Classical and Quantum Mechanics via Lie algebras

[Rap]

I was really intrigued by Neumaier's approach until I read this discussion and what it predicts for this case.

I guess I missed it - what exactly is Neumaier's prediction (measurement-wise) for one or many buckyballs (or other particles not present in the detector) sent through a double slit? What would happen if one went looking for individual buckyballs at the detector?

 

[Varon]

I guess I missed it - what exactly is Neumaier's prediction (measurement-wise) for one or many buckyballs (or other particles not present in the detector) sent through a double slit? What would happen if one went looking for individual buckyballs at the detector?

Neumaier said that since there is no particle, there is no need to explain where the particle (or Buckyball) goes. Here's Neumaier answer in message #35:

"Most electrons in a real material are there smeared out in a way that the particle picture is misleading. Chemists use electron densities, not electron positions to describe things. Thus a newly arriving delocalized electron is nothing very special to the detector.

In an interference experiment, neither the electron nor the buckyball is a particle, since the latter is a semiclassical concept without meaning in case of interference. Since there is no particle, there is no need to explain where the particle goes.

The density of the electron field or the buckyball field increases at the target - that's all that can be said, and this is enough for verifying what one can actually measure - e.g. the silver film in a Stern-Gerlach experiment after a macroscopic amount of silver accumulated."

What do you think?

 

[Rap]

Neumaier said that since there is no particle, there is no need to explain where the particle (or Buckyball) goes. Here's Neumaier answer in message #35:

"Most electrons in a real material are there smeared out in a way that the particle picture is misleading. Chemists use electron densities, not electron positions to describe things. Thus a newly arriving delocalized electron is nothing very special to the detector.

In an interference experiment, neither the electron nor the buckyball is a particle, since the latter is a semiclassical concept without meaning in case of interference. Since there is no particle, there is no need to explain where the particle goes.

The density of the electron field or the buckyball field increases at the target - that's all that can be said, and this is enough for verifying what one can actually measure - e.g. the silver film in a Stern-Gerlach experiment after a macroscopic amount of silver accumulated."

What do you think?

Well, I read that, but it is still not clear to me what the prediction is. If we shine a beam of buckyballs (plane wave function for buckyballs) on the double slit, what happens at the detector?

I think that the "beam" will be diffracted, and its intensity at a point on the detector will give the probability of detecting a buckyball strike at that point. For many buckyballs, this will give the density of buckyball strikes in the neighborhood of that point. If a buckyball just embeds in the detector without being destroyed, then you should be able to use an electron microscope to find it.

 

[Varon]

Isn't it that Arnold Neumaier approach supposed to make the measurement problem non-existent? But according to The_Duck reply in the Quantum forum about QFT and Particles that:

"The measurement problem has nothing to do with particles in particular. The measurement problem is how we get from a superposition of states to one single observed reality. QFT has superposition in exactly the same way as nonrelativistic quantum mechanics, only now it is superpositions of different possible field states instead of different possible particle positions or whatever."

What really is Neumaier position about this?
(btw.. I love to call him Neumaier as it is unique and like von Neumann.. both of them very skill mathematician... calling him Arnold would keep reminding me of Arnold Schwarzenegger... a brute physical force compare to von Neumann pure intellectual might... lol)

 

[Varon]

Well, I read that, but it is still not clear to me what the prediction is. If we shine a beam of buckyballs (plane wave function for buckyballs) on the double slit, what happens at the detector?

I think that the "beam" will be diffracted, and its intensity at a point on the detector will give the probability of detecting a buckyball strike at that point. For many buckyballs, this will give the density of buckyball strikes in the neighborhood of that point. If a buckyball just embeds in the detector without being destroyed, then you should be able to use an electron microscope to find it.

