Ballentine's Ensemble Interpretation Of QM

[stevendaryl]

Says who? Your word against experimentalists that have already proven you wrong multiple times? I can also post random noise but have little time for that.

Let's take spin-1/2 wave functions, as an example:

If |+\rangle is the state where the spin is in the z-direction, and |-\rangle is the state where the spin is in the negative z-direction, then the superposition:

\frac{1}{\sqrt{2}}(|+\rangle + |-\rangle) is the state where the spin is in the x-direction.

A superposition of two pure states is another pure state.

 

[Ken G]

I think it is unlikely this message is going to get through. Some people will always insist that quantum mechanics requires a particle to go through both slits at the same time, while others will hold the more nuanced position that if the apparatus does not determine which slit, then the reality is itself noncommital on the issue, but that does not require the particle go through both slits. It's very surprising that there is an alternative to "both slits" or "one slit but we just don't know which", but some of us find that to be the most interesting aspect of all the quantum surprises. Still, the key point is, if reality can't tell us what happened there, then it is up to our imagination-- we cannot say another interpretation has been negated by the observation, we can only say we prefer a different interpretation of what happened.

 

[vanhees71]

I'm a proponent of the ensemble interpretation.

In the usual double-slit experiment it doesn't make sense to say that a single particle goes through either one or both slits at the same time. The position of the particle at the time when it's hitting the screen is simply undetermined, and I can only give the probability with which it is going through anyone slit (or both slits, what ever this means) and where it will hit the screen. Sending through a lot of equally prepared particles, I get a certain intensity pattern on the screen, which can be predicted from quantum theory. It turns out that this intensity pattern shows interference effects when I use particle beams that are rather well prepared in momentum (and thus have wide-spread position distributions due to the uncertainty relation).

The interferences always occur, when there is no way to know with a large certainty, through which slit they have come.

This is most simply understood using photons and polarization filters at the slits. To precisely know, through which slit the photons come, I must put the polarization filters with 90^{\circ} relative angle to each other, say one let's only horizontally and the other only vertically polarized photons through. Then, (at least in in principle) I know through which slit a single photon has come (if it has come through at all of course), because I could measure its polarization, and this tells me through which slit it has come, but then also the interference effect in the intensity pattern on the screen has vanished, because the polarization states of photons going through the one or the other slit are orthogonal to each other, and so the interference term in the probability distribution is gone.

In the ensemble representation there is no need for esoteric assumption on deciding the question through which slit a single photon has come, because either it's simply indetermined (in the case, where I don't mark the photons in any way through which slit they have gone) or you mark it with help of the polarization-filter trick such that you can (at least in principle) know through which slit it has come. Then, it's well determined through which slit it has come, and it also explains naturally, why there is no interference pattern appearing for this setup when measuring a large ensemble of equally prepared photons running through the double slit.

 

[atyy]

@Maui, I haven't studied this, but Phillip Roser's talk at the Perimeter Institute seems interesting.
http://www.perimeterinstitute.ca/videos/quantum-computing-perspective-de-broglie-bohm-formulation-quantum-mechanics

Anyway, there are two distinct issues here:

1) Can a superposition be described as a system being in some sense simultaneously in several states? Yes, that's an ok way of thinking about it. For example, in http://arxiv.org/abs/quant-ph/0605249 Schlosshauer writes "Superpositions cannot be interpreted as classical ensembles of their components states. Instead, the phenomenon of interference shows that all components in the superposition must be understood as, in some sense, simultaneously present."

2) Does the existence of superpositions imply that Bohmian mechanics is wrong? Not necessarily, as long as the Bohmian interpretation gives all the same experimental predictions as naive quantum mechanics. As I understand, Bohmian mechanics has no problems with non-relativistic quantum mechanics, but whether that can be extended to relativistic quantum mechanics is still a matter of research.

 

[Cthugha]

I do not claim that(show me where I did, or I will report you for spreading misinformation!)

Sure, no problem. Feel free to report me. I have given peer reviewed publications so far. You have not. However, you do it right in the next sentence:

I did claim that particles in BM had definite positions at all times which is contradicted in experiments and prototypes of quantum computers that were already tested(so particles cannot have definite position at all times, experiements, however short, prove that this is not so).

You explicitly claim that BM is contradicted in experiments which means you claim it is ruled out. These forums work by giving credible (peer reviewed) evidence for claims. So please provide peer reviewed publications saying that BI is contradicted by experiments or showing that quantum computers do not work in BI.

Can you show that a quantum computer uses indistiguishibility of particles instead of superpositions? Preferably something peer reviewed and not a random opinion, like the opinions expressed in this thread.

Did you not like Aaronson's paper (he is one of the really big fishs in QC theory)? In case the style of writing is too dense for immediate understanding, here is a watered down summary from his grad level course "quantum computing since Democritus" which shows why he dislikes BI, but how quantum computing still works in terms of degenerate wave functions in BI: http://www.scottaaronson.com/democritus/lec11.html.

Ok, there are more. It is most clearly expressed in publications on linear optical quantum computing. For example:

Phys. Rev. A 71, 032320 (2005) stating "Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable."
This one is about the dual rail qubit. The guinea pig of LOQC.

Then the more recent problem-specific (non-universal) boson sampling implementations all just rely on indistinguishable photons in a multiport interference setup requiring just indistinguishable photons:
Science 339, 798 (2013) (http://www.sciencemag.org/content/339/6121/798).
Science 339, 794 (2013) (http://www.sciencemag.org/content/339/6121/794)
Nature Photonics 7, 540–544 (2013) (http://www.nature.com/nphoton/journal/v7/n7/full/nphoton.2013.102.html).
Nature Photonics 7, 545–549 (2013) (http://www.nature.com/nphoton/journal/v7/n7/abs/nphoton.2013.112.html).

