On 8/27/2025 1:13 PM, Quentin Anciaux wrote:
Brent,
In Everettian QM, the Born rule applies to coarse-grained outcomes,
not to individual fine-grained sequences treated as equiprobable.
Not what they told me in graduate school.
The amplitudes are not just bookkeeping: their squared norm defines
the measure, which determines how observer-instances are distributed.
Which is why I chose a=b to illustrate that the difference was due to
different weights.
Think of a lottery with one million tickets, but where 400,000 of them
are identical copies of the same number. All tickets "exist," but they
are not equally weighted when predicting what a typical observer will
see.
Only if you implicitly define "typical" as probable under the Born rule.
Similarly, in your N=6 example, 011000 and 001010 belong to the same
coarse-grained class of "2 successes out of 6," and the combined
measure of all such sequences follows the Born rule.
But there's no "coarse graining" the multiple worlds. They are all
separate and orthogonal. There is no observer who can see more than one
of them.
Assuming each branch has equal weight and uniform observer sampling
creates the contradiction, Everett’s formulation does not require that
assumption.
That's right. Everett's formulation /*allows adding the Born rule*/ as
a axiom giving different weight to different worlds. But it's not
implicit in MWI.
Brent
Quentin
All those moments will be lost in time, like tears in rain. (Roy
Batty/Rutger Hauer)
Le mer. 27 août 2025, 21:16, Brent Meeker <[email protected]> a
écrit :
I think some specificity would help this debate. Suppose N=6, so
there are 64 different sequences in 64 different worlds. The
number of observers is irrelevants; we can suppose the results are
recorded mechanically in each world. Further suppose that a=b so
there is no question of whether amplitudes are being respected.
Then in one of the worlds we have 011000. Per the Born rule its
probability is 0.2344. In MWI it is 1/64=0.0156. The difference
arises because the observers applying the Born rule looks at it as
an instance of 2 out of 6 successes.
So why can't the MWI observer do the same calculation? He
certainly can. /He can apply the Born rule./ But when he does so,
it can't be interpreted as a probability of his branch since such
probabilities would add up to much more than 1.0 when summed over
the 64 different worlds. From the standpoint of statistics 011000
is the same as 001010 and their probabilities sum. Their
difference is just incidental, but they are different worlds in
MWI and summing them makes no sense.
Brent
On 8/26/2025 11:39 PM, Quentin Anciaux wrote:
Bruce,
Everett’s original formulation describes a universal wavefunction
evolving unitarily, not discrete worlds with one observer per
branch. Your argument assumes this mapping, but it is an
interpretative choice, not a result derived from the Schrödinger
equation.
Also, your claim that all 2^N sequences have equal measure only
holds if amplitudes are treated as irrelevant. In standard
quantum mechanics, amplitudes directly determine observed
frequencies via the Born rule, which has strong experimental
support. Ignoring amplitudes means you are no longer analyzing
Everett’s framework but a different model where the Born rule
indeed fails.
To refute Everett with Born included, you would need to show that
even when squared amplitudes define a natural measure, the
predicted observed frequencies still fail. Assuming uniform
sampling over sequences does not establish that.
This is why your derivation is not accepted: it relies on a
hidden premise, one observer per branch with uniform sampling,
which is not part of Everettian quantum mechanics.
Quentin
All those moments will be lost in time, like tears in rain. (Roy
Batty/Rutger Hauer)
Le mer. 27 août 2025, 07:32, Bruce Kellett
<[email protected]> a écrit :
On Wed, Aug 27, 2025 at 3:26 PM Quentin Anciaux
<[email protected]> wrote:
Bruce,
If your derivation is as solid as you claim, then a
skeptical referee is exactly who you should want to
convince. Repeating the same argument here without
engaging with the role of amplitudes will not make it any
stronger. You cannot dismiss amplitudes entirely and then
claim to have explained why measure must be uniform, that
is circular.
If you truly believe your reasoning refutes the Born rule
within Everett’s framework, then publishing it is the
only way to settle the matter. Otherwise, endlessly
asserting it here looks less like confidence and more
like avoidance.
Your entire argument hinges on assuming uniform observer
sampling by postulating one observer per branch.
The argument does not depend on this. This shows nothing more
than that you have not understood the argument.
But that is precisely the point under debate, not a
derived result. If you ignore the role of amplitudes in
defining the structure of the wavefunction, you're not
engaging with Everett's formulation, only with your own
simplified model.
Until you demonstrate why amplitudes should be irrelevant
within unitary evolution, claiming equal weights is just
assuming your conclusion.
I think, rather, that you should show how the argument I have
made depends on amplitudes when it clearly does not. It
depends merely on the proportion of zero outcomes in each
sequence. And that does not depend on the amplitudes.
Bruce
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