Re: Probability in Everettian QM

[Philip Thrift]

On Saturday, September 5, 2020 at 2:21:26 PM UTC-5 johnk...@gmail.com wrote:

> 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
>


In one case (MWI): The consciousness you have now splits - again and again 
and again - and there are many, many "you-#x" consciousnesses an hour from  
now that are "you" right now. 

In the other case (FET): All the so-called measurements that people say the 
earth is not flat are an illusion, like a hologram.

MWI, FET: Equally fantastic.

@philipthrift

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Re: Probability in Everettian QM

['scerir' via Everything List]

Bruce: "The idea of a large ensemble of pre-existing worlds that just get 
distinguished by results has never been taken seriously by anyone outside of 
this list. It has never been worked through in detail, and it is doubtful if it 
even makes sense. It certainly has nothing to do with the Schrodinger equation."

Vaidman, speaking of quantum teleportation, 
https://en.wikipedia.org/wiki/Quantum_teleportation , pointed out that when Bob 
receives the message from Alice, he will know which of the four states his 
particle is in, and using this information he performs a unitary operation on 
his particle to transform it to the desired state. But (as Vaidman pointed out) 
before Bob receives the message from Alice there are four pre-existing 
equiprobable states, one of them (Bob doesn't know which one) is already the 
right one.  α | 0 ⟩ B + β | 1 ⟩ B {\displaystyle \alpha |0\rangle _{B}+\beta 
|1\rangle _{B}}

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Re: Probability in Everettian QM

[Bruce Kellett]

On Sun, Sep 6, 2020 at 6:55 PM 'scerir' via Everything List <
everything-list@googlegroups.com> wrote:

> Bruce: "The idea of a large ensemble of pre-existing worlds that just get
> distinguished by results has never been taken seriously by anyone outside
> of this list. It has never been worked through in detail, and it is
> doubtful if it even makes sense. It certainly has nothing to do with the
> Schrodinger equation."
>
> Vaidman, speaking of quantum teleportation,
> https://en.wikipedia.org/wiki/Quantum_teleportation , pointed out that
> when Bob receives the message from Alice, he will know which of the four
> states his particle is in, and using this information he performs a
> unitary operation on his particle to transform it to the desired state. But
> (as Vaidman pointed out) before Bob receives the message from Alice there
> are four pre-existing equiprobable states, one of them (Bob doesn't know
> which one) is already the right one.
>

Serafino,
 I am sorry to have to say this, but Lev Vaidman is something of an idiot
about these things. Don't take anything he says seriously, even though he
has been around for many years. This quote is irrelevant to my point. MWI
is incompatible with the Born rule. The Born rule makes sense only in
single world settings.

Bruce

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Re: Probability in Everettian QM

[John Clark]

On Sat, Sep 5, 2020 at 7:59 PM Bruce Kellett  wrote:

*> 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. *


Yes, many worlds is bare-bones Quantum Mechanics, it contains everything
that's needed and nothing more. The only reason people add additional
mathematical gunk is they personally dislike all those worlds for one
reason or another and want to get rid of them. I think Schrodinger's
Equation is hard enough to solve as it is and needlessly making it even
more complicated is not progress.

*> You're saying that since Everett says some sequence occurs he is
> predicting it with probability 1.*


Everett Is saying a world exists where 30 seconds from now all the air
molecules in the room you're in right now gather in one small corner due to
random motion and you suffocate. But all Everettian worlds are not equal,
they have different Complex Number amplitudes. The square of the absolute
value of the amplitude of such a world would be the probability of you
being in such a world and experiencing suffocation, and that positive real
number although greater than zero would be extremely small. And I do mean
extremely!

*> it is relatively easy to see that there is no way in this picture for
> the self-locating uncertainty to favour any probability other that p = 0.5*


That is just flat out untrue. If you want to know the probability that you
will be in a universe (there will be many not just one) in which you
observe the electron go left rather than right you need to take the square
of the absolute value of the amplitude of that electron and, depending on
the specific circumstances of how the experiment is set up, that might or
might not be 0.5. It can't be emphasized too much that Everettian worlds
don't have positive real number probabilities associated with them, they
have complex number amplitudes.


