Ballentine's Ensemble Interpretation Of QM

[atyy]

I believe your question was answered above by bhobba, when he stressed that the ensemble is a conceptual tool, not a physical entity, in cases where there is only one realization of the system under study (like the universe). In effect, an ensemble interpretation of the CMB is a multiverse picture, but it differs from the standard multiverse picture in the sense that it does not require we view the multiverse as something real, but rather as a conceptual device. The same could be said for how the ensemble interpretation regards Everett's many worlds. One can get all the expository benefits of Everett's picture using the ensemble picture, yet without holding that decohered subspaces of the unitary superposition continue to be real even after the decoherence has assured no information can cross between them. In short, the ensemble picture is what you get when you cross many-worlds with the CI, and notice that you can eliminate all the seeming contradictions by simply throwing out everything that requires taking QM mechanics "seriously" as a description of what is actually happening.

bhobba, can you confirm this? It seems different from Ballentine 1970 http://www.kevinaylward.co.uk/qm/ballentine_ensemble_interpretation_1970.pdf , p361: "Because this ensemble is not merely a representative or calculational device, but rather it can and must be realized experimentally"

 

[bhobba]

bhobba, can you confirm this? It seems different from Ballentine 1970 http://www.kevinaylward.co.uk/qm/ballentine_ensemble_interpretation_1970.pdf , p361: "Because this ensemble is not merely a representative or calculational device, but rather it can and must be realized experimentally"

Yea - I think I have mentioned a number of times that Ballentine seems to have changed his view between writing that paper and the book.

I gave the quote from his book that clearly shows he now views it as purely conceptual.

Thanks
Bill

 

[Maui]

You really have to distinguish between superpositions and multiple states at the same time. In classical electrodynamics, we have superpositions as well. This doesn't imply that there are multiple states. At a time t₀, a unique state is given by the electric field E(x,t₀), the magnetic field B(x,t₀) and their derivatives. In dBB, a unique state of a particle is given by its position x₀ and its guiding field ψ(x,t₀) (note that this doesn't depend on the system being "microscopic"). It doesn't make sense to claim that dBB is proven wrong by experiments which have reconstructed a certain ψ from their measurements unless dBB predicts a different ψ for this situation.

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. In DeBB every particle has a unique position at all times(the experiements I cited rule this out), whereas the wave spreads throughout the universe.

 

[kith]

It seems different from Ballentine 1970 http://www.kevinaylward.co.uk/qm/ballentine_ensemble_interpretation_1970.pdf , p361: "Because this ensemble is not merely a representative or calculational device, but rather it can and must be realized experimentally"

I'm not sure how big this difference really is. For example if you need multiple copies of the universe, your theory doesn't apply to the universe because you don't have these copies. The conceptual ensemble view applies but how would you determine the state of the universe? You can't even in principle because you would have to determine your own state, too. So I think these may be two sides of the same coin.

 

[kith]

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.

That's wrong. Please write down a superposition which is not a unique state.

 

[Maui]

I apologize for that. I will not post blogs again but if responses in your previous thread topic from both theoretical and experimental physicists did not convince you, then I have no hope in hell, since there's nothing I can add.

Do the SQUID experiments falsify Bohmian mechanics?
https://www.physicsforums.com/showthread.php?t=610085

Obviously you do not understand what the debate is about. The views are 100.00% opinions(expressed as facts) that are now even funnier to hold in light of the further experimental and practical developments in the field. But if you think someone's opinion and interpretations are what you are looking for and do not need to bother yourself with the details, ok.

 

[Maui]

That's wrong. Please write down a superposition which is not a unique state.

You can prepare an electron into a state where there is a 50/50 percent probability of finding it in a spin up or down state e.g.

|\psi> =(1/2)|up>+(1/2)|down>

 

[kith]

|\psi> =(1/2)|up>+(1/2)|down>

The unique quantum state of this superposition is |\psi>. So you are wrong.

 

[Nugatory]

a system in superposition does not have a unique state but occupies all possible quantum states simulataneously.

You've said this about 93 bazillion times now, but I still don't see how it makes sense when applied to even the simplest states. If I pass a particle through a horizontally oriented Stern-Gerlach device, and it is deflected to the right, is it not in the unique state "spin right"? And is it not also in a superposition of spin up and spin down?

