How observation leads to wavefunction collapse?

[Fra]

Ensemble is simply a collection of N identical systems prepared in identical condition.

A theory for reality must I think to a larget extent be formulated in terms of data. Consider how to make a real measurement (taking a certain amount of time each), to probe the measurements on an ensemble and I think the issues I raise should reveal themselves.

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).

One problem I have with this is the interpretation of probabilities - A collection of identically prepared systems, which you in principle can prepare and determine the probability distribution as N -> infinity - this sounds scientific and good, but it's not so trivial.

To observe an infinite amount of equal initial conditions is hard, not to mention that it would be infinite time. Some may think that, this is only a practical problem and has no relevance to our ensembles in principle. But I think it does.

QM has move the Newtonian ideals from particle level, to probability level. And that in the probability world every thing can in principle be exactly known. You can know the probability EXACTLY. But this is what doesn't make sense.

If you adapt the probabilistic thinking, the insight that should come is that, by the same token, we can only know the probability to a certain probability as well. And there is probably a relation here with space and time, a kind of uncertainty relation on the ensemble itself. This is another way of reasoning that does lead to suggest the second quantization. But the problem is that, that's not the end. There is nothing that stops the 3'rd and n'th quantization. I am trying to understand this. I think there is in fact a logic here that does explain WHY quantization stops at certain level. I don't have the answer yet, but my point is not to present the answer, just to try to present the question.

This is a question I rarely see aqcknowledged. Why I don't know. That's the other mystery. I have suspected it's because solving it may seem tricky, and there is no point in asking questions we can't answer. That has a point, but I ask it because I do have a vision on howo resolve it. And I think going this way, will incorporate gravity into the information world of QM, in a much deeper way, they will be united from construction. Not by merging two theories that where grown on competely different grounds.

/Fredrik

 

[meopemuk]

Consider how to make a real measurement (taking a certain amount of time each), to probe the measurements on an ensemble and I think the issues I raise should reveal themselves.

In some experiments, accumulating sufficient statistics is a problem. In others it is just a piece of cake. For example, in the double-slit experiment you can measure simultaneously landing places of billions of particles by measuring the brightness levels on the scintillating screen.

If you adapt the probabilistic thinking, the insight that should come is that, by the same token, we can only know the probability to a certain probability as well.

This is an interesting idea, which would imply complete re-writing of quantum mechanics. However, I don't think there is any empirical evidence to support this idea.

And there is probably a relation here with space and time, a kind of uncertainty relation on the ensemble itself. This is another way of reasoning that does lead to suggest the second quantization. But the problem is that, that's not the end. There is nothing that stops the 3'rd and n'th quantization. I am trying to understand this. I think there is in fact a logic here that does explain WHY quantization stops at certain level. I don't have the answer yet, but my point is not to present the answer, just to try to present the question.
/Fredrik

I don't know who invented this term "second quantization", but this is probably the most misleading phrase in physics. In QFT we do *not* quantize wave functions second time and thus obtain quantum fields. So, 3rd and n'th quantization does not make sense at all. QFT is just ordinary quantum mechanics applied to systems with variable number of particles. That's all there is to QFT.

 

[meopemuk]

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.
/Fredrik

This discussion would lead us too far from the topic of the present thread. I offered this paper for discussion in the "Independent research" section of this forum. If it will be approved by moderators, we'll have ample opportunities to discuss these issues. Meanwhile, we can talk about quantum gravity privately through e-mail.

 

[Fra]

In some experiments, accumulating sufficient statistics is a problem. In others it is just a piece of cake. For example, in the double-slit experiment you can measure simultaneously landing places of billions of particles by measuring the brightness levels on the scintillating screen.

Yes I agree compteley. This is of course why QM is highly successful in these cases. But these cases is not the general case. I'm not suggesting this abstraction is generally invalid, I'm suggesting that it's not generally valid.

This is an interesting idea, which would imply complete re-writing of quantum mechanics. However, I don't think there is any empirical evidence to support this idea.

I disagree about not beeing evidence supporting this. Also this has to do with the scientific method. I read your comment like "there is no empirical evidence to support that we can't do this assumption". In fact in the connection to gravity is very intuitive, since gravity can be thought of as the "DC component" of information, and particles are superpositioned information. The abstraction we make, could be what excludes gravity.

But yes QM has to be reconsidered from it's foundations. But that's not a bad thing. It would make a good theory, better. At least that's what I think.

I don't know who invented this term "second quantization", but this is probably the most misleading phrase in physics. In QFT we do *not* quantize wave functions second time and thus obtain quantum fields. So, 3rd and n'th quantization does not make sense at all. QFT is just ordinary quantum mechanics applied to systems with variable number of particles. That's all there is to QFT.

