When Quantum Mechanics is thrashed by non-physicists #1

[bhobba]

Do you agree that statistical ensemble interpretation of QM requires that something which is not a wave function must exist?

Of course it does - the ensemble is a conceptualisation of the outcomes of an observation.

What's the difference between that and viewing the length of a queue in a statistical modelling problem as an ensemble of possible lengths? What its the length of is not germane to the model.

Thanks
Bill

 

[atyy]

Its pretty well known eg
http://en.wikipedia.org/wiki/Wave_function_collapse
On the other hand, the collapse is considered a redundant or optional approximation in:
the Consistent histories approach, self-dubbed "Copenhagen done right"
the Bohm interpretation
the Many-worlds interpretation
the Ensemble Interpretation

In the ensemble interpretation state and preparation procedure are the same thing. If you have a filtering type observation all you have done is prepared the system differently. I suppose to some extent if that's the same as collapse or not depends on what you mean by collapse. I side with it isn't because it's consistent with the Bohmian interpretation and it doesn't have collapse. Indeed in Ballentine's original paper some say its really BM in disguise. I don't think it is, but he did express it a bit poorly in that paper - and it has been corrected in his textbook.

Thanks
Bill

One needs an aditional postulate beyond {unitary evolution + Born rule without collapse}.

Ballentine's book is immensely problematic, but he does postulate collapse in Eq 9.28, where he gives the quantum state after obtaining a classical result in a filtering measurement.

 

[Demystifier]

Of course it does - the ensemble is a conceptualisation of the outcomes of an observation.

What's the difference between that and viewing the length of a queue in a statistical modelling problem as an ensemble of possible lengths? What its the length of is not germane to the model.

That, of course, is obvious to me, but apparently not to vanhees.

 

[vanhees71]

Not at all, but maybe the right answer lies in post #117.

Of course, I meant that it's clarified what I think. I don't expect that we can find a conclusion about these issues.

 

[Demystifier]

Of course, I meant that it's clarified what I think.

If that means that you think that wave function exists syntactically while observations exist ontologically, and that we can't be certain how to relate these two types of existence, than it's clear.

 

[rubi]

Would all philosophers agree with you on that? For example would Penrose agree with that - he believes the mathematics is the only reality - what we experience is just a platonic shadow of that reality.

Philosophers rarely agree on anything, so I doubt that all philosophers agree on this. :D However, I'm not enough of a philosopher to answer that question.

So the path traced out by a ball is just a string of symbols on a bit of paper. Actually it can be modeled by all sorts of things.

Well, I'm making a difference between the path of the ball that you can see with your eyes and the mathematical object that we use for its description. Unfortunately, we refer to both things using the word "path".

You are making good points!

So, would you say that the fight between "physicists" and "philosophers" on the meaning of quantum theory is to a large extent caused by the fact that they are not aware that they talk about two different types of "existence"?

I'm not an expert in the philosophy of physics, so I don't know to what extent this fight is caused by this unawareness, but at least in the discussions I'm having, this unawareness plays a big role (in my opinion).

 

[bhobba]

That, of course, is obvious to me, but apparently not to vanhees.

Yea - but is it germane to the issue. Its simply something you unconsciously do when you apply it. Its all part of the modelling process.

Its like good old Euclidean geometry. A point is this abstract thing with position and no size but when we apply it its applied to all sorts of things that are not that. That in no way changes it validity.

In the ensemble interpretation a state is the equivalence class of all preparation procedures that have the same statistical observational outcomes.

Added Later
After re-reading it I think I need to make it clear I am in zero doubt Vanhees is well aware of this rather obvious point.

Thanks
Bill

 

[Demystifier]

I'm not an expert in the philosophy of physics, so I don't know to what extent this fight is caused by this unawareness, but at least in the discussions I'm having, this unawareness plays a big role (in my opinion).

In my opinion too. Thanks for pointing this out!

 

[bhobba]

Philosophers rarely agree on anything, so I doubt that all philosophers agree on this. :D However, I'm not enough of a philosopher to answer that question.

Whenever I discuss philosophy with actual philosophers I get done like a turkey dinner so I certainly don't know the answer except they never seem to a reach a conclusion on anything.

