Ballentine's Ensemble Interpretation Of QM

[wuliheron]

Please don't bring politics into this, I'm sure no one is interested.
Irrelevant point. Your argument hinges on Einstein not knowing anything about the role of metaphysics in physics because he failed to find a theory that no one else has found in 100 years either. Not a particularly logical position.

That no one else has found any metaphysical solution after a hundred years supports my position. He insisted one must exist despite the evidence to the contrary and history has proven him wrong thus far. That's called "empirical evidence" if you were wondering. My family is from Missouri, the "show me" state, and you'll just have to prove there is any underlying metaphysics to quantum mechanics before I'll assume such a thing exists. As far as I'm concerned metaphysics is nothing more then a useful analytic tool and not to be confused with the territory anymore then a road map.

 

[wuliheron]

Where did you get the idea he rejected it? He didn't think it was wrong - merely incomplete. He tried to derive it from a more fundamental theory not reconcile it with relativity - it and QFT were already reconciled with that.

Split semantic hairs all you want. If you prefer, he rejected it as "incomplete".

 

[bhobba]

Split semantic hairs all you want. If you prefer, he rejected it as "incomplete".

Splitting semantics? Rejecting QM would be like rejecting Thermodynamics. Thinking QM is correct but incomplete, being a limiting case of another theory would be like thinking Thermodynamics is correct but incomplete and a limiting case of another theory - which it is. Einstein accepted the ensemble interpretation of QM - in fact he was a major supporter of it. He just thought, just like the ensembles of statistical physics, they were determined by a deeper theory. I am inclined to agree with him.

Thanks
Bill

 

[wuliheron]

Splitting semantics? Rejecting QM would be like rejecting Thermodynamics. Thinking QM is correct but incomplete, being a limiting case of another theory would be like thinking Thermodynamics is correct but incomplete and a limiting case of another theory - which it is. Einstein accepted the ensemble interpretation of QM - in fact he was a major supporter of it. He just thought, just like the ensembles of statistical physics, they were determined by a deeper theory. I am inclined to agree with him.

hairsplitting [ˈhɛəˌsplɪtɪŋ]
n
the making of petty distinctions
adj
occupied with or based on petty distinctions
hairsplitter

I don't need lessons in the English language and I don't need lessons in Einstein. My advice would be to learn to ask questions, stop trying to read between the lines of everything people write, and stop trying to lecture people. Meaning can be implied as well as explicit and only a computer is incapable of inferring meaning from context.

 

[Fredrik]

I also strongly disagree with the claim that Einstein rejected QM. It's not a matter of semantics, it's just wrong.

 

[bhobba]

I don't need lessons in the English language and I don't need lessons in Einstein. My advice would be to learn to ask questions, stop trying to read between the lines of everything people write, and stop trying to lecture people. Meaning can be implied as well as explicit and only a computer is incapable of inferring meaning from context.

OK I will ask a question. What in your view is the standard QM theory?

Thanks
Bill

 

[Ken G]

That no one else has found any metaphysical solution after a hundred years supports my position.

No it doesn't. First of all, Einstein was not looking for a "metaphysical solution," he was looking for a new theory, using metaphysics as his guide, just as he had done with relativity. I doubt the success of relativity should be viewed as a bad reason to try a similar approach again, yet apparently that is your only argument. Secondly, the fact that he did not succeed is not a logically valid argument that it was some kind of fools errand. Many physicists have failed at attempts to find something that was later found by someone else, sometimes by using the groundwork they laid even if unsuccessful on its own. Your argument is worse than just opinion- it is demonstrably bad logic.

The ultimate irony is how badly you have sidetracked this thread, apparently on the grounds that this thread is some kind of sidetrack. Threads like this work just fine in a section on quantum physics as long as they are only read and posted to by people who understand how that works.

 

[qsa]

in some earlier thread a reqular PF contributer posted a paper of his , which is sort of a new interpretation but looks very close to ensemble one.

here is what he claims in his paper. What do you think?

http://arxiv.org/PS_cache/quant-ph/p.../0509044v1.pdf

It seems that there may exist a somewhat different
interpretation of real charged fields: the one-particle Ψ-
function may describe a large (infinite?) number of particles moving along the above-mentioned trajectories. The
total charge, calculated as an integral of charge density
over the infinite 3-volume, may still equal the charge
of electron. So the individual particles may be either
electrons or positrons, but all together they may be regarded as one electron

 

[Ken G]

That link is coming up dead. But there are certainly many applications where one might imagine the electron charge is effectively spread out over its wave function when calculating an expectation value-- I'm not sure how that view is advanced by including more particles than just the one, there's not much difference between an expectation value and an ensemble value. It sounds like the particles would have to be virtual ones, so that gets into the usual issues with whether or not it is a good idea to take virtual particles literally in the interpretation.

