How observation leads to wavefunction collapse?

[Fra]

If you believe (i), then you will claim that there is more than QM; and if you believe (ii) then you will claim that there may be more than QM (as any model of the universe can be superseded by a new one that contains the old one in the limit of a parameter, or something), but we are stuck with probabilites forever.

Ok, I read it more carefully. That makes it look a bit better, I was too quick to comment. My apologees.

But I still think that the two options overlap.

(I)

If you believe (i), then you will claim that there is more than QM

(II)

there may be more than QM (as any model of the universe can be superseded by a new one that contains the old one in the limit of a parameter, or something), but we are stuck with probabilites forever.

I'm not trying to silly or play games, I do understand what you probably suggest the difference is, but I am still of the opinion that the distincion is more fuzzy than what the first impression suggests. This was my point.

This suggest that (as I also suggested) that the two views is not necessarily (unless we can refine the notions here) _fundamentally_ incompatible after all.

So both approaches seem to think there is more than QM as we currently know it? The question seems to be what this extension is like?

/Fredrik

 

[Fra]

even the limits themselves are evolving. I think that there are somehow limits of the rate of change as well, but even this limit is changing.

In conclusion this is where the standard QM makes no sense to me. So wether this "there more to QM" makes me (i) or (ii) seems a matter of definition, I'd probably say (ii), but it depends on how the question is posed.

One implication is that things that are banned in standard QM shouldn't be banned. Unitarity is at stake here. If someone can come up with a reasonable proper evolutionary framework and still cling onto some unitary ideals, I'd be interested, but I have yet to see it.

Some people try to make a bigger model, that encapsulates the old one, and still preserves unitarity. But that's not true evolution. It's replacing the old theory with a new one. A proper evolutionary strategy should explain exactly how a new models grows out of the old one. This should not be theorist magic!

/Fredrik

 

[Fra]

Look at master nature. Mammals don't evolve new spieces by starting over from microbiological evolution, it would be a highly unsuccessful strategy. The evolve smoothly. The problem I have with some methods is that this isn't appreciated. It's too much ad hoc still, if not in the models - in the method.

So when looking at theories, it's not just a matter of if they make correct predictions in a snapshot of time. It's a matter of how these theories can live and adapt to REALITY.

/Fredrik

 

[masudr]

So both approaches seem to think there is more than QM as we currently know it?

No; the second approach is accepting that we may not have a complete description of nature (as per the Laplacian dream). I only added that QM may not be the best model, since any current model can be superseded by a later one. I cannot suggest that QM is the final word -- none of us can. This is not a comment about QM in particular, but to any model of the universe.

 

[Fra]

Ok. I guess we could leave it here as it's not that much to discuss but a final comment.

I agree with you completely that this discussion is indeed not specifically about QM, it's about modelling in general. And that was what I tried to say, becuase I had the impression that the discussion had a confusing focus.

IMO, if we are talking about different theories and strategies, and which one makes more sense, I suggest it should be done in the larger context of general modelling or scientific method, otherwise the mere comparasion is unclear. Without a connection whatsoever the comparastion easily gets ambigous.

I suggest that any specific model of reality can not be separated completely from the scientific method that generated it, and the various abstractions used.

/Fredrik

 

[lightarrow]

Consider the following. Arrange a single slit experiment (as discussed by Mr Virtual in post #68, one even doesn't need two slits to see quantum "weirdness") and shoot electrons one-by-one. Notice that each electron lands at a different place on the screen. Recognize that there is absolutely no way to predict where each individual electron will land. Quantum mechanics can predict only the total probability distribution, but not the fate of each individual particle. So, we have a measurable physical fact (an electron hit a certain point on the screen), but we have no theoretical means to explain or predict this fact. Honestly, there could be only two conclusions from this observation:
1. Our present theory (quantum mechanics) is not a complete description of nature. There should be a deeper theory, which eventually will explain/predict the place of landing of each electron, or exact times of clicks of Geiger counters, or other events, which are currently described only probabilistically.
2. Events occurring with individual systems are fundamentally random. We will never know more than their probabilities. Quantum mechanics is the best possible (but not all-powerful) tool to describe nature.
There is no rational way to choose between these two conclusions. One should follow his/her intuition, philosophy, religion, etc.
Conclusion 1. is a path to "hidden variable" theories. This is a wrong path, in my humble opinion. I choose conclusion 2., which means that there are certain things about nature, that we will never understand.