 

[Maui]

The unique quantum state of this superposition is |\psi>. So you are wrong.

OK but the spin is not definite until a measurement is made. Care to address the point I made instead of delving into semantics?

 

[Nugatory]

You can prepare an electron into a state where there is a 50/50 percent probability of finding it in a spin up or down state e.g.

|\psi> =(1/2)|up>+(1/2)|down>

True, but the preparation procedure consists of passing the electron through a horizontally oriented Stern-Gerlach device, leaving it in the unique state $|right\rangle$.

 

[kith]

OK but the spin is not definite until a measurement is made. Care to address the point I made instead of delving into semantics?

This isn't about semantics at all but about the very core of the issue.

First of all, note that you have written "not definite" which is very different from your previous assertions that it is "both at once". If it is "not definite", we can supplement QM with something else to make it definite. dBB does this and unless you can derive contradictions with established experimental results from dBB, this point of view has to be valid.

Secondly, being "in" a superposition is not a property of the system. The system is in its unique quantum state. Whether this state is a superposition of eigenstates or not depends on the measurement you are going to perform. Your electron state "psi" is the eigenstate "up" of a certain alignment of the measurement apparatus (Nugatory called it "right" which is just a different name), the eigenstate "down" of another alignment and a superposition of eigenstates with respect to various other alignments. It all depends on the measurement you are going to perform.

 

[Ken G]

Yes, I think this discussion is bringing out the problems that appear when we think of a superposition as being a function of the system, rather than a function of the relationship between a preparing measurement and a concluding measurement, mediated by some system. The coordinates of a superposition are matrix elements like <i|f>, where <i| is the outcome of the preparing measurement, and |f> is the (presumably hypothetical) outcome of the concluding measurement. Quantum mechanics predicts those coordinates, interpreted as probability amplitudes. The system isn't "in" any of those states, the relationship is between measurements.

 

[kith]

The system isn't "in" any of those states, the relationship is between measurements.

This requires a very broad definition of measurement. For example I wouldn't call the interactions which lead to observable quantum effects in astrophysics "measurements".

 

[Ken G]

Yes, I don't mean to parse those kinds of distinctions, it certainly isn't easy to do so! For me, a "measurement" can be interpreted broadly, as any phenomenon that fits into the general language we use to interpret quantitative objectively studied outcomes, without itself necessarily being a quantitative objectively studied outcome.

 

[Len M]

There isn't. The junk you read in the popular press may be true. That's not the point, or why it generally makes me want to run away screaming - the point is they say it as if its the only view. A much more rational view exists - for example bog standard CI is much more rational than this observer created tripe - but they don't say it - because its not 'sensationalist' enough.

When was the last time you saw any populist book say Copenhagen assumes a world out there entirely common-sensical, trees make sounds when there is no observer, and all our every day intuition holds true? That's not going to sell is it - so they don't say it. But that is precisely what Copenhagen, and the Ensemble interpretation this thread is about says.

I understand that what you say above is entirely in the context of CI being miss represented, and it is within the outline of that interpretation you make the remarks concerning “observer created tripe” and “trees making sounds when there is no observer” and I don't want to detract from that at all.

However I would just like to step outside of any interpretation of QM and its relationship with our macroscopic reality and make just a few comments concerning those two remarks in the context of how I see realism, idealism and the role of physics.

I think that the falling tree and its sound is a much misunderstood scenario. What can we say about that scenario outside of phenomena? In the same vein, what can we say about the birth of stars before humans ever came on the scene? All we can actually say is that we extrapolate the experience of phenomena to these events as if there were a hypothetical sentient being present at the birth of the star and present when the tree falls. What actually exists without these hypothetical sentient beings present to record the experiences is unknown and will always be unknown because we cannot do physics without invoking observation and measurement which by definition invokes phenomena.