For the last 10 years or so more or less every paper on efficient sources of indistinguishable photons was motivated by mentioning the need of indistinguishable photons for LOQC. See for example:

Nature Nanotechnology 8, 213–217 (2013) (http://www.nature.com/nnano/journal/v8/n3/full/nnano.2012.262.html?WT.ec_id=NNANO-201303)
which introduction starts with
"Single photons have been proposed as promising quantum bits (qubits) for quantum communication, linear optical quantum computing and as messengers in quantum networks. These proposals primarily rely on a high degree of indistinguishability between individual photons to obtain the Hong–Ou–Mandel (HOM) type interference that is at the heart of photonic controlled logic gates and photon-interference-mediated quantum networking".

Finally, there is a whole thesis on quantum computing in BI:
http://arxiv.org/abs/1205.2563. But yes, I am aware that a thesis is only somewhat peer reviewed and.

You can write a rebuttal to the researches that implemented the first quantum computer at MIT and the Institute of Waterloo because they say:
http://iqc.uwaterloo.ca/welcome/quantum-computing-101

Why? That is a pop-sci summary. It is handwaving and simplifying.

Says who? Your word against experimentalists that have already proven you wrong multiple times? I can also post random noise but have little time for that.

If it is that easy, you can surely come up with some peer reviewed publication backing your claim that experimentalists have proven me wrong. And to say it again: the pure existence of working quantum computers does not. Strange that everybody here says that you are wrong, including people working on quantum computing, no?

 

[kith]

Can a superposition be described as a system being in some sense simultaneously in several states? Yes, that's an ok way of thinking about it.

As the "in some sense" indicates this is mostly about semantics. If we stick to the textbook definition of a state as a vector in Hilbert space, a sum of states obviously is not two simultaneous states but a single state. There are infinite possibilities to decompose such a state into sums. So once you go down the road of "two states at once", you instantly get "infinite many states at once", many of which can't occur in measurements in principle. This sounds much less appealing. But if you try to get a nicer picture by classifing states according to measurement outcomes how is this different from the viewpoint that superpositions get their meaning from these measurements and are not a property of the system in the first place?

I don't disagree that for example "two positions at once" may be a possible interpretation of some experiment. It is just a very uncommon one because of what I have written above. The statement is neither true in "shut up and calculate", nor in the CI, nor in the ensemble interpretation, nor in dBB and you can argue a lot about the semantics of the MWI wrt this. And independent of the popularity, we have to keep in mind that it is an interpretative statement and thus cannot prove or disprove anything, as has been claimed in this thread.

 

[atyy]

Is the Hamiltonian considered a property of a single system in Ballentine's Ensemble interpretation, or is it also only a property of the conceptual ensemble?

 

[kith]

Is the Hamiltonian considered a property of a single system in Ballentine's Ensemble interpretation, or is it also only a property of the conceptual ensemble?

Like all observables it refers to the ensemble.

 

[atyy]

Like all observables it refers to the ensemble.

If the density matrix is like a distribution in classical mechanics, ie. refers to an ensemble, then isn't it a puzzle that classically the Hamiltonian is a property of single members of the ensemble but not in quantum mechanics, especially since the Hamiltonian generates determinstic dynamics?

 

[kith]

[...] isn't it a puzzle that classically the Hamiltonian is a property of single members of the ensemble [...]

It seems obvious to interpret the classical Hamiltonian as referring to single systems but you don't have to. Also classically, knowledge is obtained by performing experiments on ensembles.

The asymmetry you mention is a puzzle for Einstein-like positions which maintain that there's an underlying hidden variable theory of single systems. It is also one reason why I dislike the dBB interpretation.

 

[strangerep]

If the density matrix is like a distribution in classical mechanics, ie. refers to an ensemble, then isn't it a puzzle that classically the Hamiltonian is a property of single members of the ensemble but not in quantum mechanics, especially since the Hamiltonian generates determinstic dynamics?

It's easier to resolve puzzles like this if one thinks of the classical system in terms of an ensemble for which all variances (and higher moments) are 0.

 

[atyy]

The asymmetry you mention is a puzzle for Einstein-like positions which maintain that there's an underlying hidden variable theory of single systems. It is also one reason why I dislike the dBB interpretation.

Is it fair to say that the Ensemble interpretation is hostile only to Many-Worlds, but is compatible with Copenhagen (or at least shut-up-and-calculate) and dBB? The Ensemble interpretation claims that wave function cannot be ascribed to single systems, whereas Many-Worlds takes unitary evolution of the wave function of the whole universe seriously.

It goes to show that questions of interpretation in QM are not devoid of practical utility.'

What you you guys think - does Ballantine have a point? Or is it just metaphysical mumbo jumbo?

http://arxiv.org/abs/0903.3297 reviews the quantum Zeno effect, including a list of experimental evidence. If I understand Ballentine correctly, he claims that the lack of a quantum Zeno effect falsifies wave function collapse. Does Ballentine's wrong prediction for the quantum Zeno effect show that his interpretation is wrong?

 

[Ken G]

The Ensemble interpretation claims that wave function cannot be ascribed to single systems, whereas Many-Worlds takes unitary evolution of the wave function of the whole universe seriously.

That seems reasonable, they would seem to be at opposite ends of the "literal reality of the state vector" spectrum.

http://arxiv.org/abs/0903.3297 reviews the quantum Zeno effect, including a list of experimental evidence. If I understand Ballentine correctly, he claims that the lack of a quantum Zeno effect falsifies wave function collapse. Does Ballentine's wrong prediction for the quantum Zeno effect show that his interpretation is wrong?

I'm confused by that, in simplest terms the quantum Zeno effect is one of the most elementary calculations you can make with the Schroedinger equation. So Ballentine cannot have thought the Schroedinger equation would be wrong if a precise enough experiment could be done, he must have just thought that the experiment would be too difficult, perhaps analogous to how Bohr might have thought an experiment that prepares a macroscopic superposition would be too difficult.

