On 2/23/2025 5:41 AM, John Clark wrote:
On Sat, Feb 22, 2025 at 7:00 PM Brent Meeker <meekerbr...@gmail.com>
wrote:
*>> You're just repeating the definition of the Born Rule, and
everyone agrees it works, but some of us would like to know
WHY it works and WHY it's even necessary given the fact that
Schrodinger's equation is deterministic *
/> Well if you don't think it's "necessary"/
*Don't be ridiculous!I said the Born Rule was necessary. What I asked
is _WHY_ is it necessary? *
/> science can only answer "why" questions if there is some more
fundamental theory on which to base the answer. /
*And that theory was introduced by Hugh Everett in 1957 and improved
by Sean Carroll and David Deutsch and many many others over the last
68 years. *
> /just taking Schroedinger's equation as the basis is not
sufficient. So it clashes with the MWI mantra of "Just the
Schroedinger equation/
*Everybody agrees that Schrodinger's equation works, and everybody
agrees it says something about what is going on at the deepest level
of reality, but some believe it can't be the entire story and there
must be something more that was happening. Many Worlds asks us to
imagine what would be the result if there was _NOT_ something more
going on and it was just Schrodinger's equation.*
*Would an observer have enough information to make a prediction with
an arbitrary level of precision?*
*
No, and the fundamental reason why is that the observer himself must
also obey Schrodinger's equation, not just the thing he is trying to
predict. So there is no alternative but to resort to probability. *
No, that can't be the fundamental reason. The HUP doesn't derive from
the quantum nature of measuring devices. SG experiment results don't
depend on quantum aspects of the apparatus. And predictions of 0 vs. 1
results don't require arbitrary levels of precision.
*Is there a way to get a real number out of the complex 4-D wave that
the equation produces such that it's always between 0 and 1 and the
probabilities always add up to exactly 1?
*
It's not 4-D. It's 4N-D where N is the number of particles.
*
*
*Yes, take the absolute value of the wave function and then square it.*
And normalize it to 1.
*Mathematically is there another way to produce a set of numbers from
Schrodinger's wave that have the properties that a probability must have?
*
Normalizing the squared modulus make it's value 1. What other numbers
it gives you depends on the assumed basis states. Which is why Zurek
proposes that there must be another effect, "envariance", whereby
interaction with the environment must select only certain a bases which
survive decoherence.
*
No, not if the complex wave is 3-D or higher.*
Yes, that's Gleason's theorem.
*
*
*What should a rational observer do if he wants to make bets about the
future? *
*
*
*Follow the Born Rule.
*
Which as I've noted depends on MORE than "Just the Schroedinger equation."
Brent*
*
*
*
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
dx5
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