On 9/5/2020 4:59 PM, Bruce Kellett wrote:
On Sun, Sep 6, 2020 at 4:11 AM 'Brent Meeker' via Everything List
<everything-list@googlegroups.com
<mailto:everything-list@googlegroups.com>> wrote:
On 9/4/2020 11:27 PM, Bruce Kellett wrote:
No, listen carefully. Everett predicts that such a sequence will
certainly occur for any N. In other words, the probability of the
occurrence of such a sequence is one. Whereas the Born rule, as
we both now seem to agree, predicts that the probability for the
occurrence of such a sequence is 1/2^N. It is the fact that
Everett and the Born rule predict different probabilities for the
same sequence that is the point -- not that either predicts the
impossibility of such a sequence. It is the predicted
probabilities that differ, not the sequences.
And if you have a theory that predicts two different values for
some result, then your theory is inconsistent. Everett and the
Born rule are inconsistent because they predict different
probabilities for this sequence of N |up>s in N trials (or any
other particular sequence, for that matter. Even though that
latter point seems to have confused you!)
But you are not using Everett's theory. You're strawmanning Evertt.
It is ultimately a waste of time to argue over exactly what Everett
(or any other figure in the history of physics) actually said or
thought. That can be the realm of historians of science, but it is not
really relevant for the working physicist. What the working physicist
is (or should be) concerned with, is the basic ideas; regardless of
how the historical figure might have worked with them.
So you can think that I am strawmanning Everett -- I actually
disagree, but I don't really care. The important point that I am
taking from Everett is that the Schrodinger equation is the whole of
quantum physics (Carroll's idea). If the wave function of the SE does
not collapse (and there is no collapse in the Schrodinger equation),
then every possible component of any superposition certainly exists,
and continues to exist. This means that when you consider the
superposition relevant to a measurement interaction, all possible
outcomes of the measurement exist (in separate branches of the
universal wave function).
You're saying that since Everett says some sequence occurs he is
predicting/*it*/ with probability 1. But that's only predicting
that /*it*/ occurs in evolution of the wave function.
Sure. I think that is what I just said -- the branch corresponding to
any possible outcome exists in the universal wave function. And, ipso
facto, by linearity, there is an observer on that branch who sees that
outcome.
It's not a prediction of the QM probability that is being tested.
And it's not following thru on Everett's interpretation that
connects the theory to observation. It's imposing your idea of
how it connects to observation; essentially cutting off Everett's
interpretation part way thru.
I disagree. The existence of observers who see sequences of results
far from the relative frequencies predicted by the Born rule is an
unambiguous consequence of Everett's approach -- nothing is being cut
off, or left out.
Everett's theory is deterministic so it's not relevant to
criticize it for "predicting probability 1" when it predicts all
the results.
I am not criticizing it for "predicting probability one" -- I see that
as a necessary consequence of the theory, since it certainly predicts
that every outcome obtains on some branch. I am criticizing the theory
for also claiming that the Born rule probabilities obtain. The Born
rule predicts low probability for certain sequences, whereas Everett
predicts that such sequences necessarily occur. In other words, the
charge is one of inconsistency -- I am not objecting to the fact that
the theory postulates that all outcomes occur in every interaction. I
doubt that that is true, but that is Everett's theory, not mine.
I agree with you that you can't get a probability out of a
deterministic theory unless you put in some additional
postulate...like ignorance or coarse graining...and that's exactly
what Everttian's do. They say that the branches are an ensemble
and you have some probability of being the observer in one of the
ensemble...an ignorance based probability measured by either
branch counting or weighting of branches.
Self-locating uncertainty is not resolved by either branch counting or
by weighting branches. You, yourself, have pointed to the fact that in
the 2^N binary sequences in the repeated two-outcome experiment peak
around the centre, corresponding to p = 0.5. If you implement
self-locating uncertainty in the abstract as the operation of taking a
random history from this set (assuming sampling from a uniform
distribution over the set), then you are more likely to end up in a
history towards the peak of the distribution rather than in a history
far out in one of the tails. If this is what one means by
self-locating uncertainty, then this has nothing to do with either
branch counting, or with differential weighting of branches. As an
interesting aside, it is relatively easy to see that there is no way
in this picture for the self-locating uncertainty to favour any
probability other that p = 0.5 -- the set of possible histories is
independent of the branch amplitudes (weights) so there is no way the
Born rule can get any purchase, and branch weights are strictly
irrelevant.
In other words, for the interpretation to get off the ground at all,
one has to deviate considerably from the "purity of the Schrodinger
equation". Increasing the number of branches on any interaction
according to the desired Born weights simply contradicts the
Schrodinger equation, and adding ad hoc weights according to the Born
rule and treating these as probabilities also throws the basic
assumption that every possible outcome occurs on every interaction
under the bus. (In practice, Everettians simply ignore this fact, and
treat the Born weights as the full story. It is not surprising that
one has to do this, because there is essentially no other way to avoid
the glaring inconsistency at the heart of the theory.) It is a bit
rich, therefore, for you to criticize me for "departing from the
original spirit of Everett."
I think this is a kind of cheat, since it is not simply a
consequence of Schroedinger's equation. On the other hand,
Gleason's theorem is a consequence. So once you cheat enough to
introduce the probability concept, getting to Born's rule is just
a matter of making up a story you like.
Exactly. It depends on how much you are prepared to fool yourself into
thinking that the MWI makes sense.
So my view is that once you've developed decoherence theory and
you've shown that the reduced density matrix is diagonalized, you
might as well then bite-the-bullet and postulate that the theory
is probabilistic. Then the math (Gleason's theorem) forces the
interpretation that those diagonals are the probabilities of
results. Then "everything happens" is just a story attempting to
back-fill a picture of how you got there based on ignorance
(self-locating uncertainty). There are some people who can't
abide probabilistic theories and will invent fantastic worlds in
order to have a deterministic ensemble which then must be reduced
by ignorance to agree with observation. They then feel they've
made great progress because they think their theory is deterministic.
So why do you defend Carroll and Everett? Even
self-locating uncertainty is an essentially probabilistic idea.
I don't defend them. I criticize your argument against them because I
think it is unconvincing for the reasons I have given; essentially
because you cut off the MWI interpretation before the step in which it
extracts probabilistic statements by using self-locating uncertainty in
the ensemble of worlds.
Brent
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