On 11/29/2023 4:00 AM, John Clark wrote:
On Tue, Nov 28, 2023 at 7:30 PM Brent Meeker <meekerbr...@gmail.com> wrote:

    /> MWI fans assert that it is superior because it doesn't assume
    the Born rule, only the Schroedinger equation.  I wouldn't claim
    that the (modern) version of Copenhagen is superior to MWI, I'm
    just unconvinced of the converse./


A pretty convincing argument can be made that if the Many Worlds idea is true then the Born Rule must have the ability to predict the most probable outcome of any quantum experiment and as an added bonus, unlike its competitors, it can do so without adding any random elements. However I admit nobody has ever been able to prove that Many Worlds is the only possible explanation of why the Born Rule works, and we already know from experiments that it does. Put it this way, if Many Worlds is true then the Born Rule works, and if the Born Rule works (and we know that it does) then Many Worlds MIGHT be true. But that's still a hell of a lot better than any other quantum interpretation anybody has managed to come up with, at least so far. I'm not certain Many Worlds is correct, but I am certain its competitors are wrong, or so bad they're not even wrong.

And as far as assumptions are concerned,every scientist, not just physicists, has no choice but to assume that probability must be a real number between zero and one, and all the probabilities mustadd up to exactly one for any given situation, because otherwise the very concept of probability would make no sense. And we know that taking the square root of the absolute value is the only way to get a number like that out of a complex function like Schrodinger's wave equation. If Many Worlds is true, and If each version of Brent Meeker makes bets In accordance with the laws of probability so derived, then more Brent Meekers will make money by following the advice given by the Born Rule than if they followed any other betting strategy. Yes some Brent Meekers will still go broke even if they follow the Born Rule, but most will not.

Yes, I knew all that.  But does it follow from the Schroedinger equation alone.  Reading the Carroll/Sebens paper is suggestive, but it depends on transforming to a basis that makes the number of components match the Born rule.  But it seems to me that one could transform to basis where the number of components did not match the Born rule.  Their example is chosen so that in the transformed basis each component has amplitude 1 ,  but that's just scaling.  They even start with eqn (33) which is not normalized.  So it shows how to convert a weighted superposition into a branch count.  But it appears to me that it could produce any number of branches.  The example is chosen to neatly produce all branches of amplitude 1, but that cannot be significant since eqn(35) is not normalized.  So the number of branches is not actually determined and could be anything.

Brent


John K Clark    See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>
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