But I did agree with the one bit of what you wrote that I quoted.

Thanks
Bill

 

[Ilja]

As you know, the position basis has a preferred role in dBB, which some people consider to be a problem. You will probably agree with me that this is not a problem for non-relativistic QM, but a generalization of dBB to relativistic quantum field theory is much more problematic. Does the preferred basis fixes a preferred Lorentz frame? If yes, which one? Should the preferred basis be associated with particles or fields? If it is fields, then what about fermions? If it is particles, then what about Unruh effect and curved spacetime? These are all non-trivial questions and neither of the proposed answers (including yours and mine) is without problems.

I don't see a preferred role for "positions", but for the configuration. But it is, of course, not a problem, but an axiom. And to prefer configuration over momentum is also done in the classical Lagrange approach, which looks much more natural compared with the Hamilton formalism.

And in the relativistic situation, there is also nothing to choose. The theory has a time parameter, which is given, by the axioms. Then it appears that the Hamilton operator, and, as a consequence, some observable probabilities, show some additional strange Lorentz symmetry, which does not have a base in the theory itself. So there is no point where one has to "choose" a preferred frame.

You may have to choose a preferred frame if you want to connect the theory with particular experiments, with the world around us. But this is nothing the theoretician has much to care about. If there are two different possible choices, above in agreement with observation, fine, the theory is not falsified. Point.

Of course, what is preferred is the configuration - whatever it is. In relativistic field theories, one could use a field as the configuration, this is nice because the relativistic Lagrangian for a field is quadratic in momentum, so that straightforward Bohmian method goes through. Now, there is the (not very beautiful IMHO) possibility to use only a part of the configuration as the "Bohmian configuration" - some people like this for incorporating spin into a particle picture, I don't. So I would suggest to use the whole configuration space.

What is the classical configuration space for fermions? A good question. My personal answer is given in section 5 of http://arxiv.org/pdf/0908.0591.pdf which shows that one can obtain fermionic fields starting from a classical configuration space. The fermion will be obtained together with a massive scalar field, but this does not seem to be a problem, even an advantage -- dark matter candidates.

So, I would say that certainly the choice of the configuration space of a theory is a problem. And this problem is more serious in dBB theory than in standard QFT, because the dBB interpretation prefers a Hamiltonian quadratic in momentum, while other approaches do not have to care about this at all. But it has nothing to do with the conceptual "preferred basis problem" of other interpretations. Because the answer is clear - what is preferred is the classical configuration.

 

[Ilja]

You're right, that giving up relativity (as the Bohm-DeBroglie interpretation does) is a way out, but it isn't a satisfying way out because there is no experimental justification for such a leap. There is absolutely no experimental support for the existence of a preferred frame.

But is there any experimental support for giving up realism (in the form used by Bell in his theorem)? Or causality (in a form including Reichenbach's principle of common cause, which would also be sufficient to prove Bell's inequality)? In above cases, quantum effects by themself are no such evidence, because dBB gives a version which is compatible with realism and causality.

So, the "no experimental evidence for the breakdown" argument can be applied by the conflicting principles - realism and causality - too.

Once we have - with the violation of Bell's inequality - a conflict between fundamental relativity, on the one hand, and realism and causality, on the other hand, we have to decide what we have to throw away. And the situation where it is almost forbidden to argue that realism and causality should be preserved, and fundamental relativity thrown away, is not very satisfactory.

Last but no least, relativistic symmetry appears automatically if we have only a single universal wave equation for all observable fields. Therefore, it can be easily obtained as an effective symmetry without fundamental character.

 

[stevendaryl]

But is there any experimental support for giving up realism (in the form used by Bell in his theorem)? Or causality (in a form including Reichenbach's principle of common cause, which would also be sufficient to prove Bell's inequality)?

No, I don't think any of the options for making sense of QM are satisfactory.

The violation of Lorentz invariance, though, is particularly strange. You're assuming the existence of something and you're also assuming that the laws of physics conspire to make it impossible to detect. In most cases like that, such as the undetectability of the phase of the wave function, you can assume that the physical state is an "equivalence class" of indistinguishable alternatives. I don't know if that would work to remove the frame dependence of Bohm-DeBroglie, or not.