I don't agree on the fact only hidden-variables theory could account of it. We are not considering the possibility that {electron/first screen with slit/last screen} form a unique system, the behaviour of which gives the location of the flash on the last screen.

Let's say, to give the idea, that the last screen is completely absorbing, and that I place a tiny photodetector in a specific point of it. I have changed the properties of the screen only, but now I see "flashes" in that point and not in others. Should I imagine "hidden properties" of the electron to account of this new behaviour?

And what if I put many tiny photodetectors tuned so that it will flash only the one that will receive, in that moment, the maximum amplitude of the electron field? Maybe the electron wavefunction's amplitude, which has been modified by the first screen with the slit, can have just little amplitude variations from a point to another, that could give rise to a flash in a point instead of another (where a "standard" computation would tell us that instead the amplitude is the same); or it could be little amplitude variations from point to point in the screen's wavefunction or, in general, both. This is really obvious to me. Is not the same for you? Don't you see the analogy between the hypothetical case I made and the real one?

 

[meopemuk]

And what if I put many tiny photodetectors tuned so that it will flash only the one that will receive, in that moment, the maximum amplitude of the electron field? Maybe the electron wavefunction's amplitude, which has been modified by the first screen with the slit, can have just little amplitude variations from a point to another, that could give rise to a flash in a point instead of another (where a "standard" computation would tell us that instead the amplitude is the same); or it could be little amplitude variations from point to point in the screen's wavefunction or, in general, both. This is really obvious to me. Is not the same for you? Don't you see the analogy between the hypothetical case I made and the real one?

What you are describing looks like a "hidden variable" theory to me. You suggest that the point of the next flash is, in principle, calculable. You talk about some "little amplitude variations" which are responsible for the location of the flash. Logically, I accept such a possibility. I just don't believe that nature works that way.

 

[gptejms]

My point is that if something satisfies a continuity equation, it does not yet imply that it describes probability. For example, a classical fluid, or a classical field, may also satisfy a continuity equation, but such a classical theory has nothing to do with probabilities. Instead, you must postulate probabilistic interpretation as an independent axiom.

Yes, of course.But once you give it a probability interpretation, it does not cease to be a field.

The problem is that the axioms of QFT, including those that refer to probabilities, do NOT imply the probabilistic interpretation of the Schrodinger field/wavefunction.

Schrodinger equation is anyway an approximate(i.e. non-relativistic) description of reality--why worry about it all when relativistic formalism is available.I think we stick to the Schrodinger equation because it's (mathematically)easier to deal with.

 

[meopemuk]

No; the second approach is accepting that we may not have a complete description of nature (as per the Laplacian dream). I only added that QM may not be the best model, since any current model can be superseded by a later one. I cannot suggest that QM is the final word -- none of us can. This is not a comment about QM in particular, but to any model of the universe.

I can easily believe that QM (quantum logic, Hilbert spaces, state vectors, Hermitian operators, etc.) IS the final word. In my view, QM is a perfect physical theory, and it is virtually impossible to add or remove anything from it. I know that I should never say "never", but I am tempted to say that QM will be never superseded by any more general theory.

 

[Fra]

QM is a perfect physical theory, and it is virtually impossible to add or remove anything from it. I know that I should never say "never", but I am tempted to say that QM will be never superseded by any more general theory.

/Fredrik

 

[Anonym]

I can easily believe that QM (quantum logic, Hilbert spaces, state vectors, Hermitian operators, etc.) IS the final word. In my view, QM is a perfect physical theory, and it is virtually impossible to add or remove anything from it. I know that I should never say "never", but I am tempted to say that QM will be never superseded by any more general theory.

Sorry, I did not follow the discussion in this session. I hope QM you mean the non-relativistic limit. I do not think even within non-relativistic QM the “quantum logic” is the final word. The approach has his roots in J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Berlin, (1931) Ch3, par. 5; definition of “eigenschaften”. I think it may be corrected by more adequate consideration. And non-Hermitian operators are still terra incognita.

Regards, Dany.

 

[lightarrow]

What you are describing looks like a "hidden variable" theory to me. You suggest that the point of the next flash is, in principle, calculable. You talk about some "little amplitude variations" which are responsible for the location of the flash. Logically, I accept such a possibility. I just don't believe that nature works that way.