What? According to the new von Neumann of the 21th century. The particle is never a particle in the first place but just quantum field or wave. So what happens is that (according to him) "It arrives at the various places of detector with different intensities, and these intensities stimulate all the electrons. But because of conservation of energy, only one can fire since the first one that fires uses up all the energy available for ionization (resp. jumping to the conduction band), and none is left for the others"

Therefore you can't find any single buckyball at the detector. They are smeared all over the detector. I don't know if he means the atoms of say a 430-atom buckyball became become fragmentalized all over the detector or the buckyball just divides into many parts that is still interconnected. Hope others can clarify.

 

[strangerep]

[...] it is still not clear to me what the prediction is. If we shine a beam of buckyballs (plane wave function for buckyballs) on the double slit, what happens at the detector?

I think that the "beam" will be diffracted, and its intensity at a point on the detector will give the probability of detecting a buckyball strike at that point. For many buckyballs, this will give the density of buckyball strikes in the neighborhood of that point. [...]

Exactly. The math (as in Mandel & Wolf) just predicts probabilities for interactions occurring (between incident field and detector) in any given region of the detector, in any given time interval. Arnold's interpretation is just an interpretation -- it doesn't make an experimentally testable prediction by itself separate from the theory. The math that actually makes a prediction is the same as mainstream quantum theory.

Strangerep (lone known supporter of Neumaier Interpretation) [...]

... maybe because I've actually worked through large amounts of the detail in his book, and his other papers on quantum theory.

I'd like to remind readers of this thread that Arnold's original purpose in opening this thread was to seek feedback on the presentation in the book prior to publication. (See opening post.) There's a LOT more in the book than just an interpretation, and much of it could benefit from feedback indicating specific areas which are unclear, or mis-sequenced, etc, etc. I.e., the sort of feedback that helps turn a draft into a publication.

Edit: One important theme in the book is already implicit in the title:
"Classical and Quantum Mechanics via Lie algebras".
Arnold addresses both the classical and quantum cases, also thermodynamics, and relates them with considerable insight into their common features, interwoven with Lie-algebraic ideas. This commonality (once comprehended) was a real eye-opener for me when I first began to understand it.

 

[PAllen]

Exactly. The math (as in Mandel & Wolf) just predicts probabilities for interactions occurring (between incident field and detector) in any given region of the detector, in any given time interval. Arnold's interpretation is just an interpretation -- it doesn't make an experimentally testable prediction by itself separate from the theory. The math that actually makes a prediction is the same as mainstream quantum theory.



... maybe because I've actually worked through large amounts of the detail in his book, and his other papers on quantum theory.

I'd like to remind readers of this thread that Arnold's original purpose in opening this thread was to seek feedback on the presentation in the book prior to publication. (See opening post.) There's a LOT more in the book than just an interpretation, and much of it could benefit from feedback indicating specific areas which are unclear, or mis-sequenced, etc, etc. I.e., the sort of feedback that helps turn a draft into a publication.

Edit: One important theme in the book is already implicit in the title:
"Classical and Quantum Mechanics via Lie algebras".
Arnold addresses both the classical and quantum cases, also thermodynamics, and relates them with considerable insight into their common features, interwoven with Lie-algebraic ideas. This commonality (once comprehended) was a real eye-opener for me when I first began to understand it.

There is a discrepancy in here somewhere. Arnold and spectracat agreed that Arnold's theory predicted that a single buckyball diffracted by a double slit would not lodge at any single location on detector screen (it would activate, e.g. electrons in the detector, but would not, itself, lodge at one point). Spectracat and I believe that standard QM predicts the buckyball will lodge at one place, with the location consistent with the propabilities of the interference pattern. Arnold agreed this experiment would distinguish his theory from convention QM.

Please clarify the situation.

 

[strangerep]

There is a discrepancy in here somewhere. Arnold and spectracat agreed that Arnold's theory predicted that a single buckyball diffracted by a double slit would not lodge at any single location on detector screen (it would activate, e.g. electrons in the detector, but would not, itself, lodge at one point). Spectracat and I believe that standard QM predicts the buckyball will lodge at one place, with the location consistent with the propabilities of the interference pattern. Arnold agreed this experiment would distinguish his theory from convention QM.

Please clarify the situation.