 

[qsa]

That link is coming up dead. But there are certainly many applications where one might imagine the electron charge is effectively spread out over its wave function when calculating an expectation value-- I'm not sure how that view is advanced by including more particles than just the one, there's not much difference between an expectation value and an ensemble value. It sounds like the particles would have to be virtual ones, so that gets into the usual issues with whether or not it is a good idea to take virtual particles literally in the interpretation.

here is the right link,SEE PAGE 3



http://arxiv.org/PS_cache/quant-ph/pdf/0509/0509044v1.pdf

 

[bhobba]

here is the right link,SEE PAGE 3

Had a quick squiz. My first reaction is in suggesting an interpretation along the lines of Bohm you run into experimental problems. See:

http://arxiv.org/PS_cache/quant-ph/pdf/0206/0206196v1.pdf

Thanks
Bill

 

[juanrga]

Hi Juaringa

Yes it does help thanks.

I still think it is by far the best interpretation though and really helps in developing the theory.

Interesting new paper by Smolin where he thinks the Ensembles could actually be real:
http://arxiv.org/PS_cache/arxiv/pdf/1104/1104.2822v1.pdf

Thanks
Bill

After explaining why the ensemble 'interpretation' is not equivalent to QM {*}, I would add that I wonder how people as Smolin want to substitute, what them perceive as the weirdness in QM, by really weird «alternative formulations» that are, in essence, just another misconception of QM, to be added to the notorious misconceptions by Einstein, Everett, DeWitt, Deutsch, Dirac {**}, Hartle, Tegmark...

{*} QM is what one finds in standard textbooks as Cohen-Tannoudji.

{**} It is fair to say that in latter years (70s), Dirac recognized some of his mistakes and claimed for abandoning his previous work in R-QM and QED, asking for the search of a new relativistic quantum theory based in sound principles and consistent mathematics.

 

[Fredrik]

After explaining why the ensemble 'interpretation' is not equivalent to QM {*},
...
{*} QM is what one finds in standard textbooks as Cohen-Tannoudji.

I haven't read Cohen-Tannouji, but I doubt that it contradicts the ensemble "interpretation", which is arguably not an interpretation at all. If QM tells us how to use a state vector to calculate probabilities of possible results of experiments, then it's undeniable that the state vector can and should be thought of as a representation of the statistical properties of an ensemble of identically prepared systems. Interpretations are about what other meanings can be assigned to it, in addition to the obvious one.

Ballentine likes to point out that the assumption that a state vector represents all the properties of a single system is unjustified. That doesn't mean that what he's doing "is not equivalent to QM". QM is the set of rules that tells us how to associate probabilities with results of experiments. That assumption isn't part of those rules. So it's not a part of QM.

 

[Ken G]

I agree, I see the ensemble interpretation as the minimum interpretation of quantum mechanics, it is the interpretation you pretty much have to have to use QM at all, but you don't attribute any ontological content to the theory, you don't think there are any messages about "how the universe is", there's just how to calculate statistical outcomes for large ensembles of seemingly identically prepared systems (without even making any claims that they are truly identically prepared, just that they are prepared a certain way). Even Copenhagen allows a little ontology to creep in-- in CI you say that the wave function is useful for making a statistical prediction because it holds some statistical information about an individual system, it has something to say about what is happening for that system. The ensemble interpetation is like studying how poker hands behave without ever introducing the concept of "a card" or "shuffling". Cohen-Tannoudji is not going to refute the ensemble interpretation anywhere, but the authors might (or might not) have a little something more than that in their minds when they think about QM.

 

[bhobba]

I haven't read Cohen-Tannouji, but I doubt that it contradicts the ensemble "interpretation", which is arguably not an interpretation at all. If QM tells us how to use a state vector to calculate probabilities of possible results of experiments, then it's undeniable that the state vector can and should be thought of as a representation of the statistical properties of an ensemble of identically prepared systems. Interpretations are about what other meanings can be assigned to it, in addition to the obvious one.