A hidden variable shoud be an objective property of the electron only, not of the entire system.

 

[meopemuk]

I hope QM you mean the non-relativistic limit.

Not at all. Relativistic quantum mechanics is fine as well. Being relativistic or non-relativistic does not change the fundamental structure of QM. It simply changes the invariance group (Galilei or Poincare).

 

[Ariste]

I think meopemuk was trying to express the idea that models of the universe can either, in principle,

(i) provide exact predictions for every event; or
(ii) provide predictions for ensembles only.

If you believe (i), then you will claim that there is more than QM; and if you believe (ii) then you will claim that there may be more than QM (as any model of the universe can be superseded by a new one that contains the old one in the limit of a parameter, or something), but we are stuck with probabilites forever.


It's not really about anyone finding anything weird. It's dependent on which of the two above you accept. A lot of people do believe (ii), in contrary to the assumptions in your post above.

I'm no expert in physics, but conceptually it's difficult for me to accept (ii), and beyond that, option (ii) is just disheartening.

Conceptually, it seems to me that (ii) defies causality. The theory behind physics is that the behavior of nature is governed by certain laws, and that we can predict the behavior of nature according to these laws. To say that we cannot, under any circumstances, accurately predict the behavior of an electron is to say either that a) the behavior of an electron is not governed by natural laws or that b) our models and/or equipment are inadequte to accurately derive these laws. To me, the second option seems much more logical and likely.

 

[masudr]

The theory behind physics is that the behavior of nature is governed by certain laws, and that we can predict the behavior of nature according to these laws. To say that we cannot, under any circumstances, accurately predict the behavior of an electron is to say either that a) the behavior of an electron is not governed by natural laws or that b) our models and/or equipment are inadequte to accurately derive these laws. To me, the second option seems much more logical and likely.

Note that these are your opinions and musings on nature. There's no reason why nature should (nor is there a reason why nature shouldn't) conform to your opinions.

 

[meopemuk]

I'm no expert in physics, but conceptually it's difficult for me to accept (ii), and beyond that, option (ii) is just disheartening.

Conceptually, it seems to me that (ii) defies causality. The theory behind physics is that the behavior of nature is governed by certain laws, and that we can predict the behavior of nature according to these laws. To say that we cannot, under any circumstances, accurately predict the behavior of an electron is to say either that a) the behavior of an electron is not governed by natural laws or that b) our models and/or equipment are inadequte to accurately derive these laws. To me, the second option seems much more logical and likely.

This is exactly why quantum mechanics was such a radical change in our understanding of the world. It was a true revolution in physics. The more we learn about microworld the less doubt we have that electron is not (entirely) governed by natural laws. Electron's behavior is partly predictable and partly random. The predictable part we managed to describe by the wave function. The random part remains a complete mystery.

Your option b) is a dream about hidden variables and Laplacian determinism. This option cannot be dismissed. However it becomes less and less attractive with each new success of quantum mechanics.

 

[Ariste]

Note that these are your opinions and musings on nature. There's no reason why nature should (nor is there a reason why nature shouldn't) conform to your opinions.

No doubt, and like I said, I'm no physicist. I'm sure many of your guys' opinions are much more educated than mine. I'm just, like you said, musing about nature and what makes sense to me.

This is exactly why quantum mechanics was such a radical change in our understanding of the world. It was a true revolution in physics. The more we learn about microworld the less doubt we have that electron is not (entirely) governed by natural laws. Electron's behavior is partly predictable and partly random. The predictable part we managed to describe by the wave function. The random part remains a complete mystery.

So is that to say that we have increasing confidence in the belief that electrons are governed by no law at all? That they are governed by nothing?

If so, that truly is revolutionary and indeed mind-boggling. I'm not even sure how to interpret that in a physical context. That, at the basest level, our universe is completely random and unpredictable - it's hard to comprehend.

 

[Fra]

When I read this thread it seems different things are discussed, confusing it all. I can identify these components.

a) Some have difficult to let go of the "Newtonian" world view, I think this is a process everyone goes through, but seemingly people come to different conclusions.

b) Given that we accept QM a little bit along (ii) (and thus, no longer ask question a) then some people thinks this is a perfect theory, and see no reason to change it.

c) Some people don't ask (a), but they still don't find QM consistent as a possibly fundamental theory. Difficulty to abandom Newtonian or laplacian ideals isn't the only reason to pick on QM, there are others. Having to do with unitarity, gravity and evolution. This was my point.

