Is Born's rule satisfied in MWI?

[Alan Grayson]

Correct me if I'm mistaken, but as far as I know the wf has never been observed; only the observations of the system it represents. This being the case, in a large number of trials. Born's rulle will be satisfied regardless of which interpretation an observer affirms; either the MWI with no collapse of the wf, or Copenhagen with collapse of the wf. That is, since we can only observe the statistical results of an experiment from a this-world perspective, and we see that Born's rule is satisfied, so I don't see how it can be argued that the rule fails to be satisfied if the MWI is assumed. I think the same can be said about the other worlds assumed by the MWI, namely, that IF we could measure their results, the rule would likewise be satisfied.AG

[Brent Meeker]

If there's no collapse then every possible sequence of results is observed in some world and the relative counts of UP v. DOWN in the ensemble of worlds will have a binomial distribution.  So for a large numbers of trials those worlds in which UPs and DOWNs are roughly equal will predominate, regardless of what the Born rule says.  So in order that the Born rule be satisfied for values other than 50/50 there must be some kind of selective weight that enhances the number of sequences close to the Born rule instead of every possible sequence being of equal weight.  But then that is inconsistent with both values occuring on every trial.

Brent

On 10/12/2025 6:56 PM, Alan Grayson wrote:

Correct me if I'm mistaken, but as far as I know the wf has never been observed; only the observations of the system it represents. This being the case, in a large number of trials. Born's rulle will be satisfied regardless of which interpretation an observer affirms; either the MWI with no collapse of the wf, or Copenhagen with collapse of the wf. That is, since we can only observe the statistical results of an experiment from a this-world perspective, and we see that Born's rule is satisfied, so I don't see how it can be argued that the rule fails to be satisfied if the MWI is assumed. I think the same can be said about the other worlds assumed by the MWI, namely, that IF we could measure their results, the rule would likewise be satisfied.AG --
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[Alan Grayson]

On Sunday, October 12, 2025 at 10:37:32 PM UTC-6 Brent Meeker wrote:

If there's no collapse then every possible sequence of results is observed in some world and the relative counts of UP v. DOWN in the ensemble of worlds will have a binomial distribution.  So for a large numbers of trials those worlds in which UPs and DOWNs are roughly equal will predominate, regardless of what the Born rule says.  So in order that the Born rule be satisfied for values other than 50/50 there must be some kind of selective weight that enhances the number of sequences close to the Born rule instead of every possible sequence being of equal weight.  But then that is inconsistent with both values occuring on every trial.

Brent

Why does Born's rule depend on collapse of wf? AG 

[Brent Meeker]

On 10/12/2025 10:18 PM, Alan Grayson wrote:

On Sunday, October 12, 2025 at 10:37:32 PM UTC-6 Brent Meeker wrote:

If there's no collapse then every possible sequence of results is observed in some world and the relative counts of UP v. DOWN in the ensemble of worlds will have a binomial distribution.  So for a large numbers of trials those worlds in which UPs and DOWNs are roughly equal will predominate, regardless of what the Born rule says.  So in order that the Born rule be satisfied for values other than 50/50 there must be some kind of selective weight that enhances the number of sequences close to the Born rule instead of every possible sequence being of equal weight.  But then that is inconsistent with both values occuring on every trial.

Brent

Why does Born's rule depend on collapse of wf? AG 

Where did I say it did?

Brent

On 10/12/2025 6:56 PM, Alan Grayson wrote:

Correct me if I'm mistaken, but as far as I know the wf has never been observed; only the observations of the system it represents. This being the case, in a large number of trials. Born's rulle will be satisfied regardless of which interpretation an observer affirms; either the MWI with no collapse of the wf, or Copenhagen with collapse of the wf. That is, since we can only observe the statistical results of an experiment from a this-world perspective, and we see that Born's rule is satisfied, so I don't see how it can be argued that the rule fails to be satisfied if the MWI is assumed. I think the same can be said about the other worlds assumed by the MWI, namely, that IF we could measure their results, the rule would likewise be satisfied.AG --

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[Alan Grayson]

On Sunday, October 12, 2025 at 11:50:58 PM UTC-6 Brent Meeker wrote:

On 10/12/2025 10:18 PM, Alan Grayson wrote:

On Sunday, October 12, 2025 at 10:37:32 PM UTC-6 Brent Meeker wrote:

If there's no collapse then every possible sequence of results is observed in some world and the relative counts of UP v. DOWN in the ensemble of worlds will have a binomial distribution.  So for a large numbers of trials those worlds in which UPs and DOWNs are roughly equal will predominate, regardless of what the Born rule says.  So in order that the Born rule be satisfied for values other than 50/50 there must be some kind of selective weight that enhances the number of sequences close to the Born rule instead of every possible sequence being of equal weight.  But then that is inconsistent with both values occuring on every trial.

Brent

Why does Born's rule depend on collapse of wf? AG 

Where did I say it did?

Brent

The greatest mathematicians tried to prove Euclid's 5th postulate from the other four, and failed; and the greatest physicists have tried to dervive Born's rule from the postulates of QM, and failed;, except for Brent Meeker in the latter case. You claimed it in the negative, by claiming that without collapse, Born's rule would fail in some world of the MWI. An assertion is just that, an assertion. Can you prove it using mathematics? AG