What (if anything) exists outside of phenomena belongs within mind independent reality. Thus, what exists outside of the falling tree or the birth of a star with no reference to phenomena (hence humans) is a matter for philosophical speculation and manifests itself in terms of various flavours of realism (or idealism if one thinks there is only phenomena). The philosophical stance one adopts, whether naive realism (a one to one relationship between mind independent reality and phenomena) or radical idealism (there is no mind independent reality only phenomena) cannot be judged to be right or wrong by anyone, rather those philosophical stances should be distinguished from what physics proper provides us within empirical reality (i.e. observer dependent reality) in terms of mathematical predictive models along with the interpretations involving interactions between phenomena.

 

[my2cts]

The advantage of Ballentine's is that is void of unnecessary and possibly unwarranted assumptions, so it is a good starting point for thinking about the interpretation of QM.

 

[bohm2]

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. In DeBB every particle has a unique position at all times(the experiments I cited rule this out), whereas the wave spreads throughout the universe.

As an aside, in BM there's a difference between the position operator and actual particle (Bohmian) position. The former is treated as all other operators as in usual QM (i.e. useful mathematical devices for calculation of statistics of experimental results).

 

[Cthugha]

Experiment says so, you live in the 1940's. Small scale prototypes of quantum computers have already been implemented and I posted links earlier in the thread.

Yes, I know. So what? That still does not back your point. You claim quantum computers need a certain interpretation of qm. They do not. They work just as well in interpretations without superposition like for example MWI (which I dislike just like BI).

That'd be all good if superpositions were not experimentally confirmed. You are completely wrong, that's why you turn this into what the maths of the BI says(it's the math that needs interpretation!). It's an interpretation, it's supposed to explain classical behavior and it does so using a pilot wave. No wonder you don't mention it anywhere.

Ehm, no. I have not been talking about what the math in BI says so far simply because I am not an expert on BI and do not intend to become one. I was talking about what the math of qm says - completely independent of applying any unnecessary interpretation.
Superpositions in the that sense: yes, they have found to be the mathematical model of choice. That still does not mean that people have shown that things exist in two states at once - people have shown the cool physics resulting from indistinguishability. I work in a lab trying to implement electron sins in quantum dots for quantum information purposes. The guys on that experiment really want to smash their head against the wall every time they hear this nonsense. I am working on superpositions in terms of vacuum Rabi oscillations and people in my field are also sick of that stuff. The point of view that particles really exist in two positions at once is rarely held by working physicists. Most experimentalists really do not care about how to interpret indistinguishability and the interferences that follow.

That's the same as asking for direct contact(touch) with the Sun to believe that it exists. And you know what you require is not possible but it's a shelter, when you have no other way out.

No, it is not. You are creating a straw man here.

What are you talking about? We are discussing superpositions of states and you are misinforming people that qm doesn't care about it. That's the ABC of qm, so what are you talking about?

Superposition of states is not the same as existing in two states at once. QM cares about linear superposition of states, but not about whether you want to consider the wave function as real and whether you want to interpret superpositions as two states being realized at the same time. If you think the latter is the abc of qm, I suggest picking up a good book on qm and learning what it really says about the meaning of indistinguishability.

How did it get to discussing collapse? What does it have to do with what I said?

Just another popular myth introduced by pop-sci summaries.

Can you please explain why the nonlocal guiding wave would mimic superpositions of states when a quasi-macro or macro system is isolated from the environment?

I am by no means an expert on BI, but if I remember correctly, the guiding wave acts as a potential and for ensembles of particles with unknown initial conditions as given by the uncertainty relation you end up with average trajectories equivalent to those governed by a probability distribution given by "things existing in two places at once". However, there are people on these forums who know that stuff way better than I do as I stick to the minimalist interpretation and do not care about going further. I agree that assuming weird trajectories seems artificial, but people have already shown experimentally that if you use weak measurements to examine the average(!) trajectories of single particles in a simple two-slit interference experiment, you really get these weird trajectories as the experimental result (see "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" by Kocsis et al., Science 332, 1170 (2011). Bare qm predicts the same weird average trajectories that BI does.

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.

As has been said before this is where you go wrong. There is nothing in QM which needs that. There is absolutely no reason to assume that a system is really in several states at once. There is also no reason against it. This is simply interpretation. Pure opinion. Or can you point out any experimental result supporting your point of view that one has to interpret qm your way? If so, please provide a reference.