> > *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*
>

Yes, Everett says there will be observers who see all sorts of bazaar
astronomically
unlikely events, but the square of the absolute value of the amplitude of
such worlds is extremely small, so the probability you will observe such a
world is also extremely small.

  > *The Born rule predicts low probability for certain sequences, *


Yes.

*> Everett predicts that such sequences necessarily occur. *


Yes.

 > *the charge is one of inconsistency*


Yes that is the charge. No I don't see any inconsistency.

John K Clark

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Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 14:26, John Clark  wrote:
> 
> 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.

OK



> 
> > 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.

OK


> 
> > 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”.


I give you an example. A person is multiplied by 100 and put in 100 different, 
but identical from inside rooms. Just the number of the room differs, like in 
some hostel. You seem to agree that, as long as they stay in the room, there is 
only one person. But the copies are asked to open the room, and the person was 
asked, before the experience what is the probability that when going out of the 
room, its number is prime.

I use the usual first person non transitive identity notion, where the identity 
if preserve in experience without amnesia.

So the HM and HW person are both the H-person, despite the HM and HW person 
have become different.

(H, M, and W refers to Helsinki, Moscow, and Washington in the Helsinki——> 
{Washington, Moscow} self-duplication experience.





> 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?


The objective ignorance of a subject about which branch of the universal wave 
he belongs, in Everett.

Or the objective ignorance of all universal Turing machines about which 
computations emulate them in arithmetic.




>  
> > Here the 3p [...]
> 
>  Bruno, can you write a post about anything without getting into Peepee?


The 3p/1p distinction need it to get the theory of both quanta and qualia, and 
to understand why they are different, and how they are related.
It is also imposed by incompleteness once you define the first person by the 
definition of Theatetus (the true justified-opinion) using Gödel’s beweisbar 
predicate for true opinion. That works well, quantum and intutionistoc logic 
appears where predicted, and verified by the actual observation until now.

With Mechanism, the burden of the proof is given to the believer in some 
irreducible physical universe. He has to explain what it is, and how it select 
the computation in arithmetic (or to abandon the digital mechanist hypothesis 
in the cognitive science).

Bruno






> 
> John K Clark
> 
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> .

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Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 20:11, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 9/4/2020 11:27 PM, Bruce Kellett wrote:
>> 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 see

Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 21:08, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 9/5/2020 2:28 AM, Bruno Marchal wrote:
>> 
>>> On 3 Sep 2020, at 16:17, John Clark < 
>>> johnkcl...@gmail.com 
>>> > 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 ? 

Assuming a perfect protocol, it is 1/2. 



> I think you are helping yourself to probabilities by implicitly assuming a 
> measure.

It is not obvious, but there is a measure for the first person views, plural 
([]p & <>t) and singular ([]p & p, []p & <>t & p).
I have realised more or less recently that the measure is inherited from a 
measure on the sigma_1 set + arbitrary oracles, that is the union of all 
sigma_1(a) for a being a real (or complex number). This requires a bit of 
Descriptive Set theory. 

So, there is a measure, even a Lebesgue Measure. There is an integral, normally 
Feynman’s one, if both Mechanism, and Quantum Mechanics are correct.

It took me some time to admit that the invariance of the first person for the 
Universal-Dovetailer-steps “delays” enforces the presence of all oracular 
computations. It is a continuum, with a complicated structure determined by the 
modes of self-reference (which are 8, although there are more like 4 + 4 * 
infinity).

Bruno




> 
> 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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>>>  
>>> .
>> 
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 5 Sep 2020, at 21:16, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 9/5/2020 2:46 AM, Bruno Marchal wrote:
>> 
>>> On 4 Sep 2020, at 00:55, Bruce Kellett < 
>>> bhkellet...@gmail.com 
>>> > 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”. 

