Re: Probability in Everettian QM

[Bruce Kellett]

On Sun, Sep 6, 2020 at 4:11 AM 'Brent Meeker' via Everything List <
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 

Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/5/2020 4:59 PM, Bruce Kellett wrote:
On Sun, Sep 6, 2020 at 4:11 AM 'Brent Meeker' via Everything List 
> 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 

Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/5/2020 2:28 AM, Bruno Marchal wrote:


On 3 Sep 2020, at 16:17, John Clark > wrote:


I don't understand Albert's position or the distinction he is trying 
to make. He says that If the world is deterministic and given his 
knowledge of the macro state of the world right now he thinks there 
is a 75% chance the Yankees will win the World Series this year. If 
things are deterministic then the Yankees will either win or they 
will not, but for practical reasons he knows he has limited knowledge 
of the micro state of the world so he can't be certain (or at least 
he shouldn't be) thus he needs to devise a number between zero and 
one to express his degree of confidence that his prediction express 
is a fundamental truth.  As time goes on as he gains more knowledge 
he will need to change the value of that number, and if he is a 
professional gambler and makes many bets of that nature and if he 
updates that number according to the rules laid out by Thomas Bayes 
then he will maximize his profits over the long term.So if you say 
there is a 75% chance the Yankees will win it tells me nothing 
objectively true about the Yankees it just tells me something about 
your state of mind.


Hugh Everett would say pretty much the same thing because he also 
believes we live in a deterministic world. Originally he may have 
only a vague idea of which branch of the multiverse is being observed 
and so he thinks there's a 50% chance, but as time goes on and he 
gains more information he still can't narrow it down to one 
particular branch but there are a great many branches that he can 
rule out and so by using the exact same Bayesian statistical rules 
that Albert used he now says the Yankees have a 75% chance of winning 
the World Series this year. But again If the world is deterministic 
then that number says nothing intrinsically true about the Yankees, 
it just says something about the state of mind of the speaker who 
made the utterance.


The analogy does not work, in Everett, like in the 
WM-self-duplication, we are in different histories at the same time, 
as long as we cannot distinguish them. If two identical brain/computer 
are run in two different rooms, there is an objective probability on 
the possible subjective future self-locating outcome.


Is there?  Can it be p=0.501 and q=0.499 ?  I think you are 
helping yourself to probabilities by implicitly assuming a measure.


Brent

Here the 3p determinism ensures the 1p-indeterminism. It is not a 
bayesian type of uncertainty (and Everett is confusing when he called 
it “subjective probabilities” where he meant more something like 
“objective first-person indeterminacy”.  Mechanism + 3p determinism 
entails 1p indeterminism.
(I have not yet look at the video, but I can guess the content from 
the posts).


Bruno





John K Clark

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Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/5/2020 2:46 AM, Bruno Marchal wrote:


On 4 Sep 2020, at 00:55, Bruce Kellett > wrote:


On Fri, Sep 4, 2020 at 8:01 AM 'Brent Meeker' via Everything List 
> wrote:


Sure.  But Albert's argument is that in a single, probabilistic
world that implements Born's rule, the number of scientist who
find something contrary to Born's rule goes to zero as the number
of repetitions increases.  But in the multiverse there are always
contrary worlds and, while their fraction decreases, their number
increases with repetitions.


That is really the essential difference between Everettian notions of 
probability and standard probabilistic theory/practice. In the 
Everettian repeated experiment case, disconfirming cases occur with 
probability one, so it is strictly incoherent to claim (as 
Everettians, such as Sean Carroll, do) that these "monster" results 
can be ignored because they have low probability. The only thing that 
that can mean is that you are justified in ignoring them because they 
have low frequency: but that is a different definition of probability 
-- a frequentist notion that all reject.


I know more people rejecting the Bayesian definition than the 
frequentist one. Graham (and Preskill, Selesnick, …) make the 
frequency approach making sense by defining (in the limit of course) a 
frequency operator, and associating an observable to it. This makes 
sense with mechanism, where the probabilities are defined on some 
limit on the number of step of the universal dovetailer, due to the 
fact that this number of the UD steps is not available to the first 
person pov.


It's a confusion to talk about "the Bayesian defintion" vs "the 
frequentist definition".  Anything satisfying Kologorov's axioms is a 
probability measure.  It's a concept, like energy or wealth, that is 
useful because it applies to different things and you can transform 
among them.  You can make a calculation based on symmetry (e.g. 
P(die->::) = 1/6) and then test it using frequency and then apply it 
using decision theory.


Brent




At best, what they might mean is that if you take all outcomes as 
equally likely, then the probability that you will get a low 
frequency outcome by chance in a random selection from the uniform 
distribution over all possibilities, is low. But that introduces yet 
another source of probability. It might be what is necessarily 
entailed in a definition of probability in terms of self-locating 
uncertainty, but it still involves one in the absurdity of claiming 
that things that necessarily happen have low probability. We cannot 
consistently claim in one breath that the probability is one, and in 
another breath, that  probability is "low”.


But there are no reason to have a relative probability one. It is one 
only "after the facts”, with classical with self-duplication, and 
quantum Mechanically with Born rules, which are unique by Gleason theorem.


Descrpitive set theory justifies the existence of a measure of 
probability for the first person views, and its uniqueness is 
justified by the completeness theorem of Solovay (plausibly), so, as 
long as this is not experimentally refuted, or as long as someone find 
a discrepancy between what mechanism predicts and the facts, Mechanism 
remains the simplest explanation for quanta and qualia.