I speak only from my own experience here, I went trough the 3 stages myself. Where there is yet more stages, I don't know, but that's quite possible. In my case stepping back to revise my "scientific method" and framework of abstractions was the resolution at each step. I haven't answered c yet of course, but I'm trying.

/Fredrik

 

[Fra]

I've also reasoned that part of the answer to (c) migth connect back to (a). This is why I think that those who are still asking (a) without satisfactory answer, might benefit from stepping directly to (c)?

/Fredrik

 

[meopemuk]

So is that to say that we have increasing confidence in the belief that electrons are governed by no law at all? That they are governed by nothing?

If so, that truly is revolutionary and indeed mind-boggling. I'm not even sure how to interpret that in a physical context. That, at the basest level, our universe is completely random and unpredictable - it's hard to comprehend.

I didn't say that electrons are governed by no law at all and that our universe is completely random and unpredictable. This would be foolish things to say. I said that there are two parts in electron's life. One part is predictable, so we do know something about what electron is doing. And this part is quite useful. It allows us to build transistors, lasers, and what not. And there is another part, which is totally unpredictable.

The classic example of this second part is the one-slit experiment, in which identically prepared electrons pass through the slit and hit the screen in different places. It is absolutely impossible to predict where the next electron will hit the screen.

With the development of quantum mechanics we made a great progress in calculations of the former (bright) side of electron's life. However, we have made absolutely no progress in understanding the latter (dark) side. This random part of electron's behavior remains just as obscure as it was 80 years ago when quantum mechanics was born. Besides some vague suggestions to introduce hidden variables (nobody has a slightest idea what these variables are and what are the laws that govern them) there was no movement in this direction at all. There are no approximations that can be compared with experiment even at a qualitative level. Nothing.

This suggests to me that the random "dark side" is an integral part of what electron is. There is another reason why I think that probabilities are inevitable. If you learn quantum mechanics at some depth you'll realize how breathtakingly beautiful this theory is. It is easy to derive laws of classical mechanics as a limit (h -> 0) of QM. At this points it seems that the reverse derivation (QM as a variant of a deterministic hidden variable theory) would be rather ugly, if possible at all.

I understand that it is very difficult to abandon the classical picture of the world in which every event is (in principle) predictable and every effect has a cause. However, when it comes to studying nature, we should leave our philosophical prejudices aside, and just listen to what nature tells us.

 

[meopemuk]

c) Some people don't ask (a), but they still don't find QM consistent as a possibly fundamental theory. Difficulty to abandom Newtonian or laplacian ideals isn't the only reason to pick on QM, there are others. Having to do with unitarity, gravity and evolution. This was my point.

/Fredrik

What are your specific problems with QM? I don't see any contradiction with unitarity, gravity and evolution.

 

[Anonym]

It is easy to derive laws of classical mechanics as a limit (h -> 0) of QM.

Nonsense as well as all your post #110.

 

[Fra]

What are your specific problems with QM? I don't see any contradiction with unitarity, gravity and evolution.

If you see no problems whatsoever I'm not sure how much effort I need to put don't to explain this. But let's just note that a kind of relational theory like that of gravity, isn't easily mixed with QM, for various reasons. Some people think it's a mathematical problem only, some thing it's a foundational problem.

Have you found a solution to all that?

If we can't agree on the question, no wonder we don't agree on the answers.

One part is predictable, so we do know something about what electron is doing. And this part is quite useful. It allows us to build transistors, lasers, and what not. And there is another part, which is totally unpredictable.

[Note I'm on (c) here] The distinction between the unpredictable part and the predictable part is IMO fuzzy. This is also why I find it difficult to be too categorical. The fuzzy part is not just something missing and lost, it's also the key to flexibility and growth. At least that's my personal idea.

To reduce a larger theory to a special case is a reductionist approach that hardly a evolutionary method. It's always far easier to discard information, than to create information. The latter is something I think we need to understand, to understand how the universe came into beeing and how it evolves. The whole meaning of evolve is just that you GROW new possibilites, not "reduce the reduction" from a larger master model. I'm not sure this makes sense to you. But maybe we can agree to disagree, which is good.

