On 9/4/2020 11:27 PM, Bruce Kellett wrote:
On Sat, Sep 5, 2020 at 3:52 PM 'Brent Meeker' via Everything List
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<mailto:everything-list@googlegroups.com>> wrote:
On 9/4/2020 10:18 PM, Bruce Kellett wrote:
On Sat, Sep 5, 2020 at 2:42 PM 'Brent Meeker' via Everything List
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<mailto:everything-list@googlegroups.com>> wrote:
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:
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.
Sure. And independence of the sequential observations is clearly
implied by the set up.
And given those assumptions your theory will be contradicted
with near certainty.
Why?
The probability of getting any given entry in the sequence is 1/2,
so the probability of getting the whole sequence right is 1/2^N .
I thought I had said that quite clearly. And that that is true for any
one of the possible 2^N different sequences.
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...
I am not attempting to predict a particular sequence.
That's what you seemed to reply when I said QM was only predicting
the relative frequency of H within the sequence. If you now agree
with that, then you will also agree that there will many sequences
with a relative frequency of 0.5 for H and given any epsilon the
fraction of such sequences repetitions with
0.5-epsilon<frequency(H)<0.5+epsilon goes 1 as N->oo. Which is
what we mean by confirming the QM prediction of 0.5.
You are off on the wrong track. I am not disagreeing with this. It is
just that this is not what I am talking about. In the single world,
stochastic case, it is, as Albert said, true that as N goes to
infinity, all sequences converge in probability to the relative
frequency of 0.5. But that is not my point.
All that I have said is that the probability of any such sequence
in N independent trials is 1/2^N. And that is simple probability
theory, which cannot be denied.
Which is what you have said above, and I agree.
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.
I have no idea what you are talking about! Nothing like that was
ever suggested. Everett predicts that in such a measurement, both
outcomes obtain -- in separate branches.
As I understand your argument you're saying Everett is falsified
because, no matter what N is, it predicts a branch HHHHHHHHHH...H
which...What? Is wrong? Doesn't occur? Is inconsistent with the
Born rule (it isn't)? Is not observed?
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.
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. 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.
Everett's theory is deterministic so it's not relevant to criticize it
for "predicting probability 1" when it predicts all the results. 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. 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.
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.
Brent
If you just say it predicts something which is not observed; then
my point is that it always predicts outcomes that are not observed
unless P=1.
Whether the sequence is observed or not was never the point.
Although, in Everett, there is always one observer of the sequence of
all |up>s. This may occur with the Born rule, but not inevitably. The
probabilities differ, which was the actual point.
Brent
But the probability of this is one. Repeat N times. N time one is
still just one.
I did not say that very well. I mean one multiplied by itself N times,
or 1^N = 1.
There is nothing more to it than that. I think you are being
desperate in your attempts to play 'advocatus diaboli'. The point
is that the Born rule is inconsistent with Everett.
Bruce
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