I would say that as well. I have read stuff that suggests the ensemble interpretation has problems, but I have not seen a detailed explanation of any, because, as you say, basically it is not an interpretation at all. All you are really doing is giving pictorial vividness to the probabilities by ensembles. However that 'picture' does suggest possible underlying processes such as Nelson's theory and Primary State Diffusion that QM is a limiting case of. I haven't read Cohen-Tannouji but know it by reputation. Most definitely it would be a reasonable candidate as the 'standard' version of QM. But then again so would Ballentines textbook.

Ballentine likes to point out that the assumption that a state vector represents all the properties of a single system is unjustified. That doesn't mean that what he's doing "is not equivalent to QM". QM is the set of rules that tells us how to associate probabilities with results of experiments. That assumption isn't part of those rules. So it's not a part of QM.

It is only part of QM if you accept an interpretation where you believe a Quantum State has a real existence like say an electric field. Ballentine examines why that view has problems but I do not think he rules them out - nor, to the best of my knowledge, can they be ruled out by our present experimental evidence. IMHO it just seems a rather unnecessary complication.

Thanks
Bill

 

[Ken G]

I'd say the whole issue strikes to the heart of what you think an interpretation is for. Those who favor "minimal" interpretations, like the ensemble interpretation, seem to basically think that an interpretation is just something you need to apply the theory and should not be anything more-- it is almost like a "necessary evil" that comes with the theory so you can use it, but it is loaded with misconceptions and traps and should be avoided unless absolutely necessary. But those who favor more "maximal" interpretations, like MWI or deBB, tend to want the interpretation to be the "way to extract the message" from the theory-- they don't view the interpretation as a necessary evil, they view it as the point of the exercise. They might not really care about the prediction that is being made, as they are not actually using the prediction to do anything but test the theory-- it is the theory they want, and more, it is the meaning of the theory, the lesson of the theory, that they want. That can only be extracted via an interpretation.

I would place CI kind of in the middle-- it wants to find a message from QM, but the message is more like a cautionary tale about our limitations as physicists. CI users interpret QM to tell them what they get to know and what they don't get to know about the world, and the limitations they encounter caused Bohr to say things like "there is no quantum world." That stark denial of a valid ontology underlying the theory seems much closer to the ensemble interpretation-- indeed, I'd say there's not a lot of difference there, CI is just more willing to make claims about the lessons of QM.

 

[juanrga]

Effectively some people don't read basic textbooks or messages. Why bother to answer, then?

 

[Fredrik]

Effectively some people don't read basic textbooks or messages. Why bother to answer, then?

Why bother to suggest that only people who have learned QM from that specific book are allowed to tell you why you're wrong?

 

[Ken G]

Effectively some people don't read basic textbooks or messages. Why bother to answer, then?

I'm quite familiar with the Cohen-Tannoudji textbook, but don't recall it mentioning any interpretations of quantum mechanics. The parts I recall are just the mathematics of quantum mechanics, which is perfectly consistent with the ensemble interpretation. The message behind that mathematics is much harder to say, and is generally not uniquely understood.

 

[kith]

{*} QM is what one finds in standard textbooks as Cohen-Tannoudji.

As far as I remember, Cohen-Tannoudji explicitly mentions in a footnote that he uses the Copenhagen interpretation.

Independent of this: Which interpretations are feasible is decided by experiments, not by textbooks. So please provide an example where the ensemble interpretation leads to different predictions than what you consider to be standard QM and we can check the experimental evidence.

 

[Ken G]

Also, I'd like a clear statement of some fundamental difference between CI and the ensemble interpretation-- something that isn't just "tomayto-tomahto". CI is a bit happier with the concept of a "state" of a single system, but in the end it never asserts any ontology for that single system that comes from that "state"-- the "state" is just a calculational tool for statistical statements, much like the ensemble interpretation.

 

[bohm2]

Einstein accepted the ensemble interpretation of QM - in fact he was a major supporter of it. He just thought, just like the ensembles of statistical physics, they were determined by a deeper theory. I am inclined to agree with him.

I realize that this is an older thread but is it accurate to say that Einstein accepted the ensemble interpretation? I have come across this post on the Physics Stack Exchange criticizing the wiki article on the ensemble interpretation:

The Wikipedia page erroneously claims that Einstein supported the Ensemble idea. This is false, but there is a quote that makes it seem true. Einstein was referring to hidden variables here, and the reason he states it in terms of ensembles is because he believed that the wavefunction described a statistical pattern for hidden variables which is analogous to statistical mechanical distributions. These statistical distributions do not describe a single particle (at least not in a straightforward interpretation), because the particle has a hidden position deep down underneath. The averages of many position measurements require an ensemble, and these measure the wavefunction. Einstein used the term "ensemble" in the context of quantum mechanics to emphasize the probabilistic nature of the wavefunction, not the inability to describe an individual system.