Once we have - with the violation of Bell's inequality - a conflict between fundamental relativity, on the one hand, and realism and causality, on the other hand, we have to decide what we have to throw away. And the situation where it is almost forbidden to argue that realism and causality should be preserved, and fundamental relativity thrown away, is not very satisfactory.

Last but no least, relativistic symmetry appears automatically if we have only a single universal wave equation for all observable fields. Therefore, it can be easily obtained as an effective symmetry without fundamental character.

Okay. Well if the appearance of Lorentz invariance can be derived from some more fundamental assumption in a natural way, then I can more easily accept giving it up as an approximate symmetry.

 

[Ilja]

I don't know if that would work to remove the frame dependence of Bohm-DeBroglie, or not.

The violation of Bell's inequality requires a preferred frame for realistic causal theories. It requires an explanation (Reichenbach's principle), and this explanation can be A \to B or B \to A because the common cause itself is unable to violate Bell's inequalities. So, if you want a causality without causal loops, you have to decide which of the two possibilities is correct. And the correct choice is hidden. Such is life.

Well if the appearance of Lorentz invariance can be derived from some more fundamental assumption in a natural way, then I can more easily accept giving it up as an approximate symmetry.

No problem, see the derivation of the EEP in http://arxiv.org/abs/gr-qc/0205035 Alternatively, think about a theory where we have, for reasons of simplicity, only one wave equation for all fields, which is essentially what we have. Then, everything you have, all what you can use to measure something, can influence any other events only through this same wave equation. This also gives you immediately local Lorentz invariance. I would guess you can derive this yourself. But this unique wave equation for all fields may be, of course, an approximation, which fails on the atomic scale of such an ether, and possibly also for extremely large energies of the waves.

 

[Demystifier]

If there are two different possible choices, above in agreement with observation, fine, the theory is not falsified.

But if there are two possible choices, and Bohmian theory requires to pick only one, don't you see that as a problem? The whole idea of Bohmian mechanics is not only to agree with observations (for that purpose the standard QM is also fine), but also to offer a reasonable ontological picture of the world. On the other hand, the two different choices propose two different ontological pictures of the world, which is a problem because then the existence of competitive pictures implies that neither of the pictures is sufficiently reasonable by itself.

 

[atyy]

Hmm, why not say that the purpose of BM is to disagree with QM at some level? Then it doesn't matter how ugly it is, since experiment will pick. And then we can say to all non-believers in reality, "nature doesn't care what we like" :)

If they say that "nature doesn't care what we like" also means maybe hardcore non-real Copenhagen may be true, we can just ask what they mean by "nature" and "we".

 

[vanhees71]

If that means that you think that wave function exists syntactically while observations exist ontologically, and that we can't be certain how to relate these two types of existence, than it's clear.

I think that pure quantum states are represented by rays in Hilbert space and that their physical meaning is given by Born's rule. What ontologically "exists" and what thus defines states physically is an equivalence class of "preparation procedures" that put the described system into this state.

 

[Demystifier]

So, I would say that certainly the choice of the configuration space of a theory is a problem. ... But it has nothing to do with the conceptual "preferred basis problem" of other interpretations.

As I said, the "preferred basis problem" takes different forms in different interpretations. But I don't think they have nothing to do with each other. In particular, a choice of configuration can also be viewed as a choice of basis, as a generalization of the fact that the the usual choice of configuration x can be viewed as a choice of the basis |x>.

 

[Demystifier]

What ontologically "exists" and what thus defines states physically is an equivalence class of "preparation procedures" that put the described system into this state.

It's important to clarify the meaning of certain terms we use, and I don't think that this kind of existence would be called "ontological" by philosophers of physics. In this context, by ontological existence one would mean individual preparations, not the equivalence class of similar preparations.

On the other hand, QM in its statistical ensemble form says nothing about individual preparations. In this sense QM in the statistical ensemble form is not complete, because individual preparations obviously exist (ontologically), and yet the theory says (syntactically) nothing about them.

