Measurements will always produce integer ratios as estimates of
probabilities. If the estimate is sufficiently close to the predicted
value it is considered consistent with the Born rule. We can never
measure exactly real number values.
Brent
On 10/20/2025 12:17 AM, Liz R wrote:
If we assume that there are distinct universes which branch, then the
Born rule isn't going to be satisfied (at least, not without some sort
of contrived epicycles) in any situation where the probabilities
aren't in some integer ratio, e.g. if they're irrational. If on the
other hand we assume that there is a continuum of identical universes
that is partitioned by a measurement (as David Deutsch suggests in
"The Fabric of Reality") then the partitioning can be as finely
divided as you like. However, continua are possibly problematic in
actual physical systems, like infinities, that is to say, not
realistic (because they effectively involve dividing by (uncountable?)
infinity). The idea that spacetime can't be infinitely warped - that
singularities are unphysical - is related to the idea that continua
can't exist. I assume a theory of quantum gravity would not allow either.
In the absence of continua the Born rule can only be satisfied in a
multiverse if all measurements split the universes into some integer
ratio. This seems rather arbitrary - a measurement with a 1% chance of
result X and 99% of result Y produces 100 branches (99
indistinguishable from each other), while a measurement with a 50-50
chance produces 2.
A multiverse has philosophical appeal - the string landscape answers
the question "why these laws of physics?" while the quantum multiverse
answers the question "why this history?" However as far as I know
there is no strong scientific (testable, refutable, etc) evidence for
either.
On Monday, 13 October 2025 at 14:56:05 UTC+13 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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