The problem of Sean Carroll is that he seems not aware of the very 
strong constraints put on self-referential correctness, and which get 
a mathematical definition when the digital Mechanist hypothesis (or 
some weakening of it) is in play.


Bruno





Bruce


Brent

On 9/3/2020 12:02 PM, Quentin Anciaux wrote:

Hi,
as there will be persons in self duplicate experiment who'll see
WWW...WW .

But most should converge on 50%.

Quentin



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Re: Probability in Everettian QM

[Tomas Pales]

On Sunday, September 6, 2020 at 12:39:24 AM UTC+2 Brent wrote:

>
>
> On 9/5/2020 3:31 PM, Tomas Pales wrote:
>
>
>
> On Friday, September 4, 2020 at 8:03:55 PM UTC+2 Brent wrote:
>
>> If there are an infinite number then frequency is ill defined and you 
>> have to introduce some measure...which is essentially the same as just 
>> postulating a probability.  This is something like Carroll's solution which 
>> is to give "weights" to branches.
>>
>
> Don't we need to postulate a measure to calculate the (frequentist) 
> probabilities of classical coin toss outcomes too? I mean, if we assume an 
> unlimited (infinite) repetition of a fair coin toss then the probabilities 
> of heads and tails are no longer 0.5 but become undefined despite the fact 
> that the coin is fair (so its properties don't favor either side). Similar 
> problem like calculating the proportion of even integers out of all 
> integers - the proportion is not defined without choice of a particular 
> measure. So it seems that we can't avoid using a particular probability 
> measure also in classical physics.
>
> The probabilities in QM are obviously defined, as expressed by the Born 
> rule or the Gleason theorem. Which means (if I understand correctly) that 
> if MWI is right then the number of branches arising at a decoherence event 
> is either finite, or it is infinite but the structure of our quantum 
> multiverse also has a particular measure that is expressed by Born and 
> Gleason or by Carroll's weights of branches. The reason why our quantum 
> multiverse has this particular measure may be that we happen to live in 
> such a multiverse and other multiverses may have other measures.
>
>
> If the other universe has the physics of quantum mechanics then the only 
> consistent way of assigning probabilities to observation is Born's rule.  
> That's what Gleason proved.
>

Ok, that reduces options for other multiverses.

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Re: Probability in Everettian QM

[John Clark]

On Sat, Sep 5, 2020 at 12:34 PM Philip Thrift  wrote:

>>If Everett is right then "John K Clark" can see both, but "I" can not.
>> John K Clark
>>
>
> *> This is how physics has become worse than flat-earth theory.*
>

How so?

 John K Clark

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Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/5/2020 3:05 AM, Bruno Marchal wrote:


On 4 Sep 2020, at 14:24, John Clark > wrote:


On Thu, Sep 3, 2020 at 7:59 PM Bruce Kellett > wrote:


> /It has nothing to do with whether the world is deterministic or
not: all that is involved is that there is some objective chance
of this particular result/


If things are deterministic then there's no such thing as objective 
chance, and probability would just be a measure of our degree of 
ignorance of hidden causes.


What would be an hidden cause in the case of the self-duplication?


Whatever resolves the "self-locating uncertainty".  It seems to me this 
concept is sneaking ignorance based probability in to avoid the 
deterministic contradiction that I see both Moscow and Washtington.


Brent








> /the chance that the Yankees will win is independent of what we
happen to think about it./


If Everettis right then there's a 100% chance the Yankees will win 
and a 100% chance the Yankees will lose because neither eventuality 
violates the laws of physics.


You cannot have a 100% probability for A, and for B, when A and B are 
incompatible events (like "feeling to be in W", and “feeling to be in 
M”, or like “seeing the spin up” and seeing the spin down.


There is no problem once we distinguish the 3P and 1P notions, which 
is also the base of the understanding of the mind-body problem.


Bruno






John K Clark

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Re: Probability in Everettian QM

[Tomas Pales]

On Friday, September 4, 2020 at 8:03:55 PM UTC+2 Brent wrote:

> If there are an infinite number then frequency is ill defined and you have 
> to introduce some measure...which is essentially the same as just 
> postulating a probability.  This is something like Carroll's solution which 
> is to give "weights" to branches.
>

Don't we need to postulate a measure to calculate the (frequentist) 
probabilities of classical coin toss outcomes too? I mean, if we assume an 
unlimited (infinite) repetition of a fair coin toss then the probabilities 
of heads and tails are no longer 0.5 but become undefined despite the fact 
that the coin is fair (so its properties don't favor either side). Similar 
problem like calculating the proportion of even integers out of all 
integers - the proportion is not defined without choice of a particular 
measure. So it seems that we can't avoid using a particular probability 
measure also in classical physics.

The probabilities in QM are obviously defined, as expressed by the Born 
rule or the Gleason theorem. Which means (if I understand correctly) that 
if MWI is right then the number of branches arising at a decoherence event 
is either finite, or it is infinite but the structure of our quantum 
multiverse also has a particular measure that is expressed by Born and 
Gleason or by Carroll's weights of branches. The reason why our quantum 
multiverse has this particular measure may be that we happen to live in 
such a multiverse and other multiverses may have other measures.

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Re: Probability in Everettian QM

[Tomas Pales]

On Saturday, September 5, 2020 at 8:11:57 PM UTC+2 Brent wrote:

> 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.
>

They are trying to give an answer why a particular possible outcome is 
observed while others just give a shrug.

