On Thu, May 5, 2022 at 9:57 AM Brent Meeker <[email protected]> wrote:
> On 5/4/2022 4:01 PM, Bruce Kellett wrote: > > On Thu, May 5, 2022 at 8:04 AM Brent Meeker <[email protected]> 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 > > 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. 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/CAFxXSLQ%3DMry5ZCV%3DYc8jE4Cr_GXnS4U4aKD4ncUP6qEOF5mK8Q%40mail.gmail.com.