Re-reading the earlier posts in this thread, I'm not sure they really "agreed" on very much. But I must leave that for Arnold to clarify since he understands his work much better than I do. :-)

I would have expected that it depends on the details of the interaction Hamiltonian between a (quantum) buckyball field and the spatial array of atoms in the detector, i.e., whether the interaction Hamiltonian allows the formation of a bound state between the buckyball and the detector atoms (both considered as localized fields), or just some sort of excitation of the electrons of the atom(s) in a region of the detector, or maybe a combination of both. I don't see it as being a test of an interpretation though, since the detailed predictions must still be calculated using standard QM/QFT machinery once the interaction Hamiltonian is specified.

 

[A. Neumaier]

Actually, I am not able to give expert critique of Neumaier's theory. From what I do understand, I like it if it were just an interpretation. I just responded the discussion with spectracat, where both agreed that standard QM and Neumaier's theory actually made a different prediction.

Standard QM makes not a single prediction different from the thermal interpretation.

The thermal interpretation simply gives a language for talking about the mathematical stuff in standard QM in a way free of the usual interpretational paradoxes.

In the above situation (interference experiment with a _single_ particle), standard single-particle quantum mechanics predicts only the lack of a responce at places of complete destructive interference, and nothing beyond, in agreement with the thermal interpretation.

On the other hand, quantum statistical mechanics predicts a complicated (and incompletely understood) interaction between the quantum field and the detector _after_ the arrival, which leads to the actual macroscopic situation that can be measured. Whether this interaction leads (a) quickly to a state in which the field concentrated to a single point or (b) only to a state in which the field remains dispersed is completely unknown, and determines the result of an actual experiment along the suggested line: in case (a), the search (which takes some time to complete) will find a single particle somewhere, in case (b) it won't find anything.

The thermal interpretation will be correct if experiment and theory both agree on (a), or if they both agree on (b). The scenario I described in detail before says only what happens until and including arrival of the quantum field, where it is obviously dispersed.

About the multiparticle phase afterwards, the thermal interpretation says that the qantum field and the detector change according to the laws of statistical mechanics, which would have to be employed to do the theoretical calculation that leads to either (a) or (b).

No prediction can be made before either the experiment has been performed reliably enough or a theoretical calculation decides between (a) and (b). Only if both are done and lead to a discrepancy, it would be a failure of quantum mechanics (and therefore also of the thermal interpetation) to describe the situation.

 

[A. Neumaier]

Yup .. that is why I proposed cooling the detector plate to 4K (or below), so that the atoms would stay in their original impact locations.

You can make that sure for the atoms of your detector.

But how do you know the effect of cooling on the behavior of a very delocalized silver field interacting with your detector?

If it turns out that the only metastable configurations are those where the silver field is localized at an approximately definite position in the detector crystal and there are no energy barriers to reach such a state then no amount of cooling would prevent the delocalized silver state to concentrate somewhere before you could do the search.

From the point of view of the thermal interpretation, your guess of the experimental outcome just amounts to the latter situation. It it is what really happens and if quantum mechnaics really predicts rthat then the thermal interpretation is validated by your experiment in spite of your cooling.

But checking whether this situation can occur requires a complex quantum statistical mechanics calculation. I don't know how easy it is to do. Without such a calculation, there is no experimental information to say what could happen.




Another question: Is it feasible to search for single silver atoms with high reliability the complete surface of your detector, if it is large enough to acrtually receive the silver atom with high probability?

I would also modify (ii) to say that exactly one silver atom impacts the surface between imaging steps.

Cooling the detector is easy .. I have multiple 4K cryostats in my own lab. A much bigger problem is making sure that you only have a single atom coming through at a time, I can imagine several approaches to achieving that, but they are all non-trivial, and I am not sure they would work. Even if you could achieve that, imaging a single atom is extremely hard, unless you can narrow down its position to a fairly small region.

They can do it fairly reliable wih photons, but I haven't seen anything in this direction about heavy atoms.

 

[A. Neumaier]

i
Then in Message #16 there. Strangerep quoting JesseM in the above "I think it's misleading to call Neumaier's interpretion a "local" one" said: "I'll leave that one for Arnold to answer in due course."