This proves that QM in the statistical ensemble form is not ontologically complete. A possible way to stop worry about that is to assume that QM in the statistical ensemble form is at least syntactically complete, i.e. that syntax (formal mathematical theory) correctly describing individual preparations - does not exist. But such an assumption is not very well grounded, especially with a known counter-example candidates such as Bohmian mechanics, many-worlds, and objective-collapse theories.

 

[vanhees71]

I don't see a problem in this since I don't think that our contemporary physical models are complete in any sense. :-)

 

[Demystifier]

Hmm, why not say that the purpose of BM is to disagree with QM at some level? Then it doesn't matter how ugly it is, since experiment will pick. And then we can say to all non-believers in reality, "nature doesn't care what we like" :)

It's too easy to construct ugly theories which disagree with QM at some experimentally testable level. For example, one such extremely ugly "theory" is that QM is always right except when experiments are performed on the dark side of the Moon, and future experiments can decide if that theory is true.

The reason why so many people like non-relativistic BM is that this theory does not look ugly to them.

 

[Demystifier]

I don't see a problem in this since I don't think that our contemporary physical models are complete in any sense. :)

That's a healthy attitude. But isn't it essentially the same as saying:
- OK, some kind of hidden "variables" (not necessarily deterministic and perhaps not even expressible by mathematics) are likely to exist, even if at the moment I cannot say anything specific about them.

 

[Ilja]

But if there are two possible choices, and Bohmian theory requires to pick only one, don't you see that as a problem? The whole idea of Bohmian mechanics is not only to agree with observations (for that purpose the standard QM is also fine), but also to offer a reasonable ontological picture of the world. On the other hand, the two different choices propose two different ontological pictures of the world, which is a problem because then the existence of competitive pictures implies that neither of the pictures is sufficiently reasonable by itself.

Different ontological pictures are, IMHO, not a problem at all. First, it is also important that we know what we don't know. So, if there are two different ontological pictures, it means, we don't know which is the true one. Such is life. We cannot know everything.
On the other hand, if all the ontological pictures share some interesting properties, this at least increases the plausibility that this shared property is correct. Or, in other words, there may be many different ontological possibilities, but they all present a similar nice picture.

In particular, why should I care which of the frames is the preferred one? Whatever it is, the resulting picture looks similar. And the question which is more interesting is if this picture looks better than that of a four-dimensional spacetime or not.

 

[Ilja]

Hmm, why not say that the purpose of BM is to disagree with QM at some level? Then it doesn't matter how ugly it is, since experiment will pick.

The point of considering interpretations is, essentially, that they ultimately tend to disagree. The point is that they usually have problems. And how are these problems solved? By a modification of the theory, of course. And after this, the "interpretation" is no longer an interpretation but a different theory.
There are, for example, interpretations using the "hydrodynamic variables" (which would better be named probability flow variables). These interpretations have a problem - the Wallstrom objection. A variant of this problem is that they have infinities - near the zeros of the wave function, the velocity of the flow becomes infinite.
These two problems can be solved by regularization: http://arxiv.org/abs/1101.5774 but the regularized theory is already a different one.

Another example. The theory proposed in http://arxiv.org/abs/gr-qc/0205035 started as an interpretation of GR - with harmonic coordinates as preferred coordinates. This interpretation had a problem - an additional equation, thus, the whole set is no longer derived from a Lagrange formalism. The problem was solved, by adding a term which leads to the harmonic condition as the equation. Problem solved - but, action equals reaction, now the original Einstein equations obtained a modification too. Thus, the theory was no longer GR in harmonic coordinates, but different.

A third one. So we have the equations, and now we add an ether interpretation. The key is the ether density defined by \rho=g^{00}\sqrt{-g}. Nicely, if the density is positive, the time coordinate is time-like. Unfortunately, the equations themself do not care. Solutions are imaginable where the density is initially positive everywhere, but becomes somewhere negative.

What to do? The ether interpretation can be preserved by modifying the theory. The regions where the ether density becomes negative are considered physically invalid, the places where this happens are considered as places where the ether tears into parts - and the continuous theory is no longer applicable. The theory, modified in such a way, is already different from the theory without this modification, some seemingly completely innocent solutions of the theory without ether interpretation are rejected as invalid. In particular, this excludes all solutions with closed causal loops.