Einstein also believed that the quantum mechanical description of an individual system, inasmuch as it was deterministic, was correct. It was only the probabilistic aspects of the description that required hidden variables, of course, just like classical thermodynamics. You don't need an ensemble to describe the motion of piston pushing a gas, only for the statistically random motion of individual molecules.

A true ensemble interpretation renounces the description of a physical system entirely, leaving only the description of the statistics of identical measurement. It is not what Einstein had in mind, and it is not reasonable in the majority of cases where quantum systems are in their ground state, and changing adiabatically, so that they essentially reproduce deterministic classical behavior.

What are specific arguments against the ensemble interpretation (as promoted by L. Ballentine)?
http://physics.stackexchange.com/qu...st-the-ensemble-interpretation-as-promoted-by

Moreover, I was under the impression that if one accepts the assumptions of PBR, PBR rules out Einstein's interpretation:

Can the quantum state be interpreted statistically?
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

On the reality of the quantum state
http://arxiv.org/pdf/1111.3328v3.pdf

 

[kith]

I realize that this is an older thread but is it accurate to say that Einstein accepted the ensemble interpretation?

There are two ways to arrive at the ensemble interpretation. Einstein thought that QM was missing something and is only an effective theory. He thought QM makes statistical statements about ensembles while the true states and dynamics are elements of a more fundamental theory from which QM can be derived.

The other way is to realize that all conclusions from experiments are based on ensembles, so we shouldn't expect our theories to be about single systems in the first place.

I don't think that this makes a difference in the interpretation. It's just a different motivation why you stick to it.

Moreover, I was under the impression that if one accepts the assumptions of PBR that PBR rules out Einstein's interpretation.

Einstein's main point was that QM is not complete, not that the wavefunction is not ontic at all. I think he would have been satisfied by an interpretation which is realistic about the wavefuntion as well as about some local realistic hidden variables.

 

[Ken G]

That question relates back to what I was asking above as well. What exactly is meant by an ensemble interpretation? Should we say it is the rejection of the idea that the behavior of a single particle is a scientifically determinable question, meaning that science relates to ensembles? If so, then it is a lot like CI, because both would be inherently empiricist, i.e., both would stipulate that "what is science" means "what can we measure and then make sense of." Identical measurements on similarly prepared systems is all we'll ever be able to do in science, so if we stick to an empiricist underpinning of science, we will always end up with something that looks a lot like either the CI or the ensemble approach. Or, should we say that the ensemble interpretation goes beyond empiricism, and asserts some hidden variables that we as yet have no empirical access to? Then it ends up sounding a lot like deBroglie-Bohm. So perhaps we should say that the ensemble interpretation lives at a kind of intersection of the CI and dB-B, whereby it maintains its empiricist underpinning, but also retains an agnostic attitude about whether or not the hidden deterministic variables that apply to individual particles will ever enter the empirical realm or not. If so, Einstein might not have enjoyed that agnostic attitude about his most closely held belief-- basic realism.

 

[kith]

That question relates back to what I was asking above as well. What exactly is meant by an ensemble interpretation? Should we say it is the rejection of the idea that the behavior of a single particle is a scientifically determinable question, meaning that science relates to ensembles?

I refer to "interpretation" as the relation between the formalism and the physical world. So the ensemble interpretation is simply the assertion that QM is about ensembles of physical systems and not about individual systems. Of course it is interesting to think about possible philosophical implications but I don't consider this to be part of the interpretation.

 

[Ken G]

So you are saying that the ensemble interpretation asserts that QM is a theory about the behavior of large collections of similarly prepared subsystems, and is agnostic about the possibility of other theories that describe individual particles. If it asserts no more than that, however, I have a hard time distinguishing it in any significant way from the CI. To me, that's just empiricism, in that it asserts "QM is a scientific theory, where a scientific theory is a mathematical model that helps us predict and understand the types of observations we can actually do." The CI, as an interpretation of quantum mechanics in the way you define, just says that observations on individual particles cannot be predicted by QM, but that's just what you get when you project the ensemble interpretation onto observations of individual particles within that ensemble. I'd say the important differences between the interpretations of QM relate to our expectations of the aspects of any improved theories that might come along, and as such, they go beyond simply interpreting QM, they become statements about our expectations around how reality works. That's the part I'm unclear on when someone holds to the ensemble interpretation-- are they expressing some expectation that the nature of ensembles is fundamentally different from the nature of individual systems, as appropriate targets for doing science, or is there no such assertion that could distinguish it from the CI?