I don't see what formal problem there could be, it seems to me if one takes the ensemble view of the probabilities of outcomes of a single experiment, one can equally also take an ensemble view of the correlations between outcomes of repeated experiments. In other words, just as there will be an ensemble average for the fraction of spins recorded as "up", there should be an ensemble average for the expected number of times that two subsequent spin measurements will give the same result, versus a flipped result, and that ensemble average should go to an expectation of zero flips in the limit as the time between the observations gets small and the number of repeated observations gets large. That's the Zeno effect in ensemble terms, it seems straightforward enough, so can you give more details on Ballentine's objection?

Added: in fact it seems that the ensemble interpretation is a kind of crossroads between all the other interpretations, morphing fairly easily into any of the others. For example, if one asserts "the ensemble is real, but we only experience a fraction of it", one gets something that sounds a lot like many worlds. If one says the ensemble is just a conceptual tool, and use a frequentist interpretation of the probabilities encountered, one gets the brand of the ensemble interpretation that bhobba pointed out. If one says the ensemble is just a conceptual tool, but use a Bayesian interpretation of the probabilities, then one gets something pretty close to CI (as bhobba explained). If one says the ensemble is just a placekeeper for hidden variables, one gets something pretty close to BM. All the interpretations can be seen as variants on the ensemble interpretation that just take one or other metaphysical stand on the meaning of the expressions being manipulated. Maybe none of those metaphysical stands are "universally correct", because maybe quantum mechanics itself is not universally correct, but each one may have its preferred context. So what you are asking might be, is the Zeno effect the preferred context of the CI?

 

[atyy]

I'm confused by that, in simplest terms the quantum Zeno effect is one of the most elementary calculations you can make with the Schroedinger equation. So Ballentine cannot have thought the Schroedinger equation would be wrong if a precise enough experiment could be done, he must have just thought that the experiment would be too difficult, perhaps analogous to how Bohr might have thought an experiment that prepares a macroscopic superposition would be too difficult.

I don't see what formal problem there could be, it seems to me if one takes the ensemble view of the probabilities of outcomes of a single experiment, one can equally also take an ensemble view of the correlations between outcomes of repeated experiments. In other words, just as there will be an ensemble average for the fraction of spins recorded as "up", there should be an ensemble average for the expected number of times that two subsequent spin measurements will give the same result, versus a flipped result, and that ensemble average should go to an expectation of zero flips in the limit as the time between the observations gets small and the number of repeated observations gets large. That's the Zeno effect in ensemble terms, it seems straightforward enough, so can you give more details on Ballentine's objection?

Added: in fact it seems that the ensemble interpretation is a kind of crossroads between all the other interpretations, morphing fairly easily into any of the others. For example, if one asserts "the ensemble is real, but we only experience a fraction of it", one gets something that sounds a lot like many worlds. If one says the ensemble is just a conceptual tool, and use a frequentist interpretation of the probabilities encountered, one gets the brand of the ensemble interpretation that bhobba pointed out. If one says the ensemble is just a conceptual tool, but use a Bayesian interpretation of the probabilities, then one gets something pretty close to CI (as bhobba explained). If one says the ensemble is just a placekeeper for hidden variables, one gets something pretty close to BM. All the interpretations can be seen as variants on the ensemble interpretation that just take one or other metaphysical stand on the meaning of the expressions being manipulated. Maybe none of those metaphysical stands are "universally correct", because maybe quantum mechanics itself is not universally correct, but each one may have its preferred context. So what you are asking might be, is the Zeno effect the preferred context of the CI?

Ballentine's error was brought up by Demystifier https://www.physicsforums.com/showthread.php?p=3598025#post3598025 and discussed also in https://www.physicsforums.com/showthread.php?t=716982. kith quotes the passage in detail in https://www.physicsforums.com/showpost.php?p=3598025&postcount=6. By writing "It is sometimes claimed that the rival interpretations of quantum mechanics differ only in philosophy, and cannot be experimentally distinguished. That claim is not always true, as this example proves.", Ballentine seems to say that his interpretation can be experimentally distinguished from others. That already seems to make Ballentine's Ensemble interpretation (as defined in his book) not an interpretation but a different theory, as DevilsAvocado says. If Ballentine's theory is different from quantum mechanics, and the experimental evidence he cites goes against him, doesn't this mean his theory is wrong?

 

[Ken G]

Certainly it would mean that. But Ballentine could be wrong that the different interpretations make different predictions. An interpretation can be a kind of moving target, even within one physicist's own views!

 

[Demystifier]

I don't think that the ensemble interpretation makes different predictions than other interpretations. I think it's only that Ballentine misunderstood one particular aspect of this interpretation.

The fact that he invented this interpretation doesn't matter. (For example, Einstein had a few misunderstandings of general relativity. In particular, he predicted that gravitational waves cannot exist.)

 

[atyy]

Certainly it would mean that. But Ballentine could be wrong that the different interpretations make different predictions. An interpretation can be a kind of moving target, even within one physicist's own views!

I don't think that the ensemble interpretation makes different predictions than other interpretations. I think it's only that Ballentine misunderstood one particular aspect of this interpretation.

The fact that he invented this interpretation doesn't matter. (For example, Einstein had a few misunderstandings of general relativity. In particular, he predicted that gravitational waves cannot exist.)

Is it fair to say that the Ensemble interpretation is simply Copenhagen, with the provision that there may be a more fundamental theory? Many standard texts already treat Copenhagen as applying only to ensembles, since it is standard to say that only expectation values can be predicted. Some versions of Copenhagen, that there cannot be a more fundamental theory must be modified, but the idea that there is possibly a more fundamental theory or at least hidden variables was known before Ballentine, because of dBB. Ken G has said this repeatedly, and if so, then why not just say we have Copenhagen, instead of Ballentine's Ensemble interpretation? With respect to the idea that unitary evolution of the wave function applies to single systems, off the top of my head, in non-foundations texts, I recall it in two places - one in Kardar's text on statistical mechanics, where he states it as a possibility in his discussion of whether collapse is the reason for irreversibility, and in Mukhanov's text on quantum cosmology where he says it is natural to try to have the wave function of the universe evolve unitarily. But apart from these extreme cases, one could take Griffiths or Feynman's interpretation to naturally apply only to ensembles, simply because they state that only expectation values can be predicted. Is Ballentine's Ensemble interpretation simply 'Copenhagen done wrong'?