OK. I should have said the Dutch book definition. It uses Bayes theorem to 
provide a definition of probability. That probability obey Kolmogorov axioms, 
but the reverse is not necessarily the case. I am not sure. The distinction if 
more conceptual than technical perhaps.


> 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.


OK

Bruno


> 
> 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

[Bruno Marchal]

> On 5 Sep 2020, at 21:21, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 9/5/2020 3:05 AM, Bruno Marchal wrote:
>> 
>>> On 4 Sep 2020, at 14:24, John Clark < 
>>> johnkcl...@gmail.com 
>>> > 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.

But Mechanism explains why the contradiction does not occur. It explains why 
the W-machine feel to be in W and not in Moscow, and vice versa. It explains 
also why the prediction in the dairy “I will see both Moscow and Washington, 
but feel to be seeing only one of them” is verified by both copies, so that it 
leads to some probability calculus.

Bruno



> 
> Brent
> 
>> 
>> 
>> 
>> 
>>> 
>>> >  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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>>>  
>>> .
>> 
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>> .
> 
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Re: Probability in Everettian QM

[Bruno Marchal]

> On 6 Sep 2020, at 01:59, Bruce Kellett  wrote:
> 
> So why do you defend Carroll and Everett? Even self-locating uncertainty is 
> an essentially probabilistic idea.

Glad to hear that :)

Bruno

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Re: Probability in Everettian QM

[Bruno Marchal]

> On 6 Sep 2020, at 08:15, Bruce Kellett  wrote:
> 
> On Sun, Sep 6, 2020 at 3:37 PM 'Brent Meeker' via Everything List 
> mailto:everything-list@googlegroups.com>> 
> wrote:
> On 9/5/2020 6:07 PM, Bruce Kellett wrote:
>> 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.
> 
> 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). 


According to some biographer, Everett did mentioned the “many-worlds” in the 
title of his first paper, but was asked by the publisher to use something less 
shocking, and that is why he used the notion of relative state.
I was a bit disappointed by this, as “relative state” is more general a priori, 
and help to avoid taking the “world” notion to much seriously or ontologically. 



> 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.
> 
> 
> Don't you see that the argument I have made above shows that the idea of 
> adding 'weights' to the branches does not work?: you cannot consistently 
> graft the Born rule on to a model in which every possible outcome occurs on 
> every trial. The set of 2^N possible branches resulting from N repetitions of 
> the binary measurement is independent of the original amplitudes or weights.


If you define the frequency operator, like in Preskill’s course, or Selesnick 
book, or Graham in the DeWitt-Graham selected pap

Re: Probability in Everettian QM

[Lawrence Crowell]

On Sunday, September 6, 2020 at 7:06:09 AM UTC-5 johnk...@gmail.com wrote:

> On Sat, Sep 5, 2020 at 7:59 PM Bruce Kellett  wrote:
>
>
>  > *the charge is one of inconsistency*
>
>
> Yes that is the charge. No I don't see any inconsistency. 
>
> John K Clark
>

A part of what I was trying to point out earlier is that where MWI has some 
issues with the definition of probability and then by corollary issues with 
the Born rules is a tiny measure over possible sets of outcomes. I am not a 
primary exponent of MWI, just as I don't uphold any interpretation of QM, 
but I fail to see the fatal inconsistency that Bruce sees. There are issues 
with all interpretations, usually in the form of various addition 
assumptions required. The most notorious for the need of auxiliary 
assumptions if Bohm's QM. MWi requires we abandon strings of outcomes that 
are outliers in Bayesian statistics, such as a long sequence of the same 
outcomes. This was the point of my discussing the infinitesimal time 
intervals in a quantum oscillation when a probability is 0 or 1. However, 
these are measure ε and contribute little. Unless there is some singular 
point associated with these this should not be that fatal a problem. 

LC

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Re: Probability in Everettian QM

['scerir' via Everything List]

BTW I've found that quote by Vaidman.