So, yes, the ultimate purpose of considering interpretations is the search for different theories. They are starting points, important for finding starting directions for modifications - the directions which solve problems of the particular interpreation.

 

[TrickyDicky]

It's important to clarify the meaning of certain terms we use, and I don't think that this kind of existence would be called "ontological" by philosophers of physics. In this context, by ontological existence one would mean individual preparations, not the equivalence class of similar preparations.

On the other hand, QM in its statistical ensemble form says nothing about individual preparations. In this sense QM in the statistical ensemble form is not complete, because individual preparations obviously exist (ontologically), and yet the theory says (syntactically) nothing about them.

This proves that QM in the statistical ensemble form is not ontologically complete. A possible way to stop worry about that is to assume that QM in the statistical ensemble form is at least syntactically complete, i.e. that syntax (formal mathematical theory) correctly describing individual preparations - does not exist. But such an assumption is not very well grounded, especially with a known counter-example candidates such as Bohmian mechanics, many-worlds, and objective-collapse theories.

If quantum theory does not, in fact, predict the result of individual measurements, but only their statistical mean, then why should one
expect a syntax describing individual preparations?

 

[atyy]

If quantum theory does not, in fact, predict the result of individual measurements, but only their statistical mean, then why should one expect a syntax describing individual preparations?

In the ensemble interpretation, there is a classical/quantum cut. One may like to call it something else, but as most proponents of the ensemble interpretation agree, there is no meaning to the "wave function of the universe" in that interpretation. If there is no "wave function of the universe", one has to say which part of the universe the wave function applies to, which is the classical/quantum cut in all but name.

So the measurement problem can be phrased in different forms, such as the question about individual systems, or removing the classical quantum cut.

 

[TrickyDicky]

In the ensemble interpretation, there is a classical/quantum cut. One may like to call it something else, but as most proponents of the ensemble interpretation agree, there is no meaning to the "wave function of the universe" in that interpretation. If there is no "wave function of the universe", one has to say which part of the universe the wave function applies to, which is the classical/quantum cut in all but name.

So the measurement problem can be phrased in different forms, such as the question about individual systems, or removing the classical quantum cut.

My question was in reference to Demistifier comment about syntactical
completeness, I don't inmediately see
how your post answers it but I will
address what you write anyway.
The reasoning about the wave function of the uiverse you use would be valid if like MW the ensemble int. considered the wave function as ontologicaly real, but it doesn't.

 

[bohm2]

If quantum theory does not, in fact, predict the result of individual measurements, but only their statistical mean, then why should one expect a syntax describing individual preparations?

Would that, then, not make the ensemble interpretation just a "shut up and calculate" interpretation in disguise?

 

[atyy]

My question was in reference to Demistifier comment about syntactical
completeness, I don't inmediately see
how your post answers it but I will
address what you write anyway.
The reasoning about the wave function of the uiverse you use would be valid if like MW the ensemble int. considered the wave function as ontologicaly real, but it doesn't.

Copenhagen does not consider the wave function real on the same level as measurement outcomes. That is the point of the classical/quantum cut. Any minimal interpretation which does not consider the wave function of the universe to be meaningful has a classical/quantum cut.

 

[TrickyDicky]

Would that, then, not make the ensemble interpretation just a "shut up and calculate" interpretation in disguise?

I think ensemble is the "shut up and calculate" genuine interpretation but done in an honest and elegant way ;-)

 

[TrickyDicky]

Copenhagen does not consider the wave function real on the same level as measurement outcomes. That is the point of the classical/quantum cut.

Yes, that's right.

Any minimal interpretation which does not consider the wave function of the universe to
be meaningful has a classical/quantum cut.

This doesn't follow. First the ensemble interpretation not only does not have an ontology for the wave function, it doesn't have an ontology for classical reality as it is the case in the Copenhagen interpretation.
There is no objective classical world in the ensemble interpretation so no classical-quantum cut. Remember that classical physics is an approximation, If it works so well in the macro world is because it is a good approximation on that scale, so reality is not classical.