 

[Nugatory]

Is it fair to say that the Ensemble interpretation is simply Copenhagen, with the provision that there may be a more fundamental theory? Many standard texts already treat Copenhagen as applying only to ensembles, since it is standard to say that only expectation values can be predicted. ... Is Ballentine's Ensemble interpretation simply 'Copenhagen done wrong'?

I'd rather say it's "Copenhagen done right", for several reasons:
- There is no single crisp and standardized definition of "the" Copenhagen Interpretation. It kind of grew along with the pioneers' earliest understanding of QM.
- Copenhagen drags in the additional and sometimes problematic assumption of wavefunction collapse.
- At least in Ballentine's hands, the ensemble interpretation stands on a more rigorous and formal mathematical base.

 

[TrickyDicky]

Is Ballentine's Ensemble interpretation simply 'Copenhagen done wrong'?

This, or is Copenhagen's simply Ballentine's done wrong? I guess it's just a matter of personal taste, if you think QM is complete and the fundamental theory you'd use one charachterization, otherwise the other. Looks like the most economic(the one making less gratuitous assumptions) given the same math and results is Ballentine's, so by Occam's should be preferred. And I think that is what the majority does when they say they lean on the "calculate and shut up" interpretation, only most identify it with CI rather than with ensembles.

EDIT:Nugatory was faster typing

 

[atyy]

I'd rather say it's "Copenhagen done right", for several reasons:
- There is no single crisp and standardized definition of "the" Copenhagen Interpretation. It kind of grew along with the pioneers' earliest understanding of QM.
- Copenhagen drags in the additional and sometimes problematic assumption of wavefunction collapse.
- At least in Ballentine's hands, the ensemble interpretation stands on a more rigorous and formal mathematical base.

This, or is Copenhagen's simply Ballentine's done wrong? I guess it's just a matter of personal taste, if you think QM is complete and the fundamental theory you'd use one charachterization, otherwise the other. Looks like the most economic(the one making less gratuitous assumptions) given the same math and results is Ballentine's, so by Occam's should be preferred. And I think that is what the majority does when they say they lean on the "calculate and shut up" interpretation, only most identify it with CI rather than with ensembles.

EDIT:Nugatory was faster typing

At any rate, it looks like Ballentine's Ensemble interpretation must be corrected with respect to the quantum Zeno effect. How should this be done?

 

[Demystifier]

At any rate, it looks like Ballentine's Ensemble interpretation must be corrected with respect to the quantum Zeno effect. How should this be done?

Easily: There is no real wave function collapse (because wave function is not real), but as for any other measurement in QM, there is an effective wave function collapse which serves as a practical rule to calculate probabilities after measurements.

 

[atyy]

Easily: There is no real wave function collapse (because wave function is not real), but as for any other measurement in QM, there is an effective wave function collapse which serves as a practical rule to calculate probabilities after measurements.

Is this equivalent to taking, at least for non-relativistic QM, dBB to be fundamental, then deriving Copenhagen as an effective theory?

 

[kaplan]

I don't see what this is supposed to prove or in what way it answers my question, but a system in superposition does not have a unique state but occupies all possible quantum states simulataneously.

Maui, (as many people have told you) the above is simply not correct. In quantum mechanics, "superposition" refers to adding two or more states together (and multiplying by the appropriate normalization factor). But quantum states are elements of a vector space, and that means the sum of two (or more) states is just another state. It is unique, and it does not "occupy all possible quantum states simulataneously". Is the sum of two ordinary vectors "not unique", and does it "occupy all vectors simultaneously"?

This is not semantics, this is basic quantum mechanics. It's one of the first things students learn when they study the topic.

As for dBB, personally I think it's silly and quite useless, but it cannot possibly be in contradiction with any prediction of non-relativistic QM, because its predictions are identical to those of non-relativistic QM.

 

[TrickyDicky]

At any rate, it looks like Ballentine's Ensemble interpretation must be corrected with respect to the quantum Zeno effect. How should this be done?

I would refer you to the posts by Demysitifier and Ken G above, and also to the first discussion you linked on this, specially posts #14 and #18 by akhmeteli.
All this is to say that I think Ballentine wasn't very fortunate in the long paragraph quoted by kith in that discussion, it is misleading at the least, and drawing consequences not warranted from his interpretation of the ensemble interpretation and what experiments seem to indicate or not about the quantum Zeno effect.
As pointed out by Demystifier, authors sometimes say goofy things even about their own constructions.
An example about which Bhobba has insisted several times is the correction introduced by Ballentine in his book to his original 1970 paper dealing with the meaning of ensemble. This is far from trivial, for instance the otherwise good account by Neumaier also linked in this thread http://arnold-neumaier.at/physfaq/topics/mostConsistent is almost ridiculed in the wikipedia article on the ensemble interpretation just because he gives counterexamples to the interpretation based on the 1970 paper by Ballentine.

 

[audioloop]

Certainly it would mean that. But Ballentine could be wrong that the different interpretations make different predictions. An interpretation can be a kind of moving target, even within one physicist's own views!

well, nonlinear quantum mechanics make different predictions than standard quantum mechanics (a linear one), then is another model.


and
Objective Collapse Models makes predictions different to other models
http://plato.stanford.edu/entries/qm-collapse/


.

 

[strangerep]

At any rate, it looks like Ballentine's Ensemble interpretation must be corrected with respect to the quantum Zeno effect.