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Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/5/2020 3:31 PM, Tomas Pales wrote:



On Friday, September 4, 2020 at 8:03:55 PM UTC+2 Brent wrote:

If there are an infinite number then frequency is ill defined and
you have to introduce some measure...which is essentially the same
as just postulating a probability.  This is something like
Carroll's solution which is to give "weights" to branches.


Don't we need to postulate a measure to calculate the (frequentist) 
probabilities of classical coin toss outcomes too? I mean, if we 
assume an unlimited (infinite) repetition of a fair coin toss then the 
probabilities of heads and tails are no longer 0.5 but become 
undefined despite the fact that the coin is fair (so its properties 
don't favor either side). Similar problem like calculating the 
proportion of even integers out of all integers - the proportion is 
not defined without choice of a particular measure. So it seems that 
we can't avoid using a particular probability measure also in 
classical physics.


The probabilities in QM are obviously defined, as expressed by the 
Born rule or the Gleason theorem. Which means (if I understand 
correctly) that if MWI is right then the number of branches arising at 
a decoherence event is either finite, or it is infinite but the 
structure of our quantum multiverse also has a particular measure that 
is expressed by Born and Gleason or by Carroll's weights of branches. 
The reason why our quantum multiverse has this particular measure may 
be that we happen to live in such a multiverse and other multiverses 
may have other measures.


If the other universe has the physics of quantum mechanics then the only 
consistent way of assigning probabilities to observation is Born's 
rule.  That's what Gleason proved.


Brent

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Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/4/2020 11:27 PM, Bruce Kellett wrote:
On Sat, Sep 5, 2020 at 3:52 PM 'Brent Meeker' via Everything List 
> 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
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 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-epsilonoo.  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 HH...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 

Re: Probability in Everettian QM

[Philip Thrift]

>
>
> If Everett is right then "John K Clark" can see both, but "I" can not.
>
> John K Clark
>


This is how physics has become worse than flat-earth theory.

@philipthrift
 

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Re: Probability in Everettian QM

[Bruno Marchal]

> On 3 Sep 2020, at 16:17, John Clark  wrote:
> 
> I don't understand Albert's position or the distinction he is trying to make. 
> He says that If the world is deterministic and given his knowledge of the 
> macro state of the world right now he thinks there is a 75% chance the 
> Yankees will win the World Series this year. If things are deterministic then 
> the Yankees will either win or they will not, but for practical reasons he 
> knows he has limited knowledge of the micro state of the world so he can't be 
> certain (or at least he shouldn't be) thus he needs to devise a number 
> between zero and one to express his degree of confidence that his prediction 
> express is a fundamental truth.  As time goes on as he gains more knowledge 
> he will need to change the value of that number, and if he is a professional 
> gambler and makes many bets of that nature and if he updates that number 
> according to the rules laid out by Thomas Bayes then he will maximize his 
> profits over the long term. So if you say there is a 75% chance the Yankees 
> will win it tells me nothing objectively true about the Yankees it just tells 
> me something about your state of mind. 
> 
> Hugh Everett would say pretty much the same thing because he also believes we 
> live in a deterministic world. Originally he may have only a vague idea of 
> which branch of the multiverse is being observed and so he thinks there's a 
> 50% chance, but as time goes on and he gains more information he still can't 
> narrow it down to one particular branch but there are a great many branches 
> that he can rule out and so by using the exact same Bayesian statistical 
> rules that Albert used he now says the Yankees have a 75% chance of winning 
> the World Series this year. But again If the world is deterministic then that 
> number says nothing intrinsically true about the Yankees, it just says 
> something about the state of mind of the speaker who made the utterance.

The analogy does not work, in Everett, like in the WM-self-duplication, we are 
in different histories at the same time, as long as we cannot distinguish them. 
If two identical brain/computer are run in two different rooms, there is an 
objective probability on the possible subjective future self-locating outcome. 
Here the 3p determinism ensures the 1p-indeterminism. It is not a bayesian type 
of uncertainty (and Everett is confusing when he called it “subjective 
probabilities” where he meant more something like “objective first-person 
indeterminacy”.  Mechanism + 3p determinism entails 1p indeterminism.
(I have not yet look at the video, but I can guess the content from the posts).

Bruno



> 
> John K Clark
> 
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 01:00, Bruce Kellett  wrote:
> 
> On Sat, Sep 5, 2020 at 5:37 AM 'Brent Meeker' via Everything List 
> 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 > > 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.

Exactly.


> 
> We are talking about the predictions of the theory, not the experiences of 
> individual observers.


We are talking about the prediction of the theory, about 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,

He is right on this.



> and ultimately makes science impossible.

On the contrary, it reduces everything to the theory of machine indexical 
self-reference. Sean is not aware of the  mathematical theory of self-reference 
(G and G*).




> 
> 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 if every result obtains on every trial, the 
> probability of each sequence is exactly one.

But as you said yourself just above: probability is relevant for predictions, 
not post hoc observations.



> 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.

You can derive both from arithmetic, once you distinguish the first and third 
person notions.


> 
> The twisting and turning we are seeing by participants on this list is not 
> going to alter this basic observation.

The universal Turing machine knows that this twisting is just a consequence of 
its inability to know that []p and ([]p & p) have to put different logics on 
the believable and the knowable, the observable, etc.

Bruno



> 
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> 
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 08:27, Bruce Kellett  wrote:
> 
> On Sat, Sep 5, 2020 at 3:52 PM 'Brent Meeker' via Everything List 
> 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 < 
>> 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 
>>> > 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-epsilonoo.  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.

So add “relative” in all situation, as we are always concerned with relative 
probability, and personal outcomes.