Ok. Arnold, Pls address JesseM argument that Neumaier Interpretation is not a local one. It seem you tried with superior mathematics to prove that Bell's Theorem and Aspect experiment are just local ones with hidden variable and they don't really have non-local correlations in spite of numerous experiments to the contrary that carries positive result of violation of Bell's Theorem. Arnold Neumaier. Are you trying to say that Bell's Theorem is not really violated. Or the violation is as a result of hidden variables?

The thermal interpretation is fully local, in the sense that it is based on local quantum field theory.
This means that influences cannot propagate faster than light.

Bell's theorem is not about influences but about correlations. There is no causal barrier against nonlocal correlations. Indeed, an ordinary local Maxwell field is causal (and local in the conventionally used terminology) but it exhibits such nonlocal feratures whenever the field is coherent enough and has a nonlocal extension.

 

[A. Neumaier]

Well, I read that, but it is still not clear to me what the prediction is. If we shine a beam of buckyballs (plane wave function for buckyballs) on the double slit, what happens at the detector?

I think that the "beam" will be diffracted, and its intensity at a point on the detector will give the probability of detecting a buckyball strike at that point. For many buckyballs, this will give the density of buckyball strikes in the neighborhood of that point. If a buckyball just embeds in the detector without being destroyed, then you should be able to use an electron microscope to find it.

Note that a ''beam'' is a field concept, not a particle concept. A beam turns into a spherical wave when going through a slit. A particle cannot.

The particle picture is appropriate only as long as one can take the beam to be well-focussed.
The particle picture becomes meaningless once the beam goes through a narrow slit - even a single slit is enough for that. This is why in the Copenhagen interpetation one cannot say anything about the particle anymore - it no longer exists.

That particles are reconstituted under certain conditions under the catalysing effect of a macroscopic detector is quite another story.

 

[A. Neumaier]

"The measurement problem has nothing to do with particles in particular. The measurement problem is how we get from a superposition of states to one single observed reality. QFT has superposition in exactly the same way as nonrelativistic quantum mechanics, only now it is superpositions of different possible field states instead of different possible particle positions or whatever."

What really is Neumaier position about this?

What counts in the thermal interpretation is the expectation of quantum fields. This is always well-defined.
Thus there is always a single reality, no matter in which superposition a system is.

Schroedinger's cat cannot be prepared, hence doesn't pose a problem.
The Schroedinger cat states that can be created experimentally have nothing macroscopic, hence are worlds apart from Schroedinger's cat. They do not really deserve their name.

 

[A. Neumaier]

Therefore you can't find any single buckyball at the detector. They are smeared all over the detector. I don't know if he means the atoms of say a 430-atom buckyball became become fragmentalized all over the detector or the buckyball just divides into many parts that is still interconnected. Hope others can clarify.

While in flight and when arriving, the atoms of a delocalized buckyball are just as delocalized as the buckyball itself. Afterwards it is a complex many-body problem involving thev field and the detector, which nobody has looked at so far. Thus I can't say what QM predicts about what happens afterwards.

Maybe, or may be not, there is a tendency to reconsitute a particle, catalyzed by the detector.

 

[A. Neumaier]

There is a discrepancy in here somewhere. Arnold and spectracat agreed that Arnold's theory predicted that a single buckyball diffracted by a double slit would not lodge at any single location on detector screen (it would activate, e.g. electrons in the detector, but would not, itself, lodge at one point). Spectracat and I believe that standard QM predicts the buckyball will lodge at one place, with the location consistent with the propabilities of the interference pattern.

Arnold agreed this experiment would distinguish his theory from convention QM.

Please clarify the situation.

What I meant was that this experiment would distinguish my interpretation of QM from conventional interpretations of QM. As explained in posts #69 and #70, it cannot distinguish my interpretation from QM itself.

