On 2/17/2020 4:09 PM, Bruce Kellett wrote:
On Tue, Feb 18, 2020 at 9:46 AM 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
On 2/17/2020 2:11 AM, Bruce Kellett wrote:
On Mon, Feb 17, 2020 at 6:04 PM 'Brent Meeker' via Everything
List <[email protected]
<mailto:[email protected]>> wrote:
On 2/16/2020 9:48 PM, Bruce Kellett wrote:
On Mon, Feb 17, 2020 at 4:13 PM 'Brent Meeker' via
Everything List <[email protected]
<mailto:[email protected]>> wrote:
But exactly the same reasoning applies for any given
true value of p. There will be different estimates by
different experimenters and they can't all be right.
Each will infer that any proportion other than the one
he observed will have zero measure in the limit N->oo.
Exactly right. That is what my example of spin measurements
on an ensemble of equally prepared spin states comes into
play. If all 2^N bit strings are realized for one
orientation of the S-G magnet, then exactly the same 2^N bit
strings are realized for every other orientation.
?? Suppose the ensemble is equally prepared in spin-up. What
does it mean to say all 2^N bit strings are realized for the
S-G oriented left/right? We may expect they will be for any
number of trials >>N. But certainly not for the S-G
oriented up/down.
I think we are beginning to argue at cross-purposes, and I may
not have understood you correctly. Let me try to restate the
position clearly, and see if you can agree.
Take a spin-half state, and prepare a linear combination in the
x-basis:
|psi> = (alpha*|x-spin up> + beta*|x-spin down>),
where we assume that neither alpha nor beta is equal to zero. We
can now measure this state in the x-direction and assume Everett,
so that every result is obtained in a separate branch on every
trial. Coding these results as zero and one, a run of N
experiments will give 2^N binary strings of results, consisting
of the set of all 2^N binary strings of length N. Now rotate the
S-G magnet from the x-direction by, say, 10 degrees. Your results
are again the set of all binary strings of length N. Similarly
for any other angle (except those for which alpha or beta rotates
to zero). Since the set of results is the same in all cases, even
though rotation of the S-G magnet is equivalent to changing alpha
and beta in the superposition, the individual sets of results
must be independent of alpha and beta. However, the Born rule
states that the probabilities depend on |alpha|^2 and |beta|^.
But we have seen that the many-worlds data are actually
independent of alpha and beta. The Born rule for probabilities is
thus disconfirmed in this Everettian case.
That is the crux of what I am trying to get across -- Everettian
QM is disconfirmed by experiment, since experiments show results
that depend on the coefficients alpha and beta, in accordance
with the Born Rule. There are other points that I have been
making, but let's get this straight first.
Yes, I agree with that
Thanks, that's progress at least.
It's another way of expressing my objection that while alpha=0.5
produces a split into two worlds, alpha= 0.499 produces a split
into a thousand worlds.
You are harking back to the branch counting idea. I agree that that is
a natural way to think of outcomes having different weights -- by
being associated with different numbers of branches. The problem, of
course, is that this is not compatible with linear evolution according
to the Schrodinger equation. Since the selling point of Everett was
supposed to be "The SWE and nothing else!", anything along these lines
is contrary to the hype.
But proponents of MWI like Sean Carroll and Bruno, essentially
assume there are already (infinitely?) many branches which, prior
to the measurement, are identical at the macroscopic level, but
which get projected (split) onto orthogonal subspaces by a
measurement.
I know that Bruno talks in these terms, but I may have missed
something in Carroll's book because I don't see that idea coming to
the fore there.
It's implicit in the diagram you posted from his book.
However, something similar has been suggested by other Everettians --
think of David Deutsch -- but since it departs even further from the
original Everettian ideal, I don't think the idea has become very popular.
I have been looking again at Sean's account of the origin of the Born
rule in his new book. He gives an argument against branch counting as
the basis for probability which I think is very weak, bordering on the
imbecilic. David Wallace gives essentially the same argument in his
book on the Emergent Multiverse. Sean's account goes like this:
"Let's first dispatch the wrong idea of branch counting before turning
to a strategy that actually works. Consider a single electron whose
vertical spin has been measured by an apparatus, so that decoherence
and branching has occurred. ... Let's imagine that the amplitudes for
spin-up and spin-down aren't equal, but rather we have an unbalanced
state |Psi>, with unequal amplitudes for the two directions.
|Psi> = sqrt(1/3)|spin-up> + sqrt (2/3)spin-down>.
Since the Born rule says the probability equals the amplitude squared,
we should have a 1/3 probability of seeing spin-up and a 2/3
probability of seeing spin-down.
"Imagine that we didn't know about the Born rule, and were tempted to
assign probabilities by simple branch counting. Think about the point
of view of the observers on the two branches. From their perspective
(1p view, Ed.), those amplitudes are just invisible numbers
multiplying their branch in the wave function of the universe. Why
should they have anything to do with probabilities? (Good question,
Ed.) Both observers are equally real, and they don't even know which
branch they're on until they look. Wouldn't it be more rational, or at
least more democratic, to assign them equal credences?
"The obvious problem with that is that we're allowed to keep on
measuring things. Imagine that we agreed ahead of time that if we
measured spin-up, we would stop there, but if we measured spin-down,
an automatic mechanism would quickly measure another spin. This second
spins is in a state of spin-right, which we know can be written as a
superposition of spin-up and spin-down. Once we've measured it (only
on the branch where the first spin was down), we have three branches:
one where the first spin was up, one where we got down and then up,
and one where we got down twice in a row. The rule of 'assign equal
probabilities to each branch' would tell us to assign a probability of
1/3 to each of these possibilities.
"That's silly. If we followed that rule, the probability of the
original spin-up branch would suddenly change when we did a
measurement on the spin-down branch, going from 1/2 to 1/3. ....."
(pp.142-4)
That argument is about as silly as me saying that I don't know the
colour of my car today because I might have it re-sprayed tomorrow!
So I don't think Sean is into branch counting. His actual argument is
little more than a decision to put the Born rule in by hand,
Right. Bruno however independently hypothesizes a big number of
branches as computational threads in his Universal Dovetailer...however,
he apparently can't get the Born rule except in the 1 and 0 cases.
since it is clear that linear evolution cannot give results that are
sensitive to the coefficients (amplitudes). It is very difficult to
make sense of his idea of branch 'weights' or 'thicknesses' when these
do not change the actual nature of a branch, and are not visible to
the 1p view from within the branch.
From within a branch there is never anything visible except sequences
of results. You can make up God's eye view (I don't call it 3p since 3p
is a possible view) hypotheses in which the sequence is created by some
deterministic process, like a random number generator, which
experimenters will never be able to infer within the life of the
universe; and then say it's not a probability. But I think that is not
a sufficiently instrumentalist view of what "probability" means. I
think of probability in science as like energy, it takes lots of
different forms: relative frequency, propensity, measure,... It's
essential characteristic is that its a way to model
uncertainty...whether there is some underlying certainty or not.
Brent
Bruce
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