I know the notion can be discussed, but set aside this, I know what the 2nd quantization is and it's been motivated in sometimes quite doubtful ways in books I've seen. I'm suggesting that there is a deeper understanding of this process. And in that case, the "n'th quantization" does make sense to me: "The probability of the probability of the probability of the ..." n times. In fact this can be thought of as an induction step in a larger process. What I mean is that, given the nature of the induction, how can you stop at one iteration and not ask why? You're comment takes the notion of a particle for granted. This isn't obvious either?

/Fredrik

 

[Fra]

This discussion would lead us too far from the topic of the present thread. I offered this paper for discussion in the "Independent research" section of this forum. If it will be approved by moderators, we'll have ample opportunities to discuss these issues. Meanwhile, we can talk about quantum gravity privately through e-mail.

I'm relatively new to this forum, what's the idea with the "independent research" section?

Does it refer to economic affiliation, or ideological affiliation to mainstream approaches?

/Fredrik

 

[jtbell]

I'm relatively new to this forum, what's the idea with the "independent research" section?

The Independent Research forum here is for fringe topics or new topics or viewpoints which are not part of discussion by the mainstream physics community. That's a bit vague, but the usual test is, "has it been published, or is it likely to be published, in a mainstream peer-refereed physics journal?" We do bend this guideline for particle physics, string theory, etc., because a lot of mainstream research in those areas is "published" on arxiv.org long before it appears formally in the journals; it's ultimately up to the moderators to decide whether something needs to go into the Independent Research forum.

 

[Fra]

Thanks for the explanation. So if I understand you right the idea is

a) to reserve a special section for those authors whose papers aren't discussed in the popular journal? and explicitly keep mainstream stuff out of there?

rather than

b) keeping "odd things" away from the mainstream sections? which other forums tend to have a "speculations" section for this.

is that close?

/Fredrik

 

[Schrodinger's Dog]

Yes that is it I think kind of.

Overly Speculative Posts:
One of the main goals of PF is to help students learn the current status of physics as practiced by the scientific community; accordingly, Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in most of the PF forums, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional scientific discussion. Posts deleted under this rule will be accompanied by a private message from a Staff member, with an invitation to resubmit the post in accordance with our Independent Research Guidelines. Poorly formulated personal theories, unfounded challenges of mainstream science, and overt crackpottery will not be tolerated anywhere on the site.

https://www.physicsforums.com/showthread.php?t=5374

Try the rules section, I agree myself that overly speculative stuff does not help people trying to learn the fundamentals, whilst it's very important we express an opinion on any subject in physics, there needs to be at least a certain amount of decorum; people posting wildly speculative stuff that has no grounding in science is not what a science forum is about. If you want to post that ensure that you do so and debunk it adequately or show why you think it is untenable, if not take it to an area that can account for it. Or even better just don't post it without permission from a mentor.

I don't think it's an unreasonable demand, some forums like to dwell on the overly speculative, and you are welcome to join them. This forum in my experience keeps it more legitimate, and that is laudable.

 

[masudr]

@Fredrik:

Yeah, the IR forum still has quite strict guidelines. They're not idle speculations. I like PF, it's like SFW but in terms of physics ideas.

 

[Fra]

There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in most of the PF forums, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional scientific discussion.

Doesn't the first and the latter slightly contradict? Or is it implicity assumed that all "intellectually sound" discussions has already been published or that someone who doesn't get payed to publish papers are not to be taken seriously? Or are exceptions to any rules allowed as long as they are "intellectually sound"?

In the strict interpretation of this, I must have violated the forum policy several times, but I haven't seen any complaints. My purposes of beeing here is to exchange ideas in areas that interest me, and for me it happens to border along the foundational and philosophical parts of physics. If I want mainstream ideas I'll read a book.

/Fredrik

 

[meopemuk]

I read your comment like "there is no empirical evidence to support that we can't do this assumption".

You are certainly welcome to make any assumptions. However, if you want to be taken seriously you must develop these assumptions into some kind of working formalism and demonstrate that your theory provides a better understanding of natural phenomena than the existing theory. Personally, I am not impressed by your "probabilities upon probabilities". However, the field of quantum gravity have seen more outrageous proposals. This field is still wide open. Nobody seems to know what to do. Maybe you are the one who got it right? Give it a try. [/QUOTE]

I know the notion can be discussed, but set aside this, I know what the 2nd quantization is and it's been motivated in sometimes quite doubtful ways in books I've seen. I'm suggesting that there is a deeper understanding of this process. And in that case, the "n'th quantization" does make sense to me: "The probability of the probability of the probability of the ..." n times. In fact this can be thought of as an induction step in a larger process. What I mean is that, given the nature of the induction, how can you stop at one iteration and not ask why? You're comment takes the notion of a particle for granted. This isn't obvious either?
/Fredrik

The idea of "third quantization" is floating around for a long time. I just typed this phrase in Google and got 219 hits. Have you checked the literature?