> 
>  
>> 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 HH...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.

But the question is not on the probability of that occurence, but on the 
relative probability that I will find myself in this or that sequence. 



> Whereas the Born rule, as 

Re: Probability in Everettian QM

[Bruce Kellett]

On Sat, Sep 5, 2020 at 3:52 PM 'Brent Meeker' via Everything List <
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 <
> 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>
>> 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-epsilonoo.
> 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 HH...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  

Re: QM gets personal

[Philip Thrift]

Jim Baggott responded to Sabine Hossenfelder on Twitter (- they interact 
frequently there):


"I didn’t cover superdeterminism because I had to be selective, and my 
judgement was based in part on interpretations that have gained some 
traction or attracted attention. I omitted Cramer’s transactional 
interpretation for the same reason. But, had I expressed some opinions 
about superdeterminism,* I doubt you would have been pleased*."

So this whole thing about writing books to inform the public on so-called 
interpretations of QM seems to be a sham: Not really honest and open 
presentations.

Not worth reading.


@philipthrift


On Friday, September 4, 2020 at 9:04:19 PM UTC-5 Brent wrote:

> I can't see being "personally offended" by failure to mention a theory 
> (unless maybe I invented it); but I would like to hear more exposition on 
> Cramer's Transactional Interpretation.  It does introduce some extra 
> structure (possibility space); but then I think MWI fails in it's attempt 
> to be pure Schoedinger equation.  The TI is like the Copenhagen 
> interpretation, except it gives an answer to the question when/where does 
> the measurement happen, which I think is compatible with Zurek's 
> decoherence and quantum Darwinism.
>
> Brent
>
> On 9/4/2020 3:59 PM, Lawrence Crowell wrote:
>
> If you want reality you must consider the wave function as nonlocal, or 
> perform measurements correspond to nonlocality. If you want to show reality 
> is lost then you have to localize measurements, such as the Wigner friend 
> argument and localized observers of observers. QM has no favor one way or 
> the other, and the needle pointing between 0 = locality and 1 = reality 
> only fits with those as we observers impose on nature. 
>
> LC
>
> On Friday, September 4, 2020 at 1:33:57 AM UTC-5 cloud...@gmail.com wrote:
>
>>
>> "I am also personally offended that Baggott gives short shrift to 
>> superdeterminism. In this approach, quantum mechanics is emergent from a 
>> deterministic hidden-variables model which acknowledges that everything in 
>> the universe is connected with everything else. He either mistakenly or 
>> accidentally leaves the reader with the impression that these have been 
>> ruled out for good, which is most definitely not the case. I cannot really 
>> blame Baggott for this, though, because this omission is widespread in the 
>> scientific literature. I have complained about this on the pages of this 
>> magazine, and will leave it at that."
>>
>> Sabine Hossenfelder, September 3, 2020
>> http://nautil.us/blog/your-guide-to-the-many-meanings-of-quantum-mechanics
>>
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>
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Re: Probability in Everettian QM

[John Clark]

On Sat, Sep 5, 2020 at 6:05 AM Bruno Marchal  wrote:

>> If things are deterministic then there's no such thing as objective
>> chance, and probability would just be a measure of our degree of
>> ignorance of hidden causes.
>
>
> *> What would be an hidden cause in the case of the self-duplication? *
>

I don't know because I don't know what self-duplication effect you want a
causal explanation for.

>> If Everett is right then there's a 100% chance the Yankees will win and
>> a 100% chance the Yankees will lose because neither eventuality violates
>> the laws of physics.
>
>
> *> You cannot have a 100% probability for A, and for B, when A and B are
> incompatible events*
>

Sure you can. If Everett Is right then there's a 100% chance that John K
Clark saw the Yankees win and there's a 100% chance that John K Clark saw
the Yankees lose, and there is a 0% chance that John K Clark found a valid
logical mathematical proof that 2+2 = 5. If everything has a probability of
either zero or 100% then probability is obviously of little use when
discussing the entire multiverse, although it can be quite useful in
individual branches of it. As I've said over and over again, Everettian
worlds don't have positive Real Number probabilities associated with them,
they have Complex Number amplitudes.

*> like "feeling to be in W", and “feeling to be in M”, or like “seeing the
> spin up” and seeing the spin down.*
>

If Everett is right then "John K Clark" can see both, but "I" can not.


> *> we distinguish the 3P and 1P* [...]
>

Peepee, it's always Peepee!

John K Clark

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Re: Probability in Everettian QM

[John Clark]

On Sat, Sep 5, 2020 at 5:28 AM Bruno Marchal  wrote:

> Hugh Everett would say pretty much the same thing because he also
> believes we live in a deterministic world. Originally he may have only a
> vague idea of which branch of the multiverse is being observed and so he
> thinks there's a 50% chance, but as time goes on and he gains more
> information he still can't narrow it down to one particular branch but
> there are a great many branches that he can rule out and so by using the
> exact same Bayesian statistical rules that Albert used he now says the
> Yankees have a 75% chance of winning the World Series this year. But again
> If the world is deterministic then that number says nothing intrinsically
> true about the Yankees, it just says something about the state of mind of
> the speaker who made the utterance.
>
> *> The analogy does not work, in Everett, like in the WM-self-duplication,
> we are in different histories at the same time, as long as we cannot
> distinguish them.*
>

If the multiple copies of John K Clark in different worlds can not
distinguish the tiny historical differences between those worlds then it
would be meaningless to insist that they are different people. If later one
of them notices something about his environment that the other does not
then they would no longer be identical and then and only then would it make
sense to say there are two different   John K Clark's.

