Is the collapse indispensable?

[atyy]

Not true.

Proof: The half-integral spectrum of quantum angular momentum is independent of the observer, hence objective. But that spectrum arises from representing rotational symmetry on a Hilbert space. Hence the Hilbert space is not subjective. $\Box$

The Hilbert space is subjective because the Hilbert space depends on the division of the universe into the unreal quantum part (described by a vector in Hilbert space) and the real classical part (not described by a vector in Hilbert space).

 

[strangerep]

The Hilbert space is subjective because the Hilbert space depends on the division of the universe into the unreal quantum part (described by a vector in Hilbert space) and the real classical part (not described by a vector in Hilbert space).

That would mean half-integral quantum angular momenta are "unreal". To disprove this, one must derive the half-integral spectrum using purely classical means. (Good luck.)

 

[atyy]

That would mean half-integral quantum angular momenta are "unreal". To disprove this, one must derive the half-integral spectrum using purely classical means. (Good luck.)

Is there anything wrong with half-integral quantum angular momenta being "unreal"?

 

[strangerep]

Is there anything wrong with half-integral quantum angular momenta being "unreal"?

That sounds like a very fine drop of port you're enjoying right now.

[ @Greg Bernhardt : we need another icon in your enhanced list: something portraying a party girl staggering around enjoying herself... ]

[Edit: Let us terminate this subdiscussion, lest we offend the OP and moderators.]

 

[atyy]

That sounds like a very fine drop of port you're enjoying right now.

[ @Greg Bernhardt : we need another icon in your enhanced list: something portraying a party girl staggering around enjoying herself... ]

Not any little girl. Has to be this one.

 

[bhobba]

In my view the big mistake in QM interpretation has been assuming that all QM dynamics must be unitary.

I don't know if its a big mistake, but I do believe that it must be unitary is open to question. Curios though about the status Wigners theorem if it isn't.

See my (peer-reviewed) papers and books for presentation of the TI alternative. Yes, the direct-action theory has been ignored and marginalized for quite some time, but there is nothing wrong with it. In fact John Wheeler was enthusiastically endorsing it in 2003, see e.g.: http://www.ijqf.org/archives/2004

Of course its a valid interpretation. But these things go thorough fads etc for no apparent reason. My favourite interpretation, ignorance ensemble, virtually no one knows about. And there are many others like that eg primary state diffusion. I don't think its anything to get worried about.

Thanks
Bill

 

[zonde]

How is the "collapse of the state" observable? I'm not aware of any example.

You are inventing your own rules.
Here are the rules: if a model makes consistent predictions and predictions are tested and verified in experiment it's valid for now.
So the only question is whether collapse is indispensable part of valid model (QM).

 

[vanhees71]

If this is so, then it should be easy for you to provide an example for a real experiment, where you need the collapse hypothesis to describe its result within quantum theory. I don't know of any. So far, the most simple description is in terms of the minimal interpretation. You just take the Born rule as one more independent assumption, i.e., the quantum mechanical state describes probabilities for the outcome of measurements and nothing more.

 

[atyy]

If this is so, then it should be easy for you to provide an example for a real experiment, where you need the collapse hypothesis to describe its result within quantum theory. I don't know of any. So far, the most simple description is in terms of the minimal interpretation. You just take the Born rule as one more independent assumption, i.e., the quantum mechanical state describes probabilities for the outcome of measurements and nothing more.

Challenge: Derive the generalized Born rule from the Born rule, but without using collapse!

 

[vanhees71]

What's the "generalized Born rule". For me the Born rule is a postulate saying that for any state, represented by a statistical operator $\hat{R}$ the outcome of the measurement of an observable $A$ to be the value $a$, represented by a self-adjoint operator $\hat{A}$ defining a (generalized) orthonormalized eigenvector basis $|a,\beta \rangle$ is given by
$$P_A(a|\hat{R})=\sum_{\beta} \langle a,\beta|\hat{R}|a,\beta \rangle,$$
where the sum can also be an integral or both a sum and an integral, depending on the specific spectral properties of $\hat{A}$.

For me that's a postulate and nothing that can be derived. Weinberg has given a thorough analysis of whether the Born rule is derivable from the other postulates (all well hidden above ;-)) coming to the conclusion that it can't be derived. I don't need an assumption about what happens to the state of the system due to the interaction between the measured object and the measure device, and I can't give a general one, because of course it depends on the details of this device. For sure I don't need a collapse for formulate the Born rule. It simply tells me that I have to do the measurement on a large ensemble of equally stochastically independent prepared systems to check whether the prediction of the Born rule concerning the probabilities is correct or not (within a given significance according to standard statistical rules).

