On Thu, May 5, 2022 at 12:12 PM Brent Meeker <meekerbr...@gmail.com> wrote:
> On 5/4/2022 5:16 PM, Bruce Kellett wrote: > > On Thu, May 5, 2022 at 9:57 AM Brent Meeker <meekerbr...@gmail.com> wrote: > >> On 5/4/2022 4:01 PM, Bruce Kellett wrote: >> >> On Thu, May 5, 2022 at 8:04 AM Brent Meeker <meekerbr...@gmail.com> >> wrote: >> >>> On 5/4/2022 12:27 PM, smitra wrote: >>> >>> In fact, that idea introduces a raft of problems of its own -- what is >>> the measure over this infinity of branches? What does it mean to >>> partition infinity in the ratio of 0.9:0.1? What is the mechanism >>> (necessarily outside the Schrodinger equation) that achieves this? >>> >>> That simply means that there is as of yet no good model for QM without >>> the Born rule. >>> >>> >>> But there is no mechanism for the Born rule. It is inconsistent with >>> pure Schroedinger evolution of the wave function. I think the problem of >>> measures on infinity is overcome if you simply postulate a very large but >>> finite number of branches to split. >>> >> >> The trouble if the number of branches is finite is that, given the large >> number of splits since the beginning of time, you will eventually run out >> of branches to split. >> >> >> There's always a bigger, but still finite number. Hilbert space already >> assumes continuous complex values. >> > > You cannot adjust the total number of branches as you go: you can't > manufacture more branches if you run short > > > Why not? "Being a branch" is only a matter of degree anyway. There are a > bazillion weakly decohered states every second which our instruments could > not distinguish. > You make the whole concept meaningless. Or why not not an continuum probability and just measure by the density >>> around the eigenvalue >>> >> >> How do you measure the density? You still need to impose a measure on an >> infinite set. >> >> >> The reals have natural measurable subsets which define the Lebesque >> measure. >> >> https://e.math.cornell.edu/people/belk/measuretheory/LebesgueMeasure.pdf >> > > > Can you put the infinite set of branches in one-to-one correspondence with > the reals? Are these, in fact, equivalent sets. What is the length of a set > of branches? > > I think there might be problems with using the Lebesgue measure over sets > of branches. You can define a Lebesgue measure over the real line because > there is a natural concept of the length of an interval. There is no such > natural concept of length over a set of branches. > > > If the branches differ by a real parameter, like the time of the > radioactive decay for Schoerdinger's cat, it should work. In general you > might have to come up with something like Zurek's quantum Darwinism to > provide a measure. > The obvious point is that the branches are not generally ordered, and are not Lebesgue measurable. It is not sufficient to claim that some measure should be possible. You have to find a measure that works for all infinite sets of branches. Quantum Darwinism is not even a starter. 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTZk8iW03onavfbJrAMGRRcNghTjgD7ykbe3k-TaPwmeg%40mail.gmail.com.