'In the framework of the MWI, the teleportation procedure does not move the 
quantum state: the state was, in some sense, in the remote location from the 
beginning. The correlated pair, which is the necessary item for teleportation, 
incorporates all possible quantum states of the remote particle, and, in 
particular, the state which has to be teleported. The local measurement of the 
teleportation procedure splits the world in such a manner that in each of the 
worlds the state of the remote particle differs form the state by some known 
transformation. The number of such worlds is relatively small. This explains 
why the information which has to be transmitted for teleportation of a quantum 
state—the information which world we need to split into, i.e., what 
transformation has to be applied—is much smaller than the information which is 
needed for the creation of such a state. For example, for the case of a 
spin-1/2 particle there are only 4 different worlds, so in order to teleport 
the state we have to transmit just 2 bits.' – Lev Vaidman in 
https://arxiv.org/abs/quant-ph/9810089


> Il 06/09/2020 12:47 Bruce Kellett  ha scritto:
> 
> 
> On Sun, Sep 6, 2020 at 6:55 PM 'scerir' via Everything List < 
> everything-list@googlegroups.com mailto:everything-list@googlegroups.com > 
> wrote:
> 
> > > 
> > Bruce: "The idea of a large ensemble of pre-existing worlds that 
> > just get distinguished by results has never been taken seriously by anyone 
> > outside of this list. It has never been worked through in detail, and it is 
> > doubtful if it even makes sense. It certainly has nothing to do with the 
> > Schrodinger equation."
> > 
> > Vaidman, speaking of quantum teleportation, 
> > https://en.wikipedia.org/wiki/Quantum_teleportation , pointed out that when 
> > Bob receives the message from Alice, he will know which of the four states 
> > his particle is in, and using this information he performs a unitary 
> > operation on his particle to transform it to the desired state. But (as 
> > Vaidman pointed out) before Bob receives the message from Alice there are 
> > four pre-existing equiprobable states, one of them (Bob doesn't know which 
> > one) is already the right one. 
> > 
> > > 
> Serafino,
>  I am sorry to have to say this, but Lev Vaidman is something of an idiot 
> about these things. Don't take anything he says seriously, even though he has 
> been around for many years. This quote is irrelevant to my point. MWI is 
> incompatible with the Born rule. The Born rule makes sense only in single 
> world settings.
> 
> Bruce
> 
> 
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> 

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Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

On 9/6/2020 5:05 AM, John Clark wrote:
On Sat, Sep 5, 2020 at 7:59 PM Bruce Kellett > wrote:


/> 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. /


Yes, many worlds is bare-bones Quantum Mechanics, it contains 
everything that's needed and nothing more. The only reason people add 
additional mathematical gunk is they personally dislike all those 
worlds for one reason or another and want to get rid of them. I think 
Schrodinger's Equation is hard enough to solve as it is and needlessly 
making it even more complicated is not progress.


/> You're saying that since Everett says some sequence occurs he
is predicting*it* with probability 1./


Everett Is saying a world exists where 30 seconds from now all the air 
molecules in the room you're in right now gather in one small corner 
due to random motion and you suffocate. But all Everettian worlds are 
not equal, they have different Complex Number amplitudes. The square 
of the absolute value of the amplitude of such a world would be the 
probability of you being in such a world and experiencing suffocation, 
and that positive real number although greater than zero would be 
extremely small. And I do mean extremely!


/> it is relatively easy to see that there is no way in this
picture for the self-locating uncertainty to favour any
probability other that p = 0.5/


That is just flat out untrue. If you want to know the probability that 
you will be in a universe (there will be many not just one) in which 
you observe the electron go left rather than right you need to take 
the square of the absolute value of the amplitude of that electron 
and, depending on the specific circumstances of how the experiment is 
set up, that might or might not be 0.5. It can't be emphasized too 
much that Everettian worlds don't have positive real number 
probabilities associated with them, they have complex number amplitudes.


> /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/


Yes, Everett says there will be observers who see all sorts of 
bazaarastronomically unlikely events,but the square of the absolute 
value of the amplitude of such worlds is extremely small, so the 
probability you will observe such a world is also extremely small.


>/The Born rule predicts low probability for certain sequences, /


Yes.