 

[Nugatory]

SI have a hard time distinguishing it in any significant way from the CI.

It is easier to reason rigorously about the theory under the ensemble interpretation. It avoids the wave function collapse assumption and short-circuits any discussion of superluminal machinery in entanglement situations. The net effect may be no more than to place "shut up and calculate" on a more solid mathematical footing; but that's still a gain.

Whether these differences are "significant" or not, and whether the cure is any better than the disease, are to some extent matters of taste.

De [STRIKE]gustibus[/STRIKE] interpretationes non est disputandum

 

[Len M]

... Or, should we say that the ensemble interpretation goes beyond empiricism, and asserts some hidden variables that we as yet have no empirical access to? Then it ends up sounding a lot like deBroglie-Bohm. So perhaps we should say that the ensemble interpretation lives at a kind of intersection of the CI and dB-B, whereby it maintains its empiricist underpinning, but also retains an agnostic attitude about whether or not the hidden deterministic variables that apply to individual particles will ever enter the empirical realm or not. If so, Einstein might not have enjoyed that agnostic attitude about his most closely held belief-- basic realism.

Bernard d’Espagnat (in his book "on Physics and Philosophy") seems to forcefully describe the ensemble theory as requiring the existence of hidden variables – he refers to a “theory” rather than an “interpretation” which is the term used in this thread and on Wiki, but since d’Espagnat doesn’t mention an ensemble “interpretation” at all, then I am going to assume that for the purpose of this thread the terms are interchangeable.

I’m a bit unsure about all of this so I would prefer to quote exactly what d’Espagnat says.

……Up to this stage the theory hardly lays itself open to criticism. But it is a fact that many experiments do involve individual systems so that the question of knowing what may be said about the behaviour of the latter cannot be evaded. For example, in the case considered above of measurements performed on an ensemble of systems we may well ask what the meaning is, with respect to an individual system, of the “relative frequency of the outcome.” To this question Ballentine answered (1970) that the said frequency is identical to the probability that, just before the system-instrument interaction took place, the quantity measured on the system had the value in question.

Obviously, whenever it is not the case that all measurement outcomes are identical this interpretation implies that, before the measurement process took place, the values of the measured quantity were not the same on all systems and that therefore these systems did not all lie in one and the same objective state. This must hold true even though the ensemble of these systems was (by assumption) described by a state vector (alias a wavefunction). It is therefore clear that the theory implies the existence of hidden variables. Now, Bells theorem shows, as we know, that any local hidden variable theory is at variance with both quantum predictions and experiment. To avoid these contradictions an ensemble theory must therefore be identified with a nonlocal hidden variable one.(d'Espagnat's footnote:It is therefore surprising that L.E. Ballentine, one of the main supporters of the ensemble theory, wrote (loc. Cit.) that in view of Bell’s theorem any hidden variable theory is physically unreasonable.) Clearly, the startling simplicity of the hypothesis on which this theory rests is thereby irretrievably lost. We observed above (chapter 9) that several aspects of such hidden variable theories render them most unattractive. It follows from what we just noted that the same is true of the ensemble theory.

 

[kye]

For more than a week. I've been contemplating how quantum computing would work if it uses the concept of ensemble interpretation, where the wavefunction is not in a single atom or electron but ensemble of them. If you'd reason quantum computing would still work using ensemble, then we can design them using classical principles? Remember one reason why quantum computing is fast is because the calculations are done in multiple worlds in the superpositions.. so how would the ensemble interpretation work here.. can quantum computing be the test where Ensemble I. can be scrutinized?

 

[bhobba]

I realize that this is an older thread but is it accurate to say that Einstein accepted the ensemble interpretation? I have come across this post on the Physics Stack Exchange criticizing the wiki article on the ensemble interpretation:

I think all you can say is the issue is controversial in some quarters.

What can be said is its the view of a number of standard texts like Ballentine. What can also be said is, on historical issues, scientists sometimes have a view that historical scholars find a little naive.

Einstein however believed QM was correct - at first he didn't - but in his later years he did - just incomplete and the Ensemble interpretation was part of the view he held in support of that.