 

[atyy]

What's the "generalized Born rule". For me the Born rule is a postulate saying that for any state, represented by a statistical operator $\hat{R}$ the outcome of the measurement of an observable $A$ to be the value $a$, represented by a self-adjoint operator $\hat{A}$ defining a (generalized) orthonormalized eigenvector basis $|a,\beta \rangle$ is given by
$$P_A(a|\hat{R})=\sum_{\beta} \langle a,\beta|\hat{R}|a,\beta \rangle,$$
where the sum can also be an integral or both a sum and an integral, depending on the specific spectral properties of $\hat{A}$.

For me that's a postulate and nothing that can be derived. Weinberg has given a thorough analysis of whether the Born rule is derivable from the other postulates (all well hidden above ;-)) coming to the conclusion that it can't be derived. I don't need an assumption about what happens to the state of the system due to the interaction between the measured object and the measure device, and I can't give a general one, because of course it depends on the details of this device. For sure I don't need a collapse for formulate the Born rule. It simply tells me that I have to do the measurement on a large ensemble of equally stochastically independent prepared systems to check whether the prediction of the Born rule concerning the probabilities is correct or not (within a given significance according to standard statistical rules).

The generalized Born rule is Eq 37 on p67 of http://arxiv.org/abs/quant-ph/0209123 .

 

[vanhees71]

No having read the complete paper, I think that's just the description of a measurement at time $t_2$ after performing an ideal von Neumann filter measurement at $t_1<t_2$. Where do you need a collapse here? It's just filtering out subensembles. I just need to block beams, i.e., local interaction of the partial beams with some "beam dumps", not an instantaneous collapse of whatever. One must not loose the foundation of physics in real-world setups of experiments to the abstract formalism! Then all esoterics concerning "interpretation" is usually absent from our description of this real-world experiments.

 

[atyy]

No having read the complete paper, I think that's just the description of a measurement at time $t_2$ after performing an ideal von Neumann filter measurement at $t_1<t_2$. Where do you need a collapse here? It's just filtering out subensembles. I just need to block beams, i.e., local interaction of the partial beams with some "beam dumps", not an instantaneous collapse of whatever. One must not loose the foundation of physics in real-world setups of experiments to the abstract formalism! Then all esoterics concerning "interpretation" is usually absent from our description of this real-world experiments.

Well, that's the Peres and Ballentine claim. Is it correct that with only unitary evolution you can derive collapse? Till this day you have never exhibited a derivation, neither have Peres nor Ballentine. It's a pity that quantum mechanics is still not understood even by experts.

 

[vanhees71]

Well, I'm pretty sure I cannot described a "beam dump" in all microscopic detail, but that's not necessary to know that fact that it filters out unwanted beams! Why should I derive something unobservable and unneeded like the collapse from QT?

 

[atyy]

Well, I'm pretty sure I cannot described a "beam dump" in all microscopic detail, but that's not necessary to know that fact that it filters out unwanted beams! Why should I derive something unobservable and unneeded like the collapse from QT?

The collapse gives the correct prediction of your uncalculatable filtering. Which should I take - collapse which makes the prediction, or filtering which you cannot calculate?

 

[vanhees71]

The collapse gives the correct prediction of your uncalculatable filtering. Which should I take - collapse which makes the prediction, or filtering which you cannot calculate?

I prefer just to use the projection operators as given in the text without assuming an instantaneous collapse, which violates fundamental principles of physics like causality.

 

[atyy]

I prefer just to use the projection operators as given in the text without assuming an instantaneous collapse, which violates fundamental principles of physics like causality.

So you do accept the collapse as necessary, just not its physicality!

In the standard interpretation, collapse is not necessarily physical.

However, the physicality of collapse cannot be rejected on the basis of relativistic causality.

 

[vanhees71]

There is no collapse in this very expression! It's just filtering out unwanted states, which is precisely described by the projection operators (for an idealized filtering). The filtering itself is not due to instantaneous action at a distance but due to local interactions (at least as long as you consider standard relativistic QFT as a correct (effective) description of nature). I'm so strictly against the collapse assumption, because it denies the fundamental property of the locality of interactions in standard relativistic QFT and it assumes dynamics outside of quantum theory.