/> Everett predicts that such sequences necessarily occur. /


Yes.

>/the charge is one of inconsistency/


Yes that is the charge. No I don't see any inconsistency.


It's because Bruce takes the Born probability as the probability that 
some sequence exists (i.e. 1) instead of the probability it is the 
observed sequence, ( |a|^2 ).


Brent

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Re: Probability in Everettian QM

['Brent Meeker' via Everything List]

Do you have a paper explaining this?

Brent

On 9/6/2020 7:24 AM, Bruno Marchal wrote:


I think you are helping yourself to probabilities by implicitly 
assuming a measure.


It is not obvious, but there is a measure for the first person views, 
plural ([]p & <>t) and singular ([]p & p, []p & <>t & p).
I have realised more or less recently that the measure is inherited 
from a measure on the sigma_1 set + arbitrary oracles, that is the 
union of all sigma_1(/a/) for /a/ being a real (or complex number). 
This requires a bit of Descriptive Set theory.


So, there is a measure, even a Lebesgue Measure. There is an integral, 
normally Feynman’s one, if both Mechanism, and Quantum Mechanics are 
correct.


It took me some time to admit that the invariance of the first person 
for the Universal-Dovetailer-steps “delays” enforces the presence of 
all oracular computations. It is a continuum, with a complicated 
structure determined by the modes of self-reference (which are 8, 
although there are more like 4 + 4 * infinity).


Bruno


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Re: Probability in Everettian QM

[Lawrence Crowell]

This is a reasonable account of teleporation.

LC

On Sunday, September 6, 2020 at 12:03:30 PM UTC-5 sce...@libero.it wrote:

> BTW I've found that quote by Vaidman.
> 'In the framework of the MWI, *the teleportation procedure does not move 
> the quantum state: the state was, in some sense, in the remote location 
> from the beginning*. The correlated pair, which is the necessary item for 
> teleportation, incorporates all possible quantum states of the remote 
> particle, and, in particular, the state which has to be teleported. The 
> local measurement of the teleportation procedure splits the world in such a 
> manner that in each of the worlds the state of the remote particle differs 
> form the state by some known transformation. The number of such worlds is 
> relatively small. This explains why the information which has to be 
> transmitted for teleportation of a quantum state—the information which 
> world we need to split into, i.e., what transformation has to be applied—is 
> much smaller than the information which is needed for the creation of such 
> a state. For example, for the case of a spin-1/2 particle there are only 4 
> different worlds, so in order to teleport the state we have to transmit 
> just 2 bits.' – Lev Vaidman in https://arxiv.org/abs/quant-ph/9810089 
>
> Il 06/09/2020 12:47 Bruce Kellett  ha scritto: 
>
>
> On Sun, Sep 6, 2020 at 6:55 PM 'scerir' via Everything List < 
> everyth...@googlegroups.com> wrote: 
>
> Bruce: "The idea of a large ensemble of pre-existing worlds that just get 
> distinguished by results has never been taken seriously by anyone outside 
> of this list. It has never been worked through in detail, and it is 
> doubtful if it even makes sense. It certainly has nothing to do with the 
> Schrodinger equation."
>
> Vaidman, speaking of quantum teleportation, 
> https://en.wikipedia.org/wiki/Quantum_teleportation , pointed out that 
> when Bob receives the message from Alice, he will know which of the four 
> states his particle is in, and using this information he performs a 
> unitary operation on his particle to transform it to the desired state. But 
> (as Vaidman pointed out) before Bob receives the message from Alice there 
> are four pre-existing equiprobable states, one of them (Bob doesn't know 
> which one) is already the right one. 
>
>
> Serafino, 
>  I am sorry to have to say this, but Lev Vaidman is something of an idiot 
> about these things. Don't take anything he says seriously, even though he 
> has been around for many years. This quote is irrelevant to my point. MWI 
> is incompatible with the Born rule. The Born rule makes sense only in 
> single world settings. 
>
> Bruce 
>
>
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>  
> .
>  
>
>
>