I am trying to merge the scientific method here with it's product. That's what I'm trying to do. And that's when the ordinary QM and QFT has issues. It's not that it's not useful, that's not what I'm saying. I'm just saying that there is something very important missing in the foundations, and it has to do with the notion of probability.

What I am saying here is not in defense of the hidden particle people, it's something different. But for what I know, perhaps the reason why some people to date can't accept QM is related to this. I don't kow how their brains work, I can only speak for mine.

/Fredrik

 

[Ariste]

I didn't say that electrons are governed by no law at all and that our universe is completely random and unpredictable. This would be foolish things to say. I said that there are two parts in electron's life. One part is predictable, so we do know something about what electron is doing. And this part is quite useful. It allows us to build transistors, lasers, and what not. And there is another part, which is totally unpredictable.

But you did say that. You've said that an electron can only be partially described; that some of the behavior of an electron is inherently indescribable and unpredictable. To take this unpredictability as a fundamental part of nature is to say that, at its basest level, nature is random and unpredictable. It's different than saying 'we simply don't know how to fully describe an electron yet.' It's saying 'it is physically impossible to fully describe the behavior of an electron.' This is saying that nature is, at least partially, completely and totally unpredictable and random.

 

[masudr]

If QM is the best model of the universe, it is impossible to provide the value of every observable, at all times for any individual system.

However, if we had an ensemble of N individual systems, QM can tell us what fraction of those N systems will have specific values of any observable. QM's predictions become more and more correct as N becomes larger, and in fact completely correct in the limit as N becomes infinity. So if we consider QM as a model for only such ensembles, then QM describes all there is that one can know.

This is another way to say that QM predicts probabilities of individual systems, but gets around some people feeling awkward about probabilites.

EDIT: I gave the correct description of ensembles, in response to meopemuk's comment below.

 

[meopemuk]

If you see no problems whatsoever I'm not sure how much effort I need to put don't to explain this. But let's just note that a kind of relational theory like that of gravity, isn't easily mixed with QM, for various reasons. Some people think it's a mathematical problem only, some thing it's a foundational problem.

Have you found a solution to all that?

If we can't agree on the question, no wonder we don't agree on the answers.
/Fredrik

Maybe you can find some answers in my paper "A relativistic quantum theory of gravity" http://www.arxiv.org/physics/0612019

 

[meopemuk]

But you did say that. You've said that an electron can only be partially described; that some of the behavior of an electron is inherently indescribable and unpredictable. To take this unpredictability as a fundamental part of nature is to say that, at its basest level, nature is random and unpredictable. It's different than saying 'we simply don't know how to fully describe an electron yet.' It's saying 'it is physically impossible to fully describe the behavior of an electron.' This is saying that nature is, at least partially, completely and totally unpredictable and random.

Yes, this is correct. That's the whole idea of quantum mechanics, as I understand it. If you want to explain quantum mechanics in one phrase, then here you go - you did it.

 

[meopemuk]

If QM is the best model of the universe, it is impossible to provide the value of every observable, at all times for any individual system.

However, we can provide the value of every observable at all times for an ensemble of systems.

I am not sure I agree with that. Ensemble is simply a collection of N identical systems prepared in identical conditions. By measuring observable F in each member of the ensemble we generally obtain N different values (unless the ensemble happened to be prepared in an eigenstate of F). QM simply tells us which values appear more frequently and which are less frequent (probabilities).

 

[masudr]

QM simply tells us which values appear more frequently and which are less frequent (probabilities).

Yes; you are quite right. That is what I meant.

 

[Fra]

Maybe you can find some answers in my paper "A relativistic quantum theory of gravity" http://www.arxiv.org/physics/0612019

I'll try to read it more later to see if you motivate it but, I skimmed through intro and you list a set of principles that must be met. I don't find these trivial enough. These are principles of the standard approaches, and I am not sure they can be preserved at all cost. And if you take them as guidance principles from square one, I'd like to see some argumentation why they must hold, not for the current models, but for a general case model.

I have come to put most emphasis on the methods. Because if the method is sound, it's not as sensitive to initial estimates. I think you are thinking differently than me.

/Fredrik