> *If two identical brain/computer are run in two different rooms,*
>

If the two rooms are different and the brain/computer has sense organs then
the brain/computer will detect those differences and so the brain/computers
will no longer be identical.

> there is an objective probability on the possible subjective future
> self-locating outcome.
>

I don't know what the hell to make of a "objective probability of a
possible subjectivity". And if things are deterministic, as they are in
Everett's Multiverse, then nothing is objectively probabilistic, thus
probability must just be a measure of an observer's ignorance. What else
could it be?

>
> * > Here the 3p* [...]
>

 Bruno, can you write a post about anything without getting into Peepee?

John K Clark

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Re: Probability in Everettian QM

[Bruno Marchal]

> On 4 Sep 2020, at 13:32, smitra  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.

But we need some philosophical assumption about what is the “universe”. If we 
bet on mechanism, we have to bet on elementary arithmetic, but then we get the 
theorem that there is an infinity of computations going through our states, and 
that physics must be recovered through a measure on the relative computational 
histories. And this works, without eliminating the qualia (consciousness), 
which is not the case in physicist metaphysics.

The burden of the proof is in the hand of the materialist (believer in 
ontological physical universe), and we already know that he has to abandon 
“indexical digital Mechanism”.

Bruno



> 
> Saibal
> 
> On 04-09-2020 00:01, 'Brent Meeker' via Everything List wrote:
>> Sure.  But Albert's argument is that in a single, probabilistic world
>> that implements Born's rule, the number of scientist who find
>> something contrary to Born's rule goes to zero as the number of
>> repetitions increases.  But in the multiverse there are always
>> contrary worlds and, while their fraction decreases, their number
>> increases with repetitions.
>> Brent
>> On 9/3/2020 12:02 PM, Quentin Anciaux wrote:
>>> Hi,
>>> as there will be persons in self duplicate experiment who'll see
>>> WWW...WW [1].
>>> But most should converge on 50%.
>>> Quentin
>>> Le jeu. 3 sept. 2020 à 20:48, 'Brent Meeker' via Everything List
>>>  a écrit :
>>> Albert makes an interesting argument against Everettian QM, i.e.
>>> that repeated experiments will not produce statistics that converge
>>> to the Born rule, i.e. there will necessarily (not just
>>> probabilistically) be experimenters in worlds supporting every
>>> possible probability value.
>>> Brent
>>> On 9/3/2020 10:59 AM, Philip Thrift wrote:
>>> This sort of way of approaching physics is no different really from
>>> theological debates about some esoteric Christian doctrine.
>>> The last of Carroll's The Biggest Ideas in the Universe series is
>>> actually interesting at the end:
>>> https://www.youtube.com/watch?v=ZqphkIO7yt4
>>> He has nowhere to go asn has no idea what to do.
>>> @philipthrift
>>> On Thursday, September 3, 2020 at 1:02:21 AM UTC-5 Brent wrote:
>>> An interesting discussion of Everettian QM in two parts.  The first
>>> part
>>> https://www.youtube.com/watch?v=FyvgBe9VV70
>>> is just David Albert and Sean Carroll.  It's quite reminiscent of
>>> JKC and Bruno, using the same thought experiments (but more civil).
>>> Brent
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 4 Sep 2020, at 08:54, Bruce Kellett  wrote:
> 
> On Fri, Sep 4, 2020 at 4:40 PM Quentin Anciaux  > wrote:
> Le ven. 4 sept. 2020 à 00:01, 'Brent Meeker' via Everything List 
> mailto:everything-list@googlegroups.com>> 
> a écrit :
> Sure.  But Albert's argument is that in a single, probabilistic world that 
> implements Born's rule, the number of scientist who find something contrary 
> to Born's rule goes to zero as the number of repetitions increases.  But in 
> the multiverse there are always contrary worlds and, while their fraction 
> decreases, their number increases with repetitions.
> 
> That's an interpretation... because I think there is no increasing or 
> decreasing of numbers of worlds there are an infinity of them always, 
> similar / identical "world" differentiate but there is no increase or 
> decrease, there is no meaningfull way of "counting"... The frequency is all 
> there is.
> 
> 
> That does not detract from the fact that in Everett, the low probability 
> worlds always occur with probability one.

After the facts. That is true for any probability theory.



> In other words, the theory is intrinsically self-contradictory -- incoherent.

Only by confusing []p and ([]p & p), or a third person description and a first 
person prescription. It is actually an error equivalent to Penrose error when 
arguing that Gödel’s incompleteness refute Mechanism. Penrose compare his 
knowledge ([]p & p) with the machine’s believability ([]p). But the machine 
refute this by showing that this distinction is unavoidable from its personal 
point of view. 

The incoherence comes only from the physicalist identity thesis between mind 
and brain, which makes no sense once we postulate digital mechanism.

Bruno



> 
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 4 Sep 2020, at 14:24, John Clark  wrote:
> 
> On Thu, Sep 3, 2020 at 7:59 PM Bruce Kellett  > wrote:
> 
> > It has nothing to do with whether the world is deterministic or not: all 
> > that is involved is that there is some objective chance of this particular 
> > result
> 
> If things are deterministic then there's no such thing as objective chance, 
> and probability would just be a measure of our degree of ignorance of hidden 
> causes.

What would be an hidden cause in the case of the self-duplication? 




> 
> >  the chance that the Yankees will win is independent of what we happen to 
> > think about it.
> 
> If Everett is right then there's a 100% chance the Yankees will win and a 
> 100% chance the Yankees will lose because neither eventuality violates the 
> laws of physics.