That's still a controversial point, imho.

How should this be done?

First, one should study Ballentine's paper refuting claims that certain experiments confirm the quantum zeno effect.
(I posted the references elsewhere -- don't have time right now to dig them out again, but will do so if anyone requests.)

 

[atyy]

That's still a controversial point, imho.

First, one should study Ballentine's paper refuting claims that certain experiments confirm the quantum zeno effect.
(I posted the references elsewhere -- don't have time right now to dig them out again, but will do so if anyone requests.)

Within Copenhagen one can explain the Zeno effect with and without collapse. They are equivalent. One still needs collapse at the end to get definite outcomes regardless. It's not as if one is right and the other is wrong - it just depends on how much of the universe you want to include explicitly in the Hamiltonian. But surely it is not contested that in a correct Ensemble interpretation the wave function does collapse upon measurement, after which it continues to evolve unitarily. It's just that collapse, like unitary evolution and the wave function are all things that predict the statistical behaviour of ensembles. If that is a correct Ensemble interpretation, then it is essentially Copenhagen, and there should be a quantum Zeno effect.

 

[bhobba]

I'd rather say it's "Copenhagen done right", for several reasons:
- There is no single crisp and standardized definition of "the" Copenhagen Interpretation. It kind of grew along with the pioneers' earliest understanding of QM.
- Copenhagen drags in the additional and sometimes problematic assumption of wavefunction collapse.
- At least in Ballentine's hands, the ensemble interpretation stands on a more rigorous and formal mathematical base.

Damn - you read my mind.

That's it.

IMHO when done right, Copenhagen and the Ensemble Interpretation are more similar than people generally think.

I am also partial to Consistent/Decoherent Histories, which some say is Copenhagen done right, but its a bit more complex than I think is necessary. To me however it's closer to MW than Copenhagen. Even Murray Gell-Mann, one of its originators, said its basically MW with only one world being real.

Thanks
Bill

 

[kye]

Max Tegmark seemed to indicate in the paper below that quantum computer can disprove the Ensemble Interpretation. So we can perhaps settle it by knowing more about quantum computer. Bill Hobba said he was not familiar with it so I hope someone can share an introductory site that has very clear presentation of how exactly quantum computer need real-time superposition to make it work. Also after reading the paper, you will get the impression many physicists are into many worlds and the Copenhagen/Ensemble is a minority (with equal believers the same small numbers as Bohmians. Also I think we have so many Copenhagenists here because PF advisors were only chosen if there were Copenhagenists to avoid spectulative ideas introduced in the discussion, agree?).

http://arxiv.org/pdf/quant-ph/0101077v1.pdf

"After this last feat, Anton Zeilinger’s group in Vienna has even started discussing doing it with a virus. If
we imagine, as a Gedanken experiment, that this virus has some primitive kind of consciousness, then the many worlds/many minds interpretation seems unavoidable, as has been emphasized by Dieter Zeh. An extrapolation to superpositions involving other sentient beings such as humans would then be merely a quantitative rather than a qualitative one.

In short, the experimental verdict is in: the weirdness of the quantum world is real, whether we like it or
not. There are in fact good reasons to like it: this very weirdness may offer useful new technologies. According
to a recent estimate, about 30% of the U.S. gross national product is now based on inventions made possible
by quantum mechanics. Moreover, if physics really is unitary (if the wave function never collapses), quantum
computers can in principle be built that take advantage of such superpositions to make certain calculations much faster than conventional algorithms would allow. For example, Peter Shor and Lov Grover have shown that one could factor large numbers and search long lists faster this way. Such machines would be the ultimate parallel computers, in a sense running many calculations in superposition. As David Deutsch has emphasized, it will be hard to deny the reality of all these parallel states if such computers are actually built."

So the hard question is whether you can make quantum computer if the superposition is not real time, what do you think, can you show any mathematical argument why it can or can't?

 

[Cthugha]

Also after reading the paper, you will get the impression many physicists are into many worlds and the Copenhagen/Ensemble is a minority (with equal believers the same small numbers as Bohmians. Also I think we have so many Copenhagenists here because PF advisors were only chosen if there were Copenhagenists to avoid spectulative ideas introduced in the discussion, agree?).

I disagree. The probability of a physicist being into many worlds/BM conditioned on the subset of physicists interested in interpretations is indeed quite high. Taking all physicists into account "shut up and calculate" and minimal interpretations are by far the most common.

"If we imagine, as a Gedanken experiment, that this virus has some primitive kind of consciousness, then the many worlds/many minds interpretation seems unavoidable, as has been emphasized by Dieter Zeh.
[...]
As David Deutsch has emphasized, it will be hard to deny the reality of all these parallel states if such computers are actually built."

And this is exactly why most physicists do not care about interpretations. It really does not matter to me what people think is hard to deny or what seems unavoidable to them. It matters if you absolutely cannot deny things or they are indeed unavoidable. What people think or how things seem to them is a matter of opinion and of arguments one likes or dislikes or considers weird. Ensemble interpretation is for minimalists. BI is for people who consider an ontologically satisfying interpretation important. Many worlds is for...I don't know, but I am sure people into many worlds can explain why they like it. A good interpretation should be inspiring.

Mathematically the standard interpretations left over are all equivalent within the scope of standard qm accessible in todays experiments.

edit:

At any rate, it looks like Ballentine's Ensemble interpretation must be corrected with respect to the quantum Zeno effect. How should this be done?