 

[Fra]

However, if you want to be taken seriously you must develop these assumptions into some kind of working formalism and demonstrate that your theory provides a better understanding of natural phenomena than the existing theory.

About "assumption", in my comment above, what I meant was that it was the standard approach that makes the "assumption", not me.

Anway, I'm fully aware of that this has to mature, and I'm working on that, as fast as I can given that this is a hobby for me. If I didn't think I could do better I wouldn't bother. There will be a formalism indeed. But I am not _near_ done yet.

The idea of "third quantization" is floating around for a long time. I just typed this phrase in Google and got 219 hits. Have you checked the literature?

Given limited time, I try to make my selection of what to read and not. I've seen people loosely associating string theory with third quantization although the word third quantization isn't that popular perhaps, and if I'm not mistaken John Baez had some notes about nth quantization long time ago on his site. (I do not like string theory btw). Not that it explained anything, but showing the the idea is out there. That idea is not mine. I'm aware of some of the ideas out there, but the closest I found related to my thinking are the work of Ariel Caticha, who is considering a ME principle as a generalisation of bayes rule and tries to dedude dynamics from the logic of subjective reasoning. Subjective here relates to subjective probabilites of particles interacting. He does not make any connection to n'th quantization though, I do that. This is just a brick in larger scheme. I will contain refined definitions of energy, mass and dimensionality as qualities induced from data which is considerd to contain information.

Given more time, I would love to present the ideas, but at this point I'm in the process of working them out, and to explain the idea to someone who is not coming from the same view, I can't just present ideas, I need to have a complete machinery to present. The completion is what will support the ideas, as viewed from someone who doesn't acknowledge the ideas from the beginning. You probably want to see the proof of success, before you acknowledge the question I ask. I can understand that, because that's the way things work. I am probably the same when it comes to other ideas. That's reality we have to accept, and I have accepted it. Meanwhile I'm working on this.

/Fredrik

 

[Demystifier]

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



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.

With such a reasoning, we have TWO independent theories (nonrelativistic QM and relativistic QFT) that are mutually logically incompatible. Therefore, at least one of them must be wrong. Still, both are in agreement with observations, although at different regimes. If you don't think that there is a puzzle here to solve, then I cannot help you ...

 

[Fra]

I may not agree with Demystifiers Bohmian view but I still feel that he is posing many good questions. I agree that there are many logical blind spots in the usual reasoning to QM and QFT. This is not satisfactory.

/Fredrik

 

[Demystifier]

I may not agree with Demystifiers Bohmian view but I still feel that he is posing many good questions. I agree that there are many logical blind spots in the usual reasoning to QM and QFT. This is not satisfactory.

To recognize the problem is sometimes not easier than to solve it. I have found that the Bohmian interpretation offers a possible solution to several fundamental problems, but I would like to see different solutions as well.

 

[Fra]

> To recognize the problem is sometimes not easier than to solve it.

I agree with this.

/Fredrik

 

[meopemuk]

With such a reasoning, we have TWO independent theories (nonrelativistic QM and relativistic QFT) that are mutually logically incompatible. Therefore, at least one of them must be wrong. Still, both are in agreement with observations, although at different regimes. If you don't think that there is a puzzle here to solve, then I cannot help you ...

When reading most QFT textbooks you can easily get an impression that QFT and QM are totally different subjects. In my opinion, this is not true. QFT is simply an application of QM to systems in which the number of particles can change. This is the point of view developed in S. Weinberg's "The quantum theory of fields" vol. 1. This book is not an easy read, but very rewarding.

Weinberg's point is that in QFT (just as in QM) we are interested in description of particles and their interactions. Then quantum fields come into the picture as an auxiliary tool that is useful for building particle interaction operators, which are consistent with relativity and cluster separability.

 

[Demystifier]

Meopemuk, I agree with you that QFT is actually a more sofisticated theory of particles. Yet, QFT does not answer the question why |\psi(x,t)|^2
represents the probability density of particle positions in the nonrelativistic limit.

 

[Fra]

Meopemuk, I agree with you that QFT is actually a more sofisticated theory of particles. Yet, QFT does not answer the question why |\psi(x,t)|^2
represents the probability density of particle positions in the nonrelativistic limit.

Demystifier, these are good questions from my point of view. I think a satisfactory answer can possible be given in a information learning approach (once more work is done on it) that I've related to in most of my comments on here. It boils down to the question of understanding how a deviation from an expectation can give birth to new concepts, and how this can be done in a systematic way that is in line with the laws of physics.

This is sort of related to your paper on motivating strings, but I see if from a completely different view. But I also see that we share some questions.

