On 9/4/2020 7:02 PM, Bruce Kellett wrote:
On Sat, Sep 5, 2020 at 11:29 AM 'Brent Meeker' via Everything List
<everything-list@googlegroups.com
<mailto:everything-list@googlegroups.com>> wrote:
On 9/4/2020 4:00 PM, Bruce Kellett wrote:
On Sat, Sep 5, 2020 at 5:37 AM 'Brent Meeker' via Everything List
<everything-list@googlegroups.com
<mailto:everything-list@googlegroups.com>> wrote:
On 9/4/2020 4:43 AM, Bruce Kellett wrote:
On Fri, Sep 4, 2020 at 9:32 PM smitra <smi...@zonnet.nl
<mailto:smi...@zonnet.nl>> wrote:
Even if the MWI is false and the wavefunction collapses
to produce only
one of the possible outcomes with a probability given by
the Born rule,
you'll still get all possibilities realized in a generic
infinite
universe, whether it's spatially infinite or a universe
that exists for
an infinite long time.
The only way to find out what exists beyond the realm
we've explored s
to do experiments. No philosophical reasoning about the
interpretation
of probabilities can ever settle whether or not the
universe is so large
or will exists for such a long time that another copy of
me exists.
That's why these discussions are not so useful as an
argument of whether
the MWI is correct or not.
I think something along those lines was Sean Carroll's
answer to the points David Albert raised. Unfortunately, it
doesn't wash!
Applying the Born rule to the repeated measurement scenario
tells you that the probability of the extreme branches is
low; whereas, the idea that all possible outcomes occur on
every trial trivially implies that the probability of the
extreme cases is exactly one. The contradiction couldn't be
more stark, and waffling about infinite universes
isn't going to change that -- the theory gives two, mutually
contradictory, results.
But the probability of /observing/ extreme cases isn't 1 for
a given observer.
And the probability isn't 1/2^N for a given observer either. The
observer observes what he observes. Probability is relevant for
predictions, not post hoc observations.
We are talking about the predictions of the theory, not the
experiences of individual observers. I think Sean tried this
evasive tactic as well, and Albert rightly pointed out that that
just makes everything idexical, and ultimately makes science
impossible.
And it is not just the extreme branches that have low
probability. Given the repeated measurement scenario we have been
talking about, there are N repetitions of the experiment, giving
2^N distinct binary sequences of results. Applying the Born rule
to each possible sequence shows that it has probability 1/2^N.
But the theory isn't about the probability of a specific sequence,
it's about the probability of |up> vs |down> in the sequence
without regard for order. So there will, if the theory is
correct, be many more sequences with a frequency of |up> near some
theoretically computed proportion |a|^2 than sequences not near
this proportion.
The theory is about the probabilitiies of observations. The
observation in question here is a sequence of |up> / |down> results,
given that the probability for each individual outcome is 0.5. If the
theory cannot give a probability for the sequence,
It can. But QM only predicts the p=0.5. To have a prediction for a
specific sequence HHTTHHHTTHTHTH... you need extra assumptions about
indenpendence. And given those assumptions your theory will be
contradicted with near certainty. Which is why I say the test of QM is
whether p=0.5 is consistent with the observed sequence in the sense of
predicting the relative frequency of H and T, not in the sense of
predicting HHTTHHHTTHTHTH...
then multiply the probabilities for each particular result in your
sequence of measurements. The number of sequences with
particular proportions of up or down results is irrelevant for this
calculation.
Again, you are just attempting to divert attention from the obvious
result that the Born rule calculation gives a different probability
than expected when every outcome occurs for each measurement. In the
Everett case, every possible sequence necessarily occurs. This does
not happen in the genuine stochastic case, where only one (random)
sequence is produced.
In the Everett theory a measurement of spin up for a particle prepared
in spin x results in two outcomes...only one is observed. If that is
enough to dismiss Everett then all the this discussion of probability
and the Born rule is irrelevant.
Brent
Bruce
Brent
But if every result obtains on every trial, the probability of
each sequence is exactly one. In other words, Everett is
incompatible with the Born rule. You can abandon the Born rule if
you like, or abandon the Everettian idea of every outcome
occurring on every trial, but you can't have both.
The twisting and turning we are seeing by participants on this
list is not going to alter this basic observation.
Bruce
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