The amplitude of the wave function may be far broader then the worthies on this mailing-list have so far proposed. That what is quantum, specifically a process space where the Multi basically like Hugh Everett + John Wheeler evoked is like is something like a spaghetti chart if we postulate observables? Bear Witness on this Hallowed Day! A couple of neighbor's from master Clark's Texas A&M produced this ARXIV publication that tries to lighten these issues of Born + Heisenberg + Schrodinger and I am bit non-plus'd to not see Wigner's' Friend astride the head of Mr. S's Cat? https://arxiv.org/pdf/2110.00580.pdf
"Introducing the ‘process dimension’One way to develop a more thorough understanding of a situation is to build a model. Modelscan be physical (like an architect’s scale model of a building), or they can be visual or conceptual, like a diagram (which requires more imagination to appreciate). Model-building alwaysinvolves making some simplifications, in order to reduce unnecessary complications and bringout essential details of the situation being modeled.Now we’re trying to model a situation where events that occur outside of space and time“collide” with our universe. But it’s difficult enough to visualize four-dimensional spacetime, letalone events that occur somewhere outside! To get a hold of this idea to begin with, we shouldtry to simplify as much as possible, without excluding the essential details. In doing this, wemay once again cite the example of Einstein, who is often quoted as saying “Everything shouldbe made as simple as possible, but no simpler.” 1" To wit, Make The Jump to Process Space... -----Original Message----- From: Bruce Kellett <[email protected]> To: Everything List <[email protected]> Sent: Fri, Dec 24, 2021 11:57 pm Subject: Re: Superdeterminism And Sabine Hossenfelder On Sat, Dec 25, 2021 at 2:18 PM John Clark <[email protected]> wrote: On Fri, Dec 24, 2021 at 8:20 PM Bruce Kellett <[email protected]> wrote: >> You're completely ignoring the amplitude of the quantum wave function, in >> other words you're completely ignoring Schrodinger's equation. > If you check carefully, you will find that Schrodinger's equation is > insensitive to the amplitude of the wave function. What in the world are you talking about. Determining the quantum wave function is the only reason the Schrodinger equation is of any use, and the Born Rule is the only reason the quantum wave function is of any use. The wave function is a vector in Hilbert space. The Schrodinger equation determines the time evolution of the vector. An observable quantity is represented by a Hermitian operator in this Hilbert space. The space is spanned by a set of basis vectors that are conveniently taken to be the eigenvectors of the related measurement operator. Any wave function can be expanded in terms of this set of basis vectors. There are as many of them as there are distinct possible outcomes from a measurement of the corresponding operator (the dimension of the Hilbert space). In MWI, it is assumed that in any measurement all possible outcomes are realized, albeit in different worlds. Any vector in a Hilbert space is expanded in terms of the same set of eigenvectors, so has the same set of possible outcomes. This set is independent of the coefficients determining different vectors in the base space. In other words, the set of possible results for any measurement involving a particular operator and base space is independent of the amplitude of any particular basis vector in the wave function. In the spin measurement case, there are two possible outcomes, |up> or |down>, so the Hilbert space is two dimensional. Any vector in this space can be expanded in terms of these basis vectors: |psi> = a|up> + b|down> and the possible results are up or down, independent of the coefficients (or amplitudes) a and b. > That is one of the reasons that the Born rule is not derivable from the > Schrodinger equation or the wave function. As I keep saying, the Born rule does not need to be derived from anything nor does it need to be assumed because we already know from a huge number of experiments that it is correct; if it wasn't the computer I'm typing this on wouldn't work, the modern world economy wouldn't work either. The Born rule works. But that does not mean that it does not need to be derived or postulated. If you look at Carroll and Sebens, they acknowledge that their prescription boils down to simple branch counting Nope. From page 143 of Sean Carroll's book "Something Deeply Hidden" "It's easy to show that this idea known as branch counting can't possibly work" That refers to naive branch counting. When the number of branches is increased so that all the amplitudes are equal -- equal probability for each branch -- then the probability of a particular result is proportional to the number of branches giving this result. This is effectively branch counting, and Carrol admits as much in one of his later papers with Sebens. > after the number of branches is supplemented to be in the proportion required > by the Born rule After the number of branches is amplified or reduced according to the amplitude of the wave function. That is essentially what I said. There must be a form of branch counting if self-locating uncertainty is going to work to give you the probability. Bruce-- 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/CAFxXSLRkEpy0CdUN0-yteofL5N2Rt7h4R%2BFum8pmJ6ZDszeEVg%40mail.gmail.com. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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