 

[bhobba]

I think that the falling tree and its sound is a much misunderstood scenario. What can we say about that scenario outside of phenomena?

What I am talking about is the common sense view of the world that scientists and applied mathematicians more or less take for granted. What you are talking about is philosophical reflection which is something different again.

Now I don't want to run such down, it obviously interests those of a certain bent, but unless it leads to testable predictions it's not really science. That's why guys like me usually don't worry about it.

You are correct in the point I was making, but there was also another point. There is no need to depart from everyday commonsense ideas unless forced to do so. The exact departure from those ideas QM requires is often misrepresented.

Thanks
Bill

 

[bhobba]

Superpositions in the that sense: yes, they have found to be the mathematical model of choice. That still does not mean that people have shown that things exist in two states at once - people have shown the cool physics resulting from indistinguishability.

As has been said before this is where you go wrong. There is nothing in QM which needs that. There is absolutely no reason to assume that a system is really in several states at once. There is also no reason against it. This is simply interpretation. Pure opinion. Or can you point out any experimental result supporting your point of view that one has to interpret qm your way? If so, please provide a reference.

I think one of the issues here is the influence of older textbooks such as Dirac's Principles of Quantum Mechanics.

I actually learned proper QM from that book and Von Neumann's classic many moons ago - just after my degree over 30 years ago now - was it that long - seems like yesterday.

Anyway Dirac states the principle of superposition this way - from page 12:
'It requires us to assume that between these states there exists peculiar relationships such that whenever the system is definitely in one state we can consider it partly in each of two or more states'

The problem is that really is an interpretive statement not actually implied by the formalism. However it undoubtedly had a strong influence on a whole generation and permeated through such discussions as this in an unchallenged sort of way.

Contrast this with Ballentine's approach which doesn't really state such - it rather is encoded in his second axiom - given an observable A, the expected value of an observation represented by that observable is Trace (AP) where P is a positive operator of unit trace and is defined as the state. In fact that follows from the representation of observables as Hermitian operators via Gleason's Theorem. This engenders an entirely different view - the state is simply something required by the formalism to help us calculate the expected outcomes. Systems do not exist in states - its more like probabilities - which also help us calculate expected values. They too can be viewed as states by writing them as vectors. Coins, dices etc do not exist in such states - they are simply used to help us calculate long term averages of a large number of trials, events or whatever terminology you want to use. Viewed this way its an entirely different paradigm than Dirac's and IMHO much less likely to lead to confusion.

Thanks
Bill

 

[Maui]

Yes, I know. So what? That still does not back your point. You claim quantum computers need a certain interpretation of qm. They do not. They work just as well in interpretations without superposition like for example MWI (which I dislike just like BI).

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

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). So no, I did not claim what you I did.

Ehm, no. I have not been talking about what the math in BI says so far simply because I am not an expert on BI and do not intend to become one. I was talking about what the math of qm says - completely independent of applying any unnecessary interpretation.
Superpositions in the that sense: yes, they have found to be the mathematical model of choice. That still does not mean that people have shown that things exist in two states at once - people have shown the cool physics resulting from indistinguishability.

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.

I work in a lab trying to implement electron sins in quantum dots for quantum information purposes. The guys on that experiment really want to smash their head against the wall every time they hear this nonsense. I am working on superpositions in terms of vacuum Rabi oscillations and people in my field are also sick of that stuff. The point of view that particles really exist in two positions at once is rarely held by working physicists. Most experimentalists really do not care about how to interpret indistinguishability and the interferences that follow.

You can write a rebuttal to the researches that implemented the first quantum computer at MIT and the Institute of Waterloo because they say:

Superposition and Entanglement? Pardon?

It’s OK to be a bit baffled by these concepts, since we don’t experience them in our day-to-day lives. It’s only when you look at the tiniest quantum particles – atoms, electrons, photons and the like – that you see intriguing things like superposition and entanglement.

Superposition is essentially the ability of a quantum system to be in multiple states at the same time — that is, something can be “here” and “there,” or “up” and “down” at the same time.

