> >>>> I worked a proof of a theorem, which may not be complete unfortunately, >>>> where the two sets of quantum interpretations that are ψ-epistemic and >>>> those that are ψ-ontological are not decidable. There is no decision >>>> procedure which can prove QM holds either way. The proof is set with >>>> nonlocal hidden variables over the projective rays of the state space. In >>>> effect there is an uncertainty in whether the hidden variables localize >>>> extant quantities, say with ψ-ontology, or whether this localization >>>> is the generation of information in a local context from quantum >>>> nonlocality that is not extant, such as with ψ-epistemology. Quantum >>>> interprertations are then auxiliary physical axioms or postulates. MWI and >>>> within the framework of what Carrol and Sebens has done this is a >>>> ψ-ontology, >>>> and this defines the Born rule. If I am right the degree of ψ-epistemontic >>>> nature is mixed. So the intriguing question we can address is the nature >>>> of >>>> the Born rule and its tie into the auxiliary postulates of quantum >>>> interpretations. Can a similar demonstration be made for the Born rule >>>> within QuBism, which is what might be called the dialectic opposite of MWI? >>>> >>>> To take MWI as something literal, as opposed to maybe a working system >>>> to understand QM foundations, is maybe taking things too far. However, it >>>> is a part of some open questions concerning the fundamentals of QM. If >>>> MWI, and more generally postulates of quantum interpretations, are >>>> connected to the Born rule it makes for some interesting things to think >>>> about. >>>> >>>> LC >>>> >>> >>> >>> QBism is not the dialectical opposite of MWI. This is: >>> >>> https://twitter.com/DowkerFay/status/1110683583570759680 >>> >>> @philipthrift >>> >> >> The MWI and this path integral interpretation are both ψ-ontic and are >> thus not opposite. >> >> LC >> > > > many worlds : deterministic > path integrals : stochastic > > > The role of path integrals in stochastic processes was anticipated by > Wiener: > > The subject began with the work of Wiener during the 1920's, corresponding > to a sum over random trajectories, anticipating by two decades Feynman's > famous work on the path integral representation of quantum mechanics. > However, the true trigger for the application of these techniques within > nonequilibrium statistical mechanics and stochastic processes was the work > of Onsager and Machlup in the early 1950's. > > > https://www.worldcat.org/title/path-integrals-for-stochastic-processes-an-introduction/oclc/830162352 > > but of course with a quantum-probability rule, e.g.: > > (a1) > > is replaced in the quantum case by the theorem of composite amplitudes > https://www.encyclopediaofmath.org/index.php/Quantum_stochastic_processes > > @philipthrift >
This is of course Bayes' theorem and the second is what might be called the "square root" of Bayes' theorem. The modulus square the the second gives probabilities that obey Bayes' theorem. LC -- 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/558d6ea2-01ad-4b73-bb92-a2bf3e4dee77%40googlegroups.com.