Not really. It helps a bit to have a look at the historical papers. The effect was first reported in Phys. Rev. A 41, 2295–2300 (1990) by some guy called David Wineland people might have heard of. Then Ballentine commented on it in Phys. Rev. A 43, 5165–5167 (1991) and the original authors commented on the comment in Phys. Rev. A 43, 5168–5169 (1991), stating that
"The choice among interpretations that yield identical predictions, including the standard Copenhagen interpretation, the "statistical" or "ensemble" interpretation favored by Ballentine, or even Everett's "relative-states" or "many-worlds" interpretation, would seem to be a matter of personal taste. Ballentine states that "collapse of the wave function" is not necessary to quantum mechanics. We agree." and "In summary, quantum mechanics can be interpreted in different ways. In this case, interpretations with and without the collapse postulate correctly predict the experimental data. Therefore, the experiment neither verifies nor falsifies the notion of "wave-function collapse. "

Great formulation. That guy should get a Nobel prize.

 

[kye]

I disagree. The probability of a physicist being into many worlds/BM conditioned on the subset of physicists interested in interpretations is indeed quite high. Taking all physicists into account "shut up and calculate" and minimal interpretations are by far the most common.



And this is exactly why most physicists do not care about interpretations. It really does not matter to me what people think is hard to deny or what seems unavoidable to them. It matters if you absolutely cannot deny things or they are indeed unavoidable. What people think or how things seem to them is a matter of opinion and of arguments one likes or dislikes or considers weird. Ensemble interpretation is for minimalists. BI is for people who consider an ontologically satisfying interpretation important. Many worlds is for...I don't know, but I am sure people into many worlds can explain why they like it. A good interpretation should be inspiring.

Mathematically the standard interpretations left over are all equivalent within the scope of standard qm accessible in todays experiments.

edit:


Not really. It helps a bit to have a look at the historical papers. The effect was first reported in Phys. Rev. A 41, 2295–2300 (1990) by some guy called David Wineland people might have heard of. Then Ballentine commented on it in Phys. Rev. A 43, 5165–5167 (1991) and the original authors commented on the comment in Phys. Rev. A 43, 5168–5169 (1991), stating that
"The choice among interpretations that yield identical predictions, including the standard Copenhagen interpretation, the "statistical" or "ensemble" interpretation favored by Ballentine, or even Everett's "relative-states" or "many-worlds" interpretation, would seem to be a matter of personal taste. Ballentine states that "collapse of the wave function" is not necessary to quantum mechanics. We agree." and "In summary, quantum mechanics can be interpreted in different ways. In this case, interpretations with and without the collapse postulate correctly predict the experimental data. Therefore, the experiment neither verifies nor falsifies the notion of "wave-function collapse. "

Great formulation. That guy should get a Nobel prize.

I think you make sense the Ensemble I. is for certain people who want the minimalist thing. But notice that for those physicists contemplating on the theory of everything (or unification or quantum gravity) need to see deeper into quantum theory.. like Tegmark, Smolin, Einstein, Perimeter institute phycisists, etc. because what's hidden inside the quantum may be related to unification (for example... we have crisis now how to solve the hierarchy problem of the higgs when there is no hint of the supersymmetric particles.. and Lisa Randal has to even go to extreme attempts like large branes to solve it). A Perimeter Institute physicist said space (or is it time) didn't fundamentally exist.. so the electron can kindly take all paths (Feynman integral approach).. the minimalist may say who care what happens in between and there is no way to know.. but you can't deny it can give us insight intoto Unification and perhaps the marriage of GR and QM. Do you have theorem that whatever is the final theory has no relations to what's hidden in QM or no extra predictions? (but isn't it quantum computer is a new prediction that a real-time superposition can bring?)

 

[atyy]

Not really. It helps a bit to have a look at the historical papers. The effect was first reported in Phys. Rev. A 41, 2295–2300 (1990) by some guy called David Wineland people might have heard of. Then Ballentine commented on it in Phys. Rev. A 43, 5165–5167 (1991) and the original authors commented on the comment in Phys. Rev. A 43, 5168–5169 (1991), stating that
"The choice among interpretations that yield identical predictions, including the standard Copenhagen interpretation, the "statistical" or "ensemble" interpretation favored by Ballentine, or even Everett's "relative-states" or "many-worlds" interpretation, would seem to be a matter of personal taste. Ballentine states that "collapse of the wave function" is not necessary to quantum mechanics. We agree." and "In summary, quantum mechanics can be interpreted in different ways. In this case, interpretations with and without the collapse postulate correctly predict the experimental data. Therefore, the experiment neither verifies nor falsifies the notion of "wave-function collapse. "

Great formulation. That guy should get a Nobel prize.

Sure, but even in Copenhagen that's possible. Ballentine claims Copenhagen is experimentally false!

Also, do you think that the passage by Ballentine quoted by kith here is correct? https://www.physicsforums.com/showpost.php?p=3598025&postcount=6

And is wave function collapse really not needed in the Ensemble interpretation? Isn't there also state vector reduction?

 

[Cthugha]

But notice that for those physicists contemplating on the theory of everything (or unification or quantum gravity) need to see deeper into quantum theory.. like Tegmark, Smolin, Einstein, Perimeter institute phycisists, etc. because what's hidden inside the quantum may be related to unification (for example... we have crisis now how to solve the hierarchy problem of the higgs when there is no hint of the supersymmetric particles.. and Lisa Randal has to even go to extreme attempts like large branes to solve it).

That is a lot of 'may' and 'could be'. Most physicists are not working on topics beyond ordinary qm. They have little to gain from adopting this or that interpretation. They may, however, spend a lot of time discussing interpretations instead of discussing physics. However, this is not helpful when the area you work in is covered by standard qm. From that point of view, a minimalist interpretation is a natural choice as it saves your time for working on your real topic instead of discussing interpretations. As I said, a good interpretation should be first and foremost inspiring. This may especially be the case if one works on physics beyond the standard model. I do not doubt that.

A Perimeter Institute physicist said space (or is it time) didn't fundamentally exist.. so the electron can kindly take all paths (Feynman integral approach).. the minimalist may say who care what happens in between and there is no way to know..

