When Quantum Mechanics is thrashed by non-physicists #1

[bhobba]

Strange. I have never heard about a minimal version without collapse.

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

 

[Demystifier]

Where do you see the preferred basis problem in the de Broglie-Bohm interpretation?

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.

 

[vanhees71]

But you do admit that probably there is something which is not the wave function (otherwise you would need either the collapse or many-worlds), even if you don't care what exactly that something might be. Am I right?

Within quantum theory there's nothing else than the mathematical setup to define it, including the Born rule. If you want a deterministic theory with hidden variables, then there's more and according to the violation of Bell's inequality it'll be a non-local model.

At the moment, however, I don't see the necessity for such a deterministic theory, because quantum theory never has been disproven by any experiment. In my opinion there are more urgent true problems to solve like: What's dark matter? How can we understand the smallness of "dark energy"? What's a consistent quantum theory of gravity? I don't see any urgent demand for a solution of the pseudo-problem of interpretation of quantum theory.

 

[stevendaryl]

I think "smart" is not the problem. Most are not ready to accept the hypothesis that relativistic symmetry is not fundamental, not even as a working hypothesis, which one accepts for the sake of the argument, to have a look at how it fails, no, it is rejected out of hand, without any discussion. Like here, where even to discuss the Lorentz ether interpretation vs. Minkowski interpretation is forbidden (BTW with a completely wrong argument that there is no difference in the predictions, in a situation where one can derive Bell's inequalities only in the Minkowski interpretation, but not in the Lorentz interpretation, which allows hidden causal influences, SCNR).

I don't completely agree with this. 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.

[Note: some people consider the frame in which the background radiation from the Big Bang is isotropic to be a "preferred frame" of sorts. It gives a standard of "rest" for every point in the universe. If you consider that a "preferred frame", then my claim could be amended to: there is absolutely no experimental evidence that this frame is special for quantum mechanical processes.]

 

[Demystifier]

Within quantum theory there's nothing else than the mathematical setup to define it, including the Born rule. If you want a deterministic theory with hidden variables, then there's more and according to the violation of Bell's inequality it'll be a non-local model.

At the moment, however, I don't see the necessity for such a deterministic theory, because quantum theory never has been disproven by any experiment. In my opinion there are more urgent true problems to solve like: What's dark matter? How can we understand the smallness of "dark energy"? What's a consistent quantum theory of gravity? I don't see any urgent demand for a solution of the pseudo-problem of interpretation of quantum theory.

You didn't answer my question, probably because you missed my point entirely. So let me try to explain my point (and my question) again.

First, I didn't talk about determinism, so why do you talk about it? I talked about ontology.

The point is the following. According to the statistical ensemble interpretation, which you said you accept, the wave function does not describe an individual observation, but only a statistical ensemble. Do you agree?

On the other hand, individual observations do exist. Do you agree with that too?

Now, if you agree with both claims above, then logically you must accept that something (individual observation) exists which is not a wave function. Q.E.D.

So to condense all these questions into one: Do you agree that statistical ensemble interpretation of QM requires that something which is not a wave function must exist?

--------------------------------------

Or if you still don't get it, here is a yet another way to put it. In individual observations we observe something. That something is either wave function or something else. So let us explore both possibilities:

1) If it is wave function, then the statistical ensemble interpretation is wrong. In that case one needs either the collapse or many worlds.

2) If it is not wave function, then, obviously, there is something which is not wave function.

 

[TrickyDicky]

At the moment, however, I don't see the necessity for such a deterministic theory, because quantum theory never has been disproven by any experiment. In my opinion there are more urgent true problems to solve like: What's dark matter? How can we understand the smallness of "dark energy"? What's a consistent quantum theory of gravity? I don't see any urgent demand for a solution of the pseudo-problem of interpretation of quantum theory.

Well, you cannot discard a link between those problems and QM incompleteness-interpretations.

 

[rubi]

I talked about ontology.

The point is the following. According to the statistical ensemble interpretation, which you said you accept, the wave function does not describe an individual observation, but only a statistical ensemble. Do you agree?

On the other hand, individual observations do exist. Do you agree with that too?

Now, if you agree with both claims above, then logically you must accept that something (individual observation) exists which is not a wave function. Q.E.D.

I don't think that follows. One has to distinguish nature and its mathematical description. Ontology is concerned with nature itself. It tries to answer questions like: "What is the real nature of the things that we - as humans - perceive? What is beyond perception?" On the other hand, we have a mathematical description of nature, which includes mathematical objects like wave functions, fields or trajectories. None of these things exist in the way ontology talks about existence. A ball for example might exist in one way or the other or it might not, but it is not a trajectory, because a trajectory is just a certain string of symbols written on a piece of paper (for example the string $x(t)=-\frac{1}{2}gt^2$ is a trajectory). Obviously, a ball that you can see in front of you is never the string of symbols $x(t)=-\frac{1}{2}gt^2$ and neither is it any other string of symbols, so a ball is definitely not a trajectory. Neither is it a wave function. I still don't know what the ball "is", but I definitely know that it is not identical with its mathematical description. Even in classical mechanics, we strictly can't know what the right ontology is to interpret it. The difference between CM and QM is just that there are no interpretational difficulties with the standard ontology of CM (which postulates the existence of tiny little balls or something like that), so nobody worries about it. But still, if we prefer to accept only analytical arguments, having a classical (mathematical) description of physics doesn't tell us anything about ontology. So having a list of individual observations doesn't tell us anything about the (ontological) existence of "something". For example, I can easily build a measurement apparatus that measures something that most definitely doesn't correspond to something that onologically exists: Take a piece of paper and write "5" on it. Whenever you look at it, it reveals the number 5. It even has a classical and a quantum observable corresponding to it (a constant function $f(x,p)=5$ or the identity operator multiplied by 5). So I don't think it is possible to analytically conclude the ontological existence of "something" (whatever it is) from having a recorded list of measurement results.