 

[atyy]

There is no collapse in this very expression! It's just filtering out unwanted states, which is precisely described by the projection operators (for an idealized filtering). The filtering itself is not due to instantaneous action at a distance but due to local interactions (at least as long as you consider standard relativistic QFT as a correct (effective) description of nature). I'm so strictly against the collapse assumption, because it denies the fundamental property of the locality of interactions in standard relativistic QFT and it assumes dynamics outside of quantum theory.

Sorry, this is just wrong.

 

[ddd123]

Sorry, this is just wrong.

Maybe he means something like this? http://arxiv.org/abs/hep-th/0205105

 

[atyy]

vanhees71 is wrong for the following reasons.

1. Unitary evolution and the "filtering" that he imagines will allow the projection to be derived cannot do it, because the unitary evolution and partial trace caused by the "filtering" only produce an improper mixture. To get the definite outcome, one must further assume that the improper mixture is converted to a proper mixture, which is the same as assuming collapse. Ballentine and Peres are probably missing this assumption in their erroneous books.

2. The "locality" of QFT that is enforced by the "local" interactions has the meaning of "no superluminal transmission of classical information" (and a little more). It does not mean local interactions and local causality. vanhees71 consistently confuses multiple meanings of "local".

3. Collapse is consistent with the "locality" of quantum field theory. It is not consistent with relativistic causality, but neither is quantum field theory.

 

[A. Neumaier]

Ballentine and Peres are probably missing this assumption in their erroneous books.

I think you should moderate your language.

The books by Ballentine and Peres are highly respectable books that provide all the information one ever needs to understand the basics of quantum mechanics in theory and practice. Calling them erroneous based on your own subjective view of the interpretation issues is inappropriate.

Your arguments are not that impeccable that you would be justified to call their treatment erroneous. (Write your own book and you'll see that it will most likely contain even more glaring problems.)

 

[atyy]

I think you should moderate your language.

The books by Ballentine and Peres are highly respectable books that provide all the information one ever needs to understand the basics of quantum mechanics in theory and practice. Calling them erroneous based on your own subjective view of the interpretation issues is inappropriate.

Your arguments are not that impeccable that you would be justified to call their treatment erroneous. (Write your own book and you'll see that it will most likely contain even more glaring problems.)

I'm quite sure I am right, and the standard interpretation is done that way for good reasons. Ballentine and Peres are wrong.

 

[A. Neumaier]

I'm quite sure I am right, and the standard interpretation is done that way for good reasons. Ballentine and Peres are wrong.

Ballentine and Peres were also sure of what they wrote (this is visible from how they defend it elsewhere in their publications). Moreover, the way they wrote it was done for good reasons.

So it is view against view. In such a case the credentials count, and you as an outsider should be temperate about your bold assertions.

By the way, there is no standard interpretation. You probably mean your favorite interpretation, or your favorite version of the Copenhagen interpretation.

 

[ddd123]

Unitary evolution and the "filtering" that he imagines will allow the projection to be derived cannot do it, because the unitary evolution and partial trace caused by the "filtering" only produce an improper mixture. To get the definite outcome, one must further assume that the improper mixture is converted to a proper mixture, which is the same as assuming collapse. Ballentine and Peres are probably missing this assumption in their erroneous books.

Wouldn't it be strange if they missed it? A book cannot contain every retort to every attack, maybe they've elaborated further on this, elsewhere.

 

[atyy]

Ballentine and Peres were also sure of what they wrote (this is visible from how they defend it elsewhere in their publications). Moreover, the way they wrote it was done for good reasons.

So it is view against view. In such a case the credentials count, and you as an outsider should be temperate about your bold assertions.

By the way, there is no standard interpretation. You probably mean your favorite interpretation, or your favorite version of the Copenhagen interpretation.

I am not an outsider. I am stating that the standard texts are right.

Ballentine and Peres are the outsiders.

 

[atyy]

Wouldn't it be strange if they missed it? A book cannot contain every retort to every attack, maybe they've elaborated further on this, elsewhere.

Wouldn't it be strange if standard quantum mechanics were wrong? Wouldn't it be strange if even Nielsen and Chuang were wrong?

 

[ddd123]

Wouldn't it be strange if standard quantum mechanics were wrong? Wouldn't it be strange if even Nielsen and Chuang were wrong?