I disagree somewhat. The minimalist would rather say there is no way to know now. We can decide, when we have experimental evidence. I simply do not see the reason for people fighting over interpretations when we know that the question cannot be decided right now. Pick your interpretation, if it helps you understand some problem. I just do not understand the people who are on a crusade for this or that interpretation (or rather: against all other interpretations).

but you can't deny it can give us insight intoto Unification and perhaps the marriage of GR and QM. Do you have theorem that whatever is the final theory has no relations to what's hidden in QM or no extra predictions? (but isn't it quantum computer is a new prediction that a real-time superposition can bring?)

Well, as I said: It is rather inspiration than insight, but a good educated guess may lead to insights, no doubt. I have no theorem. I am also not claiming that there will be no relation. I am just trying to establish that "I honestly do not know which interpretation is right and I really cannot see any being better than the other" is a perfectly valid opinion.

Quantum computers are not really a new prediction, by the way. The role of superpositions in quantum computers is overplayed anyway, in my opinion. They do not necessarily give correct results, so you need to rerun a problem many times anyway, so quantum computing relies on an ensemble of experimental runs anyway.

Sure, but even in Copenhagen that's possible. Ballentine claims Copenhagen is experimentally false!

Also, do you think that the passage by Ballentine quoted by kith here is correct? https://www.physicsforums.com/showpos...25&postcount=6

No, Ballentine was simply all out wrong there. Ballentine was wrong on many occasions, often also about his own ensemble interpretation. That does not invalidate the ensemble interpretation, though. It actually disagrees with Ballentine's views on these points.

And is wave function collapse really not needed in the Ensemble interpretation? Isn't there also state vector reduction?

Yes, you have state vector reduction. However, if you do not consider the wave function as real, you also do not need to interpret state vector reduction as collapse.

 

[atyy]

No, Ballentine was simply all out wrong there. Ballentine was wrong on many occasions, often also about his own ensemble interpretation. That does not invalidate the ensemble interpretation, though. It actually disagrees with Ballentine's views on these points.

OK. So would it be possible to say that there is a correct ensemble interpretation, but it is not exactly that in Ballentine 1970 or Ballentine 1998, both of which contain errors?

Yes, you have state vector reduction. However, if you do not consider the wave function as real, you also do not need to interpret state vector reduction as collapse.

Is it possible to take state vector reduction (in the ensemble interpretation) as synonym for wave function collapse (in shut up and calculate, ie. with interpretation removed, or acknowledging that QM only applies to ensembles anyway)?

 

[bhobba]

Ballentine claims Copenhagen is experimentally false!

Ballentine only considers the version of Copenhagen that thinks the wavefunction is real. That has issues as pointed out by Ballentine - collapse is a very unnatural assumption if you think it actually real.

But most versions of Copenhagen aren't like that - they don't consider it as actually real - it represents purely a state of knowledge a theorist has about the outcomes of observations - it applies to individual systems which separates it from the Ensemble interpretation - but its not real so collapse is of zero concern.

Thanks
Bill

 

[bhobba]

I disagree. The probability of a physicist being into many worlds/BM conditioned on the subset of physicists interested in interpretations is indeed quite high. Taking all physicists into account "shut up and calculate" and minimal interpretations are by far the most common.

I think it goes further than that. I suspect they simply accept the formalism. If you pinned them down and said what do you understand by probability, it would likely be some vague frequentest idea of it it. If they had a background in math maybe it would be Kolmogorv's axioms. Either way I don't think it would be a formal interpretation, or at the most some vague ideas from Copenhagen along the lines of the sketchy treatment books like Griffith give.

Thanks
Bill

 

[bhobba]

No, Ballentine was simply all out wrong there. Ballentine was wrong on many occasions, often also about his own ensemble interpretation. That does not invalidate the ensemble interpretation, though. It actually disagrees with Ballentine's views on these points.

Glad you noticed that as well. Best book on QM I know and I can't praise it highly enough - everyone should study it IMHO. But perfect it aren't.

Thanks
Bill

 

[Demystifier]

Is this equivalent to taking, at least for non-relativistic QM, dBB to be fundamental, then deriving Copenhagen as an effective theory?

Yes. Indeed, dBB theory can be viewed as one particular realization of the ensemble interpretation. In fact, Ballentine discusses dBB theory in his textbook.

 

[Devils]

That you Prof Hobba for your enlightened responses. I think YOU should write a book on the ensemble interpretation that fixes Ballentine.

 

[bhobba]

That you Prof Hobba for your enlightened responses. I think YOU should write a book on the ensemble interpretation that fixes Ballentine.

Mate the (minor) issues with Ballentine has been discussed before - they are well known.

And of course I am no Prof - like you I am simply a math graduate with an interest in physics.

Thanks
Bill

 

[Devils]

Mate the (minor) issues with Ballentine has been discussed before - they are well known.

And of course I am no Prof - like you I am simply a math graduate with an interest in physics.

Thanks
Bill

Meh I have always though of you as Prof Hobba since we met 30 years & 9 months ago.

 

[TrickyDicky]

I found this a valuable account of the ensemble interpretation:

http://statintquant.net/siq/siq.html#siqse5.html

 

[vanhees71]

I found this a valuable account of the ensemble interpretation:

http://statintquant.net/siq/siq.html#siqse5.html

Already the interpretation of the Heisenberg uncertainty relation is, as discussed in this forum, at least questionable. The Heisenberg uncertainty relation in this form is not the measurement-disturbance relation as it was first adovated by Heisenberg. It doesn't tell us something about simultaneous measurements of incompatible observables but about the possibility to prepare a system with regard to accuracy of two such incompatible observables (here position and momentum components in the same direction).