You cannot have a 100% probability for A, and for B, when A and B are 
incompatible events (like "feeling to be in W", and “feeling to be in M”, or 
like “seeing the spin up” and seeing the spin down.

There is no problem once we distinguish the 3P and 1P notions, which is also 
the base of the understanding of the mind-body problem.

Bruno




> 
> John K Clark
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 04:02, Bruce Kellett  wrote:
> 
> On Sat, Sep 5, 2020 at 11:29 AM 'Brent Meeker' via Everything List 
> 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 
>> > wrote:
>> On 9/4/2020 4:43 AM, Bruce Kellett wrote:
>>> On Fri, Sep 4, 2020 at 9:32 PM smitra >> > 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, 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.

In the eye of God, not in the eye of the individual making the experience. He 
cannot get both 00010... and 10100…

You talk like if in the WM-dup experience, you can bet on both W and M, which 
is a case of not remembering that the question is about what we will feel, not 
about in which branch some other people can find us. You can find me in both W 
and M, but from what I feel, in any branch, I feel to be only in that branch. 

Bruno



> This does not happen in the genuine stochastic case, where only one (random) 
> sequence is produced.
> 
> 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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Re: Probability in Everettian QM

[Bruno Marchal]

> On 4 Sep 2020, at 15:36, John Clark  wrote:
> 
> On Fri, Sep 4, 2020 at 7:43 AM Bruce Kellett  > wrote:
> 
> > 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,
> 
> If it does it violate the laws of physics then the probability of an 
> Everettian world existing is always exactly one, which means that probability 
> is not a useful concept when discussing the existence or nonexistence of such 
> a world, although probability can be useful for other things, like self 
> localization.

Nice! You make my point. I hope you can keep this about self-localisation in 
the classical mechanist self-multiplication. The situation are isomorphic, and 
entanglement becomes partial collective self-multiplication. The math justifies 
that this gives a quantum logic and quantum probability calculus. Some work 
remains to be done so that we can apply Gleason theorem in the phenomenological 
reality of he machine multiplied by at least aleph_zero in the arithmetical 
reality.

Bruno



> 
> John K Clark
> 
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 01:10, Bruce Kellett  wrote:
> 
> On Sat, Sep 5, 2020 at 9:03 AM Lawrence Crowell 
> mailto:goldenfieldquaterni...@gmail.com>> 
> wrote:
> On Friday, September 4, 2020 at 6:21:49 AM UTC-5 Bruce wrote:
> On Fri, Sep 4, 2020 at 7:49 PM Lawrence Crowell > 
> wrote:
> On Friday, September 4, 2020 at 1:54:34 AM UTC-5 Bruce wrote:
> On Fri, Sep 4, 2020 at 4:40 PM Quentin Anciaux > wrote:
> Le ven. 4 sept. 2020 à 00:01, 'Brent Meeker' via Everything List 
> > a écrit :
> Sure.  But Albert's argument is that in a single, probabilistic world that 
> implements Born's rule, the number of scientist who find something contrary 
> to Born's rule goes to zero as the number of repetitions increases.  But in 
> the multiverse there are always contrary worlds and, while their fraction 
> decreases, their number increases with repetitions.
> 
> That's an interpretation... because I think there is no increasing or 
> decreasing of numbers of worlds there are an infinity of them always, 
> similar / identical "world" differentiate but there is no increase or 
> decrease, there is no meaningfull way of "counting"... The frequency is all 
> there is.
> 
> 
> That does not detract from the fact that in Everett, the low probability 
> worlds always occur with probability one. In other words, the theory is 
> intrinsically self-contradictory -- incoherent.
> 
> Bruce
> 
> I am not so sure this is self-contradictory, but rather that with the 
> renormalization of probability in each branched world there is a sort of 
> catastrophe where for some oscillating probability amplitude there is one 
> point where P = 0 or P = 1 and the branching has a discontinuity. Hence there 
> is this interesting nonlocal property where an eigenbranch can occur 
> continuously along the time parametrization or evolution of a wave function, 
> but this is not continuous.  For extremely high frequency quantum states this 
> has a sort of quantum Zeno phenomenology to it. At these break-points there 
> is only one possible outcome and for a set of events corresponding to these 
> there is no consistent Bayesian interpretation of them. In that sense there 
> is something funny going on.
> 
> 
> You do talk a lot of nonsense, don't you, Lawrence.
> 
> Bruce
> 
> What is nonsense? All I am saying is when the probability for an amplitude is 
> 0 or 1 there is no branching. So in general a quantum amplitude has a 
> discrete set of branching evolutes separated by no branching points. What is 
> wrong?
> 
> 
> Your comments are not relevant to the discussion, which was about probability 
> in a branching scenario. If you predict that a certain branch will certainly 
> exist, then you are assigning a probability equal to one to the possibility 
> of this branch.

The probability is one for the existence of the branch does not entail that I 
will see, or feel to be in, that branch. This is again a case of obliterating  
the 1P / 3P distinction.



> The trouble is that the Born rule assigns a probability of 1/2^N to the same 
> branch. Hence the contradiction.

The Born rule assign 1/2^N before the experience, and 1 after (and 0 for all 
other branches). But with Everett, that does not make the other branches 
getting non existence, just non accessibility.


> 
> If your theory gives two ways to predict the probability of a particular 
> outcome, and these two calculations give different results, then your theory 
> is inconsistent.

It is the 1p-3p confusion which leads to an inconsistency.

