On 1/5/2025 2:14 PM, Jesse Mazer wrote:
On Sun, Jan 5, 2025 at 12:44 AM Bruce Kellett <[email protected]>
wrote:
On Sun, Jan 5, 2025 at 7:46 AM John Clark <[email protected]>
wrote:
*About a month ago Sean Carroll uploaded a very good video
explaining the Many Worlds theory, but it's over an hour long
so I know there's about as much chance of a dilettante such as
yourself of actually watching it is there is of you reading a
post of mine if it's longer than about 100 words. *
*
*
*The Many Worlds of Quantum Mechanics | Dr. Sean Carroll
<https://www.youtube.com/watch?v=FTmxIUz21bo&t=8s> *
I watched this video, but it is not as comprehensive as Carroll's
book "Something Deeply Hidden".
However, something came up in the question period that might
warrant a comment. Talking about the Born rule, Carroll justifies
it by saying that if you measure the spin of 1000 unpolarized
particles, you get 2^1000 different UP-DOWN sequences. However,
the vast majority of these sequences will show proportions of UP
vs DOWN close to the Born rule prediction of 50/50. In the limit,
if such a limit makes sense, the proportion of sequences that show
marked deviations from the Born Rule proportions will form a set
of measure zero, and can be ignored.
That is just the law of large numbers at work, and is all very
well if the amplitudes are such that the Born probabilities are
equal to 0.5. But it is easy to rotate your S-G magnets so that
the Born probabilities are quite different, say, 0.9-Up to
0.1-DOWN. Now take 1000 trials again. According to Everett, you
necessarily get the same 2^1000 sequences of UP-DOWN that you had
before. The law of large numbers will then tell you that the
majority of these will have approximately a 50/50 UP/DOWN split,
which is grossly in violation of the Born rule result of a 90/10
split. In other words, MWI. or Everettian QM. has a problem
reproducing the Born rule. It works in the simple case of equal
probabilities, but fails miserably once one departs substantially
from equal probabilities.
Bruce
David Z Albert mentions that if you define a measurement operator that
just tells you the *fraction* of spin-up vs. spin-down in a large
sequence of identical measurements,
then even without any collapse assumption, in the limit as #
measurements goes to infinity the wavefunction will approach an
eigenstate of this operator that matches the probability that would be
predicted by the Born rule. See his comments on p. 238 of The Cosmos
of Science at
https://books.google.com/books?id=_HgF3wfADJIC&lpg=PP1&pg=PA238#v=onepage&q&f=false
<https://books.google.com/books?id=_HgF3wfADJIC&lpg=PP1&pg=PA238#v=onepage&q&f=false>
He contemplates an example in which p=0.5 and then generalizes that
since in the limit of large number of measurements will find p~=0.5 that
this generalizes in sense that many measurements for p=h must converge
to the right value!? That's contrary to the branch counting as noted by
Bruce.
Brent
"Then, even though there will actually be no matter of fact about what
h takes the outcomes of any of those measurements to be, nonetheless,
as the number of those measurements which have already been carried
out goes to infinity, the state of the world will approach (not as a
merely probabilistic limit, but as a well-defined mathematical
epsilon-and-delta-type limit) a state in which the reports of h about
the statistical frequency of any particular outcome of those
measurements will be perfectly definite, and also perfectly in accord
with the standard quantum mechanical predictions about what the
frequency out to be."
Jesse
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