Entanglement is an extremely strong correlation that exists between quantum particles — so strong, in fact, that two or more quantum particles can be inextricably linked in perfect unison, even if separated by great distances. the particles remain perfectly correlated even if separated by great distances. The particles are so intrinsically connected, they can be said to “dance” in instantaneous, perfect unison, even when placed at opposite ends of the universe. This seemingly impossible connection inspired Einstein to describe entanglement as “spooky action at a distance.”

Why do these quantum effects matter?

First of all, they’re fascinating. Even better, they’ll be extremely useful to the future of computing and communications technology.

Thanks to superposition and entanglement, a quantum computer can process a vast number of calculations simultaneously. Think of it this way: whereas a classical computer works with ones and zeros, a quantum computer will have the advantage of using ones, zeros and “superpositions” of ones and zeros. Certain difficult tasks that have long been thought impossible (or “intractable”) for classical computers will be achieved quickly and efficiently by a quantum computer.

http://iqc.uwaterloo.ca/welcome/quantum-computing-101

Superposition of states is not the same as existing in two states at once.

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.

 

[Maui]

First of all, note that you have written "not definite" which is very different from your previous assertions that it is "both at once".

Now I do again, it's in both states at once and my assertion is backed by experiment and technology already out there.

Your opinion is backed by what? Theory from the 1930's or your personal preference?

Spin based quantum computing has already been implemented:

http://iqc.uwaterloo.ca/faculty-research/spin-based-quantum-information-processing

 

[Jano L.]

Sorry, I don't see how your explanation shows that two electrons that are shared and on unique trajectories between two atoms can hold the two atoms together.

I do not see that exactly either, unfortunately. The only directly understandable thing is that the Coulomb interaction for proton-electron is attractive, while the surrounding noise may allow the electrons to assume large range of possible states to conform to Schr. equation.

But I do not see the converse either; it is equally hard to prove that the electrons cannot move in trajectories. Since trajectories make a lot of sense otherwise, I prefer to assume they retain their validity. So it is just one of possible viewpoints.

The assertion that electrons follow unique trajectories(i.e. they are not in superposition of states)

Here you probably meant "at many places at the same time" instead of "superposition of states". The difference is the former refers to the electron, the latter to the function $\psi$ describing it (or more correctly, describing a system of many electrons and protons).

As you may have inferred from the above discussion, the view that superposition implies "being at many different states at the same time" has no solid ground in the mathematical theory. It is just something somebody once said and it was so mysterious that journalists keep writing it down to make their articles look "cool", while they only make them inaccurate.

...the paper you referenced that claims that background radiation keeps atoms from falling apart is wild speculation, not fact...

I did not claim it a fact. The paper assumes it to show its implications in the EM theory of point-like electron. Zero-point field (ZPF) is an additional assumption in the classical EM theory and necessary consequence of the commutation relations in quantum theory, of great explanatory value and proven success.

In classical theory, ZPF is the most natural thing to maintain charged particles in non-zero mutual distance and to prevent the infamous atomic collapse. In quantum theory, it is necessary to maintain commutation relations in time (see P. W. Milonni, Quantum Vacuum: An Introduction to Quantum Electrodynamics, Academic Press 1994, sec 2.6), which is motivated by the same reason.

It may be that our current picture of the zero-point field is inaccurate, for example the high-frequency tail of its spectrum, and the physical significance of the spectrum itself, but it is a fruitful idea that will stay with us for some time. Without it, we have little ideas left to explain why the atomic systems maintain their stable average size.

There are areas where high levels of cosmic or environmental radiation are very unlikely to be found(e.g. the Earth's core) ...

Not necessarily. The ZPF field is $assumed$ to be present everywhere, even in the Earth's core. Can you prove that is inconsistent with the basic equations? Maxwell's equations are linear, which means their solution can contain homogeneous solution which is uniform and isotropic in space. Can you show the presence of the matter will shield this kind of noisy field inside the Earth? Noise is hard to shield, especially its higher frequencies.

 

[kith]

Now I do again, it's in both states at once and my assertion is backed by experiment and technology already out there.

Yet still you haven't managed to show us the math of how dBB is supposed to fail. Curious, isn't it? I think I'm done with this discussion.

 

[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.