Bruno



> 
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Re: Probability in Everettian QM

[smitra]

On 04-09-2020 13:43, Bruce Kellett wrote:

On Fri, Sep 4, 2020 at 9:32 PM smitra  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.

Bruce


Reading also the other replies in this thread, it seems to me that you 
are actually disagreeing with the MWI on the issue of how this 
interpretation should work. But then you have a different version of the 
MWI that you can then falsify. In the MWI one ends up copies of an 
observer who observer the different possible outcomes, but with the 
density given by the Born rule, such that in a classical ensemble with 
those densities you also would have those same Born rule probabilities.


Saibal

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Re: Probability in Everettian QM

[Bruno Marchal]

> On 4 Sep 2020, at 00:55, Bruce Kellett  wrote:
> 
> On Fri, Sep 4, 2020 at 8:01 AM 'Brent Meeker' via Everything List 
> mailto:everything-list@googlegroups.com>> 
> wrote:
> Sure.  But Albert's argument is that in a single, probabilistic world that 
> implements Born's rule, the number of scientist who find something contrary 
> to Born's rule goes to zero as the number of repetitions increases.  But in 
> the multiverse there are always contrary worlds and, while their fraction 
> decreases, their number increases with repetitions.
> 
> That is really the essential difference between Everettian notions of 
> probability and standard probabilistic theory/practice. In the Everettian 
> repeated experiment case, disconfirming cases occur with probability one, so 
> it is strictly incoherent to claim (as Everettians, such as Sean Carroll, do) 
> that these "monster" results can be ignored because they have low 
> probability. The only thing that that can mean is that you are justified in 
> ignoring them because they have low frequency: but that is a different 
> definition of probability -- a frequentist notion that all reject.

I know more people rejecting the Bayesian definition than the frequentist one. 
Graham (and Preskill, Selesnick, …) make the frequency approach making sense by 
defining (in the limit of course) a frequency operator, and associating an 
observable to it. This makes sense with mechanism, where the probabilities are 
defined on some limit on the number of step of the universal dovetailer, due to 
the fact that this number of the UD steps is not available to the first person 
pov.




> At best, what they might mean is that if you take all outcomes as equally 
> likely, then the probability that you will get a low frequency outcome by 
> chance in a random selection from the uniform distribution over all 
> possibilities, is low. But that introduces yet another source of probability. 
> It might be what is necessarily entailed in a definition of probability in 
> terms of self-locating uncertainty, but it still involves one in the 
> absurdity of claiming that things that necessarily happen have low 
> probability. We cannot consistently claim in one breath that the probability 
> is one, and in another breath, that  probability is "low”.

But there are no reason to have a relative probability one. It is one only 
"after the facts”, with classical with self-duplication, and quantum 
Mechanically with Born rules, which are unique by Gleason theorem.

Descrpitive set theory justifies the existence of a measure of probability for 
the first person views, and its uniqueness is justified by the completeness 
theorem of Solovay (plausibly), so, as long as this is not experimentally 
refuted, or as long as someone find a discrepancy between what mechanism 
predicts and the facts, Mechanism remains the simplest explanation for quanta 
and qualia.

The problem of Sean Carroll is that he seems not aware of the very strong 
constraints put on self-referential correctness, and which get a mathematical 
definition when the digital Mechanist hypothesis (or some weakening of it) is 
in play.

Bruno



> 
> Bruce
> 
> 
> Brent 
> 
> On 9/3/2020 12:02 PM, Quentin Anciaux wrote:
>> Hi,
>> as there will be persons in self duplicate experiment who'll see WWW...WW 
>> .
>> 
>> But most should converge on 50%.
>> 
>> Quentin
> 
> 
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 4 Sep 2020, at 13:43, Bruce Kellett  wrote:
> 
> On Fri, Sep 4, 2020 at 9:32 PM smitra  > 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.

Not true for the relative probability, as the average witnesses (of the most 
numerous histories) knows.


> 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.

There is no contradiction if you add the words “relative” and “first person” to 
“probability” in this case.

Bruno



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Re: Probability in Everettian QM

[Bruce Kellett]

On Sun, Sep 6, 2020 at 10:25 AM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

> On 9/5/2020 4:59 PM, Bruce Kellett wrote:
>
>
> 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.
>


I think that the only way this comment makes sense is if the number of
worlds multiplies in proportion to the Born probabilities on each
interaction. That is an even bigger departure from Everett than anything
you might have accused me of doing.

Let us revisit this problem using David Albert's example of Captain Kirk's
transporter malfunction, so that when Kirk is beamed down to the surface of
a planet, two "Kirks" arrive, one dressed in blue and the other in green.
(One could make the same argument in terms of Bruno's WM duplication
experiment.)

If, after transportation, the Kirks re-ascend to the Enterprise and each
copy again transports down: being duplicated in the same way. After N
iterations, there are 2^N Kirks on the surface of the planet. If each
carries a notebook in which he has recorded the sequence of colours of his
outfits, all possible binary sequences of B and G will be recorded in some
book or the other. A simple application of the binomial distribution shows
that the notebook records peak around sequences showing approximately equal
numbers of blue and green outfits. This is experimental verification of the
probability of p(blue) = 0.5 = p(green).

Now let us try to vary the probabilities, say to p(blue) = 0.9 and p(green)
= 0.1. How do we do this?

OK, we transport Kirk and, with probability p = 0.9, we colour one of the
uniforms blue. The other must, therefore, be coloured green. But then we
simply have two Kirks on the surface of the planet, one in a blue uniform
and one in a green uniform -- exactly as we had before. It is easy to see
that, no matter how we imagine that we have changed the relative
probabilities of uniform colours, we must always end up with just one blue
uniform and one green uniform. Our attempt to change the probabilities has
failed.