On other issues with the interpretation I have read a lot of guff about people views on it. If you really want to know about it read Ballentine's book.

But a few points are in order:

1. In Ballentine's original 1970 article he advocated it as part of a hidden variable interpretation in that he considered the conceptual ensemble to be the value prior to observation, which you can't do because of Kochen-Specher - this was probably because that was Einstein view - who of course didn't know about this fundamental result. In his textbook he moved away from that position for the ensemble to it being the ensemble of system and observational apparatus combined, so the system does not have that value prior to observation.

2. Some people claim it has problems with single systems. That shows a very poor understanding of the interpretation. The ensemble is a conceptualization - it doesn't exist in any sense that's real - it applies to systems of any size. It's like if you adhere to the frequentest interpretation of probability and someone claimed it has problems in describing single coin tosses - again that would show a very erroneous understanding of it.

Thanks
Bill

 

[bhobba]

For more than a week. I've been contemplating how quantum computing would work if it uses the concept of ensemble interpretation, where the wavefunction is not in a single atom or electron but ensemble of them.

I think the semantics you are using here does not reflect the interpretation.

It associates the wave-function, and observation, with a CONCEPTUAL Ensemble. Those two together, via the Born rule, gives the probability of a certain outcome. The Ensemble interpretation gives pictorial vividness to it by saying that the Ensemble contains, in proportion to its probability, the outcomes of the observation and the actual observation selects an element from that ensemble. Its virtually identical to the frequentest interpretation of probability. Indeed one could argue the Ensemble interpretation is basically just the QM mathematical formalism - but strictly speaking since it has a specific view of probability it has added an interpretive aspect - although IMHO a very minor one.

Personally I view probabilities in the mathematical formalism of QM via the Kolomogorov axioms and look upon the Ensemble interpretation as its realization in the frequentest interpretation and Copenhagen (in most versions anyway) as its Bayesian realization.

Thanks
Bill

 

[bhobba]

So the ensemble interpretation is simply the assertion that QM is about ensembles of physical systems and not about individual systems.

That true. But I also want to add these are CONCEPTUAL ensembles - not real ones that exist out there. In many circumstances its true we derive our experimental knowledge of QM from actual ensembles - but that's not what the interpretation is about.

Thanks
Bill

 

[bhobba]

I want to add with regard to the Ensemble interpretation the bible on it is Ballentine's superb book - QM - A Modern Development.

The CORRECT view of ensembles in that interpretation is found on page 46 (emphasis mine):

'However it is important to remember this ensemble is the CONCEPTUAL infinite set of all such systems that may potentially result from the state preparation procedure, and not a concrete set of systems that co-exist in space'

The only thing I will add is I do not view it as infinite, because my mathematics background has issues with such things, merely so large the law of large numbers applies giving an ensemble with proportion of outcomes the same as probability. And to avoid issues with the property being there prior to observation the ensemble is of system and observational apparatus combined - although in Ballentine's text its pretty obvious that's what he is talking about since it refers to the usual system preparation, transformation, then measurement one often finds in such discussions.

Thanks
Bill

 

[kye]

I think the semantics you are using here does not reflect the interpretation.

It associates the wave-function, and observation, with a CONCEPTUAL Ensemble. Those two together, via the Born rule, gives the probability of a certain outcome. The Ensemble interpretation gives pictorial vividness to it by saying that the Ensemble contains, in proportion to its probability, the outcomes of the observation and the actual observation selects an element from that ensemble. Its virtually identical to the frequentest interpretation of probability. Indeed one could argue the Ensemble interpretation is basically just the QM mathematical formalism - but strictly speaking since it has a specific view of probability it has added an interpretive aspect - although IMHO a very minor one.

Personally I view probabilities in the mathematical formalism of QM via the Kolomogorov axioms and look upon the Ensemble interpretation as its realization in the frequentest interpretation and Copenhagen (in most versions anyway) as its Bayesian realization.

Thanks
Bill

How do you apply quantum computing (qbit) to it? Deuch said something like in quantum computing and parallelism, the reason it can solve factors and cracks encryptions millions of times faster than conventional computer is because the computation is done in millions of worlds at once.. the ensemble interpretation is the opposite of many worlds.

 

[Ken G]

Personally I view probabilities in the mathematical formalism of QM via the Kolomogorov axioms and look upon the Ensemble interpretation as its realization in the frequentest interpretation and Copenhagen (in most versions anyway) as its Bayesian realization.

This sounds interesting, can you elaborate?