Instead of considering an initial value problem of position, momentum and so on, and consider some "mechanical evolution". I instead think it's fruitful to consider an initial value problem which is an opinion, or relative information. You can consider an initial value problems where the different particles have different information about each other. Now the dynamics of this will be closely related to learning. This way of thinking gives a deeper insight to the particle -> field transitions, and also to the nature of time. One may think that the notion of information requires a human brain but that isn't hte idea. A particle can store information about other particles by encoding it in it's own physical states. This also implies a limit of resolution, because a small particle can't encode arbitrary amounts of information. This relates to mass and energy too.

It might even be possible to give an interpretation of the "bohmian particles" in that view, using this thinking. The notion of a "particle" is relative. In the mechanistic thinking this is werid, but in terms of information physics this is completely natural.

I don't know when something is readable but I'll definitely ask you for comments once I've got something readable. Even though you like Bohm, I've got a feeling this may or may not be at least partly appealing to you considering the questions you ask.

/Fredrik

 

[Demystifier]

Thanks Fra, I would like to see your results when they become available.

 

[gato_]

about the question of waveform collapse, i found this usefull
http://arxiv.org/ftp/quant-ph/papers/0306/0306072.pdf
I think decoherence gives the right answer

 

[Demystifier]

about the question of waveform collapse, i found this usefull
http://arxiv.org/ftp/quant-ph/papers/0306/0306072.pdf
I think decoherence gives the right answer

See also
http://xxx.lanl.gov/abs/quant-ph/0312059
It seems that now most experts agree that decoherence does NOT solve the problem of wave-function collapse.

 

[meopemuk]

Meopemuk, I agree with you that QFT is actually a more sofisticated theory of particles. Yet, QFT does not answer the question why |\psi(x,t)|^2
represents the probability density of particle positions in the nonrelativistic limit.

What is \psi(x,t) in your formula? Is it quantum field or wave function? Quantum fields have nothing to do with probability densities. Particle wave functions can be defined in both nonrelativistic QM and in QFT.

 

[Demystifier]

What is \psi(x,t) in your formula? Is it quantum field or wave function? Quantum fields have nothing to do with probability densities. Particle wave functions can be defined in both nonrelativistic QM and in QFT.

\psi is a wave function. I know that it can be defined in QFT. But is it consistent to attribute a probabilistic interpretation to \psi in QFT?

 

[meopemuk]

\psi is a wave function. I know that it can be defined in QFT. But is it consistent to attribute a probabilistic interpretation to \psi in QFT?

Yes, it is possible to define particle wave functions in QFT with a probabilistic interpretation. The only diifculty is that in QFT the number of particles is not specified and is not conserved, so the most general wave function is a superposition of wave functions with different numbers of particles: 0-particle, 1-particle, 2-particle, ... etc.

 

[Demystifier]

Yes, it is possible to define particle wave functions in QFT with a probabilistic interpretation. The only diifculty is that in QFT the number of particles is not specified and is not conserved, so the most general wave function is a superposition of wave functions with different numbers of particles: 0-particle, 1-particle, 2-particle, ... etc.

So let us take the simplest possible case: massless uncharged scalar in a 1-particle state. For a given \psi, write the formula for calculating the probability density of particle positions!

 

[rewebster]

> To recognize the problem is sometimes not easier than to solve it.

I agree with this.

/Fredrik

Yes, and sometimes I think the problem is just too many parameters (some not recognised and/or adjusted for the specific situation)

 

[meopemuk]

So let us take the simplest possible case: massless uncharged scalar in a 1-particle state. For a given \psi, write the formula for calculating the probability density of particle positions!

This should be easy. I'll take | \psi \rangle as a vector in the Fock space. As you said, it is an one-particle vector, so it lies entirely in the 1-particle sector of the Fock space. In this sector I can define the Newton-Wigner position operator \mathbf{R} and its eigenvectors | \mathbf{r} \rangle. Then the position-space wave function corresponding to the state | \psi \rangle is given by formula


\psi(\mathbf{r} ) = \langle \mathbf{r} | \psi \rangle

and the probability of finding the particle in a space region V is given by

\int \limits_{V} |\psi(\mathbf{r} )|^2 d^3r

With minor modifications, this construction can be repeated for multiparticle states as well.

 

[Demystifier]

OK, fine.
Of course, there is a problem of covariance, but there is no reason to repeat it.

Anyway, perhaps you might like my less radical (not Bohmian and still covariant) proposal for the solution of this problem:
http://xxx.lanl.gov/abs/quant-ph/0602024

 

[meopemuk]

OK, fine.
Anyway, perhaps you might like my less radical (not Bohmian and still covariant) proposal for the solution of this problem:
http://xxx.lanl.gov/abs/quant-ph/0602024

Thanks for the reference. I actually had this paper in my collection for a while. You can guess that I have a few objections. Many of them have been posted on this forum already. I am not sure if you want to start another round. Maybe we can agree to disagree, and heal our wounds for a while?