 

[Demystifier]

So I don't think it is possible to analytically conclude the ontological existence of "something" (whatever it is) from having a recorded list of measurement results.

Are you saying that, even if nothing exists in the ontological sense, it is still logically possible to have measurement results?

 

[bhobba]

None of these things exist in the way ontology talks about existence.

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.

A ball for example might exist in one way or the other or it might not, but it is not a trajectory, because a trajectory is just a certain string of symbols written on a piece of paper

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.

I think discussion of such philosophical issues is best taken up on a forum dedicated to such - not one discussing science.

Thanks
Bill

 

[rubi]

Are you saying that, even if nothing exists in the ontological sense, it is still logically possible to have measurement results?

I'm not adressing that situation, because obviously, something exists ("I think, therefore I am"). I'm basically arguing that the word "existence" can refer to different things and we should not mix them. On the one hand, we have the mathematical meaning of existence, which can be rigorously defined in mathematical logic and it is mainly a syntactic notion that has no inherent meaning. On the other hand, there is the ontlogical meaning of the word "existence", which talks about a loosely defined philosophical idea. My claim is that either notion of "existence" doesn' tell us anything about the other notion, respectively. So there are two things that we can't conclude analytically:
1. From having a list of measurement results that exists in an ontological way (I can see it), we can't conclude anything about the (syntactic) existence of mathematical objects that describe them.
2. From having a mathematical descrption of nature using (syntactically) existing mathematical objects, we can't conclude anything about ontological existence.

 

[bhobba]

From having a mathematical descrption of nature using (syntactically) existing mathematical objects, we can't conclude anything about ontological existence.

Actually I agree with that. Physics is a mathematical model - what relation it has to this 'ontology' thing is best left to the subject that analyses such - philosophy.

Thanks
Bill

 

[Demystifier]

I'm not adressing that situation, because obviously, something exists ("I think, therefore I am"). I'm basically arguing that the word "existence" can refer to different things and we should not mix them. On the one hand, we have the mathematical meaning of existence, which can be rigorously defined in mathematical logic and it is mainly a syntactic notion that has no inherent meaning. On the other hand, there is the ontlogical meaning of the word "existence", which talks about a loosely defined philosophical idea. My claim is that either notion of "existence" doesn' tell us anything about the other notion, respectively. So there are two things that we can't conclude analytically:
1. From having a list of measurement results that exists in an ontological way (I can see it), we can't conclude anything about the (syntactic) existence of mathematical objects that describe them.
2. From having a mathematical descrption of nature using (syntactically) existing mathematical objects, we can't conclude anything about ontological existence.

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"?

 

[vanhees71]

You didn't answer my question, probably because you missed my point entirely. So let me try to explain my point (and my question) again.

First, I didn't talk about determinism, so why do you talk about it? I talked about ontology.

I think if it comes to "ontology" it means that you need determinism, but that's perhaps another topic.

The point is the following. According to the statistical ensemble interpretation, which you said you accept, the wave function does not describe an individual observation, but only a statistical ensemble. Do you agree?

Yes, that's the very point of quantum theory with Born's rule, and Born's rule is crucial. As is marvelously demonstrated in Weinbergs textbook, Lectures on Quantum Mechanics, it's a postulate independent of the others.

On the other hand, individual observations do exist. Do you agree with that too?

Sure, otherwise I couldn't measure any individual system, which one definitely can (nowadays even single elementary particles or photons).

Now, if you agree with both claims above, then logically you must accept that something (individual observation) exists which is not a wave function. Q.E.D.

First of all: QT is incomplete if you insist on wave functions. You can live with wave function alone only in (part) of non-relativistic QT. I don't know, why individual observations should be beyond quantum theory. The only constraint by QT compared to classical theory (CT) is that about individual observations you can in general make only probabilistic statements, even if you have complete knowledge about the system (i.e., if you know in which pure state it has been prepared).
[/QUOTE]

So to condense all these questions into one: Do you agree that statistical ensemble interpretation of QM requires that something which is not a wave function must exist?

I think, that's answered now, right?

 

[vanhees71]

Well, you cannot discard a link between those problems and QM incompleteness-interpretations.

I don't think that any physical theory is complete. It's great. So there's still enough left to be discovered for us and hopefully many future generations of scientists :-).

 

[Demystifier]

I think, that's answered now, right?

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

 

[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.