Taking the ensemble interpretation, it's no problem to interpret it in the correct way: You assign a (pure or mixed) state by some preparation procedure to the particle. Then preparing a lot of particles in this state (the ensemble), on each individual system you measure either the position component with high precision or the momentum component with high precision, determine the standard deviations of these measurements. Then the Heisenberg uncertainty relation tells you that, independtly from the prepared state,
\Delta x \Delta p \geq \hbar/2.
This relation, however doesn't tell you how the measurement of position affects the state of the system with respect to the precision of the momentum and vice versa. This is a much more difficult issue, and whether such an uncertainty relation holds in the sense of measurement-error-disturbance relations depends on how you define the corresponding measures for error and disturbance.

 

[atyy]

Yes. Indeed, dBB theory can be viewed as one particular realization of the ensemble interpretation. In fact, Ballentine discusses dBB theory in his textbook.

OK, maybe the book has some merit after all:)

But given that dBB is one realization of the ensemble interpretation, shouldn't we credit the ensemble interpretation to dBB (instead of Ballentine), ie. once dBB was discovered and rediscovered, the conceptual possibility of such a theory and the possibility that it is not unique showed that the impression conveyed by some textbooks (like Feynman's wonderful lectures) of there being no deeper reality to the wave function isn't necessarily true.

Ballentine only considers the version of Copenhagen that thinks the wavefunction is real. That has issues as pointed out by Ballentine - collapse is a very unnatural assumption if you think it actually real.

But most versions of Copenhagen aren't like that - they don't consider it as actually real - it represents purely a state of knowledge a theorist has about the outcomes of observations - it applies to individual systems which separates it from the Ensemble interpretation - but its not real so collapse is of zero concern.

Is collapse problematic if the wave function is real, but quantum mechanics an incomplete theory? Standard QM is incomplete because it requires classical apparatus to make a measurement and produce an outcome - so classical physics remains fundamental, and QM is only an effective theory which always requires a division of the universe into observer and observed. The big problems from a more fundamental viewpoint are - what is the classical measurement device, and why are there outcomes? Neither is solved by the ensemble interpretation.

Collapse is only problematic if one asks what is the fundamental theory under QM. Assuming unitary evolution of the wave function (let's call that MWI) is a very natural attempt from at least two areas in basic physics:

1) What is the origin of thermodynamic irreversibility? Is it wave function collapse? If we wish to answer no, then attempting to explain thermodynamic irreversibility as deterministic evolution of many-particle systems is natural. (But maybe a viable approach is that wave function collapse is partly involved, since the reduced density matrix, which assumes collapse, often shows an approach to thermality even though it is part of a system which evolves unitarily.)

2) What happens when we attempt to apply quantum theory to the universe, and there seems to be no observer left? (An answer may be that as long as we wish physics to be an experimental science, there will always be an observer left.)

In both cases, MWI has the advantage over dBB in that, if it works, it is unique. With dBB we don't know what the most natural underlying hidden variables and dynamics are (could be non-unique).

 

[Nugatory]

Is collapse problematic if the wave function is real, but quantum mechanics an incomplete theory?

It depends (as with all interpretations) on what you consider to be a problem. How do you feel about the faster-than-light propagation of the collapse? Or the notion that the wave function that collapses is real, it collapses simultaneously at two different points, but no information is conveyed by its collapsing?

(Come to think of it, I could parody some of the arguments in this thread by asserting that entanglement at a distance "falsifies" Copenhagen while denying the sea of unstated assumptions from which that assertion emerges).

 

[atyy]

It depends (as with all interpretations) on what you consider to be a problem. How do you feel about the faster-than-light propagation of the collapse? Or the notion that the wave function that collapses is real, it collapses simultaneously at two different points, but no information is conveyed by its collapsing?

(Come to think of it, I could parody some of the arguments in this thread by asserting that entanglement at a distance "falsifies" Copenhagen while denying the sea of unstated assumptions from which that assertion emerges).

If it is correct as I and Demystifier think, to consider the ensemble interpretation as equivalent to QM being an effective theory by ignoring the pilot wave and other hidden variables, then there is no problem (especially afer Bell, who was inspired by dBB).

It's also no problem if one does not exclude that special relativity may be emergent, eg. http://arxiv.org/abs/0808.2495 .

Actually, isn't the wave function real in dBB? For example, http://arxiv.org/abs/0706.2661 classifies the wave function as real but incomplete in dBB.

 

[kith]

IMHO when done right, Copenhagen and the Ensemble Interpretation are more similar than people generally think. I am also partial to Consistent/Decoherent Histories, which some say is Copenhagen done right, but its a bit more complex than I think is necessary. To me however it's closer to MW than Copenhagen.

The more I learned about interpretations, the more similar they seemed to me. If we sort them from classical to literal quantum mechanical, we only get gradual differences for adjacent ones. dBB could be viewed as underlying the ensemble interpretation. If we take a more empiricist viewpoint, the ensemble interpretation is very similar to Copenhagen which in turn is very similar to consistent histories if you are right. From there, it is only a minor step to the MWI. And since dBB could be considered a single branch of the MWI, we are back at the start.

 

[kith]

But given that dBB is one realization of the ensemble interpretation, shouldn't we credit the ensemble interpretation to dBB (instead of Ballentine)

As I and Ken G have written in some earlier posts, there are different motivations to stick to the ensemble interpretation. Many people use it because they think that theories cannot do better in principle than to relate experimental ensembles to models about these ensembles. For example, I don't think van Hees would agree with your statement and he is one of the most prominent advocates of the ensemble interpretation here.

 

[atyy]

As I and Ken G have written in some earlier posts, there are different motivations to stick to the ensemble interpretation. Many people use it because they think that theories cannot do better in principle than to relate experimental ensembles to models about these ensembles. For example, I don't think van Hees would agree with your statement and he is one of the most prominent advocates of the ensemble interpretation here.

But that point of view had no teeth against a claim that there is necessarily no more fundamental reality than the wave function, until dBB.

 

[kith]

But that point of view had no teeth against a claim that there is necessarily no more fundamental reality than the wave function, until dBB.

I don't understand. Why should it have "teeth" against something which it doesn't oppose?