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Re: Probability in Everettian QM

[John Clark]

On Sun, Sep 6, 2020 at 9:34 AM Bruno Marchal  wrote:

>> I don't know what the hell to make of a "objective probability of a
>> possible subjectivity”.
>
>
> *> I give you an example. A person is multiplied by 100 and put in 100
> different, but identical from inside rooms. Just the number of the room
> differs, like in some hostel. You seem to agree that, as long as they stay
> in the room, there is only one person. But the copies are asked to open the
> room, and the person was asked, before the experience what is the
> probability that when going out of the room, its number is prime.*
>

In that thought experiment there is no objective probability because John
Clark is always in a prime numbered room or John Clark is not. So there is
only subjective probability. There is a 100% chance John Clark will walk
out, look at the number on the door and see a prime number, and a 100%
chance he will not see a prime number. And the question "What is the
probability I will see a prime number?" has no answer because in this
hypothetical the personal pronoun "I" is ambiguous.

However if you were to ask one of the individual John Clarks in one of
those rooms AFTER the duplication "What is the probability you will see a
prime number on the door when you walk out?" then that would be a
legitimate unambiguous question, and the answer would be 25% because there
are 25 prime numbers less than 100. But that probability would just be a
subjective probability because he is either in a prime numbered room or he
is not, So that probability figure must just be a measure of that John
Clark's ignorance.

John K Clark

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Re: Probability in Everettian QM

[Bruce Kellett]

On Mon, Sep 7, 2020 at 3:34 AM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

>
> It's because Bruce takes the Born probability as the probability that some
> sequence exists (i.e. 1) instead of the probability it is the observed
> sequence, ( |a|^2 ).
>


That is the source of the disagreement. There are two possible questions:
1) In the N repeats of the binary outcome experiment, what is the
probability that the sequence containing all ones will occur?; and 2) what
is the probability in this scenario that I will experience the sequence of
all ones?

If we are using the theory to calculate probabilities, the first question
is the relevant one, and the theory gives two different answers , so the
theory is inconsistent. If our concern is only about ourselves, and not
about what the theory says, then the second question is the appropriate
one. Then there is no inconsistency, because we know that we will only see
one sequence -- which one we do see can only be determined post hoc, and
that is not a probabilistic matter. The 1p/3p confusion here is all yours,
not mine. What gives you the right to maintain that the Born rule is only
about what you will experience? And not about objective probabilities?

Bruce

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Re: Probability in Everettian QM

[Stathis Papaioannou]

On Mon, 7 Sep 2020 at 08:50, Bruce Kellett  wrote:

> On Mon, Sep 7, 2020 at 3:34 AM 'Brent Meeker' via Everything List <
> everything-list@googlegroups.com> wrote:
>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> It's because Bruce takes the Born probability as the probability
>>
>> that some sequence exists (i.e. 1) instead of the probability it is
>>
>> the observed sequence, ( |a|^2 ).
>>
>
>
> That is the source of the disagreement. There are two possible questions:
> 1) In the N repeats of the binary outcome experiment, what is the
> probability that the sequence containing all ones will occur?; and 2) what
> is the probability in this scenario that I will experience the
> sequence of all ones?
>
> If we are using the theory to calculate probabilities, the first question
> is the relevant one, and the theory gives two different answers , so the
> theory is inconsistent. If our concern is only about ourselves, and not
> about what the theory says, then the second question is the appropriate
> one. Then there is no inconsistency, because we know that we will only see
> one sequence -- which one we do see can only be determined post hoc, and
> that is not a probabilistic matter. The 1p/3p confusion here is all yours,
> not mine. What gives you the right to maintain that the Born rule is only
> about what you will experience? And not about objective probabilities?
>

An observer knows (under MWI) with certainty that some version of him will
see a particular outcome, but he wants to know what the probability is that
he will see that outcome. If you think that this is not a legitimate
interest then it is more a psychological issue than a scientific one.


-- 
Stathis Papaioannou


-- 
Stathis Papaioannou

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