On 10/3/2024 12:16 PM, John Clark wrote:
On Wed, Oct 2, 2024 at 7:03 PM Brent Meeker <[email protected]> wrote:
*>> All Many Worlds says is that everything always obeys
Schrodinger's Wave Equation, it never collapses,*
/> That's right. It never says where the Born rule comes from. /
*1) Many worlds is the only quantum interpretation that even tries to
derive the Born Rule, the others just assume it's true. *
*2) Gleason's theorem mathematically proves that in dimensions of 3 or
greater and if all probabilities are required to be non-negative, and
add up to exactly 1, then the only consistent way to assign
probabilities isthe squared amplitudes of the wavefunction, provided
you also insist that any combination of two valid quantum states is
also a valid quantum state. *
*So the real question Many Worlds needs to answer is not why is
probability the squared amplitudes of the wavefunction but rather why
is probability necessary at all given the fact that Schrodinger's wave
equation is 100% deterministic? The answer is because of self locating
uncertainty. In the instant after the split but before an observer has
registered the outcome of a measurement there is only one rational way
to apportion credence as to which branch of the wave function he is on
and that is the Born Rule.*
But how many branches are there and how does the evolution of the
Schroedinger equation produce those numbers? It would be equally
rational, and empirically consistent, to suppose that the Born rule
assigned a probability weight to one branch representing each possible
result. Many Worlds has no answer to these questions except to point
out that they give the right answer...the same answer as Copenhagen's
collapse rule gives.
Brent
*Sean Carrolland Charles Sebens go into much more detail here: *
*Many Worlds, the Born Rule, and Self-Locating Uncertainty*
<https://arxiv.org/pdf/1405.7907>
John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>
slu
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