There is a way out, however. If, instead of simply duplicating the Kirks on
transportation, the transporter manufactures 10 copies on the surface of
the planet. Then we can suppose that 9 of these have blue uniforms, and the
remaining Kirk is dressed in green. Iterating this procedure, we end up
with 10^N Kirks on the surface of the planet, the vast majority of whom are
dressed in blue. We have, thereby, changed the probability of a blue
uniform for Kirk to 0.9 -- in the majority of cases.

The trouble with this is that such a scenario cannot be reproduced with the
Schrodinger equation. If the universal wave function is represented by a
vector in Hilbert space, for a two-outcome experiment the Hilbert space is
two-dimensional, and we cannot fit 10 independent basis vectors into such a
two-dimensional space. So the multiple branches for each outcome solution
is not available in quantum mechanics. We might be able to dream up a
theory in which this multiplication of branches would work, but that is not
Everett, and it is not quantum mechanics as we know it. (Carroll and Zurek
attempt to get around this by expanding the dimensionality of the operative
Hilbert space by "borrowing" degrees of freedom from environmental
decoherence. I doubt that this is actually convincing, or even possible.
Whatever, it is a hopelessly ad hoc violation of the underlying dynamics.)

I can, therefore, see no way in which the Born rule can be made compatible
with strictly deterministic Everettian Schrodinger evolution.

Note that (pace Bruno) this conclusion does not depend on any 1p/3p
confusion. It depends only on the details of the assumed dynamics.

Bruce

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Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/5/2020 6:07 PM, Bruce Kellett wrote:
On Sun, Sep 6, 2020 at 10:25 AM 'Brent Meeker' via Everything List 
> wrote:


On 9/5/2020 4:59 PM, Bruce Kellett wrote:


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.



I think that the only way this comment makes sense is if the number of 
worlds multiplies in proportion to the Born probabilities on each 
interaction.


Or if you postulate some kind of weighting as Carroll does.

That is an even bigger departure from Everett than anything you might 
have accused me of doing.


I didn't mean Everett himself.  He didn't even propose multiple worlds; 
he talked about the relative state of the observer (meaning relative to 
the observed value).  I was saying you were not attacking the argument 
actually put forward by Everttians, i.e. MWI advocates.




Let us revisit this problem using David Albert's example of Captain 
Kirk's transporter malfunction, so that when Kirk is beamed down to 
the surface of a planet, two "Kirks" arrive, one dressed in blue and 
the other in green. (One could make the same argument in terms of 
Bruno's WM duplication experiment.)


If, after transportation, the Kirks re-ascend to the Enterprise and 
each copy again transports down: being duplicated in the same way. 
After N iterations, there are 2^N Kirks on the surface of the planet. 
If each carries a notebook in which he has recorded the sequence of 
colours of his outfits, all possible binary sequences of B and G will 
be recorded in some book or the other. A simple application of the 
binomial distribution shows that the notebook records peak around 
sequences showing approximately equal numbers of blue and green 
outfits. This is experimental verification of the probability of 
p(blue) = 0.5 = p(green).


Now let us try to vary the probabilities, say to p(blue) = 0.9 and 
p(green) = 0.1. How do we do this?


OK, we transport Kirk and, with probability p = 0.9, we colour one of 
the uniforms blue. The other must, therefore, be coloured green. But 
then we simply have two Kirks on the surface of the planet, one in a 
blue uniform and one in a green uniform -- exactly as we had before. 
It is easy to see that, no matter how we imagine that we have changed 
the relative probabilities of uniform colours, we must always end up 
with just one blue uniform and one green uniform. Our attempt to 
change the probabilities has failed.


There is a way out, however. If, instead of simply duplicating the 
Kirks on transportation, the transporter manufactures 10 copies on the 
surface of the planet. Then we can suppose that 9 of these have blue 
uniforms, and the remaining Kirk is dressed in green. Iterating this 
procedure, we end up with 10^N Kirks on the surface of the planet, the 
vast majority of whom are dressed in blue. We have, thereby, changed 
the probability of a blue uniform for Kirk to 0.9 -- in the majority 
of cases.


The trouble with this is that such a scenario cannot be reproduced 
with the Schrodinger equation.


I agree.  That's why MWI advocates must resort to "weights", which are 
just amplitudes.  Or add some structure like an infinite or very large 
ensemble of already existing worlds that just get distinguished by results.


Brent

If the universal wave function is represented by a vector in Hilbert 
space, for a two-outcome experiment the Hilbert space is 
two-dimensional, and we cannot fit 10 independent basis vectors into 
such a two-dimensional space. So the multiple branches for each 
outcome solution is not available in quantum mechanics. We might be 
able to dream up a theory in which this multiplication of branches 
would work, but that is not Everett, and it is not quantum mechanics 
as we know it. (Carroll and Zurek attempt to get around this by 
expanding the dimensionality of the operative Hilbert space by 
"borrowing" degrees of freedom from environmental decoherence. I doubt 
that this is actually convincing, or even possible. Whatever, it is a 
hopelessly ad hoc violation of the underlying dynamics.)


I can, therefore, see no way in which the Born rule can be made 
compatible with strictly deterministic Everettian Schrodinger evolution.


Note that (pace Bruno) this conclusion does not depend on any 1p/3p 
confusion. It depends only on the details of the assumed dynamics.


Bruce
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