I have no idea :D
I guess we should just stick to the pure arguments (or rather, you, I'm too low level).

 

[A. Neumaier]

I am not an outsider. I am stating that the standard texts are right.

Ballentine and Peres are the outsiders.

Which standard texts are you referring to? Who but you decided that they are the standard?

These two books, together with the commented reprints in Wheeler and Zurek, are the modern standard! (There is also decoherence theory, which is newer than these; but this is silent on collapse.) They devote considerable space to the foundations, whereas typical textbooks on quantum mechanics only have short sections where they parrot what they glean from elsewhere, often from the long past.

 

[ddd123]

I'm afraid this thread is at risk of getting closed. Would be a pity if nobody actually answered or provided a source with an answer to atyy's point I quoted in post #104.

 

[A. Neumaier]

To get the definite outcome, one must further assume that the improper mixture is converted to a proper mixture, which is the same as assuming collapse.

Could you please (possibly in a new thread) explain these terms and how you think the conclusion follows, according to your understanding, so that your statement can be critically discussed?

 

[atyy]

Which standard texts are you referring to? Who but you decided that they are the standard?

These two books, together with the commented reprints in Wheeler and Zurek, are the modern standard! They devote considerable space to the foundations, whereas typical textbooks on quantum mechanics only have short sections where they parrot what they glean from elsewhere, often from the long past,

That is not correct. Wheeler and Zurek are research papers. Incidentally, Zurek states standard QM with collapse. His attempt at Quantum Darwinism is a research attempt to remove collapse. Removing collapse from QM is not standard, but a matter of research till this day, and is BTSM.

Standard texts include Landau & Lifshitz; Cohen-Tannoudji, Diu & Laloe; Nielsen & Chuang; Sakurai; Weinberg; Holevo.

 

[kith]

So you do accept the collapse as necessary, just not its physicality!

I wouldn't say that the use of projection operators necessarily needs a justification. If we use the quantum description for the full filtering system, the final state is a superposition which contains a term where the particle leaves the apparatus and a term where the particle is trapped inside the apparatus. The second term has zero overlap with states localized outside the apparatus. So the Born rule gives a probability of zero for all outcomes of all future measurements for the second term. So the predictions are the same whether we use both terms or only the first. In this case, the use of a projection operator to get rid of the second term is purely a matter of convenience.

I thought that you and I had already reached agreement on something similar in an older thread. The conclusion I remember is that we need more sophisticated situations like Bell tests to analyze whether collapse is necessary or not.

 

[atyy]

I wouldn't say that the use of projection operators necessarily needs a justification. If we use the quantum description for the full filtering system, the final state is a superposition which contains a term where the particle leaves the apparatus and a term where the particle is trapped inside the apparatus. The second term has zero overlap with states localized outside the apparatus. So the Born rule gives a probability of zero for all outcomes of all future measurements for the second term. So the predictions are the same whether we use both terms or only the first. In this case, the use of a projection operator to get rid of the second term is purely a matter of convenience.

I thought that you and I had already reached agreement on something similar in an older thread. The conclusion I remember is that we need more sophisticated situations like Bell tests to analyze whether collapse is necessary or not.

I thought we had agreed that collapse was not necessary provided that successive measurements were not made, eg. using something like the https://en.wikipedia.org/wiki/Deferred_Measurement_Principle.

 

[A. Neumaier]

Standard texts include Landau & Lifshitz; Cohen-Tannoudji, Diu & Laloe; Nielsen & Chuang; Sakurai; Weinberg; Holevo.

Why are they today's standard regarding the foundations, while Ballentine and Peres are not? What is the criterion that makes them standard?

None of these except perhaps Holevo (would have to check) specializes on the foundations but treats it in a very short way, that disqualifies it as a standard. For example Nielsen & Chuang devote just 16 pages (Section 2.2) to the topic, out of a total of over 600 pages. And even in these pages they cover a lot of ground, not just the postulates and their discussion.

The collapse is a frequently used textbook device simply because it is a convenient starting point, allowing one to bridge the abyss of quantum foundations in a few words, in agreement with the early history but without having to spend time on getting it fully correct.

You never find it discussed in a quantum field theory book, which is the true foundation of modern theoretical physics. Here everything is in terms of (in principle measurable) correlation functions, which is enough for all uses of quantum mechanics and quantum field theory in the applications.