If a single particle diffracted by a double slit would necessarily be found upon inspection to lodge at one place, it would be because both
(i) detection takes a significant amount of time, and the quantum field interacts nontrivially with the detector during the whole time, thus changing the picture I drew (based on the free evolution, ending at the moment the field reaches the detector) and
(ii) the solution of the quantum-mechanical manybody system composed of particle field and detector has such states as the only metastable states with a lifetime long enough compared to a typical detection scale. This is a question that can be determined in principle by a quantum-mechanical calculation.

Thus there is not necessarily a discrepancy between your belief and the thermal interpretation.
But some theoretical analysis is missing to decide what actually happens (assuming that QM is valid).

For those concerned about money: Probably doing this calculation costs far less than 1 million dollars.
Funding of the thesis of an excellent Ph.D. student should be enough.

 

[Varon]

The thermal interpretation is fully local, in the sense that it is based on local quantum field theory.
This means that influences cannot propagate faster than light.

Bell's theorem is not about influences but about correlations. There is no causal barrier against nonlocal correlations. Indeed, an ordinary local Maxwell field is causal (and local in the conventionally used terminology) but it exhibits such nonlocal feratures whenever the field is coherent enough and has a nonlocal extension.

So your thermal interpretation with local quantum field theory has the same mysterious non-local "correlations" as that shown by Aspect experiment? But what cause the correlations at say 100 billion light years distance?? Note I say correltions and not influence (because no information is transfered), but the mere existent of universe wide instantaneous correlation is the issue. Or are you saying that with your superior mathematics you can replace the correlations with local hidden variables? What is the local hidden variable then in your model that has fool all other physicists into thinking there are instantaneous correlations? (beyond the reach of the light cone)

 

[Varon]

What counts in the thermal interpretation is the expectation of quantum fields. This is always well-defined.
Thus there is always a single reality, no matter in which superposition a system is.

Schroedinger's cat cannot be prepared, hence doesn't pose a problem.
The Schroedinger cat states that can be created experimentally have nothing macroscopic, hence are worlds apart from Schroedinger's cat. They do not really deserve their name.

I need to know something.

Supposed you want to send an electron to a double slit. What must be the separation of the slits if they are say 1 meter away?

What is the size of the initial electron field? When it travels to the slits, does the electron field expand in size? Why?

I'm asking this because I'd like to know if the initial electron field emitted from the emitter can become larger than the slits separation when it reach the slits. If it indeed expand, Is this also believed by other physicists, or only you?

Schrodinger preferred the pictures of waves representing particles but Lorentz made him realized that waves can spread. How come Schrodinger didn't think in terms of field that naturally spread (if it does)?

Note in this message I simply wanted to understand the field extend and behavior of the electron, not the behavior of the wave function. Thanks.

 

[A. Neumaier]

So your thermal interpretation with local quantum field theory has the same mysterious non-local "correlations" as that shown by Aspect experiment?

Of course. This is a matter of quantum mechnaics, not of its interpretation. No interpretation can get rid of these facts.

But what cause the correlations at say 100 billion light years distance??

Quantum field theory has local fields and hence local field expectations. In Bell's terminology, the latter are the beables of the thermal interpretation. However, the dynamical degrees of freedom of QFT form a much bigger set, including nonlocal correlation functions of arbitrarily high order.

Thus the dynamics of QFT has the nonlocal correlations built into the dynamical laws.

 

[A. Neumaier]

I need to know something.

Supposed you want to send an electron to a double slit. What must be the separation of the slits if they are say 1 meter away?

It depends what you want. You can arrange distance and width of the slits as you like, and compute the effects of aan electron field passing the slits. But to get nontirival diffraction (and with it the associated loss of the particle interpretation) the slits must be narrow (independent of their distance),
of the order of the Compton wavelength of an electron, and to get an interesting interference pattern, the distance between the slits must be also of this order.

What is the size of the initial electron field? When it travels to the slits, does the electron field expand in size? Why?

Again, this can be arranged in many ways by a corresponding preparation of the source. But the ''size'' of a field is not well-defined.

The intensity can be arbitrary, but if you send a single electron only, this detyermines the intensity (it is then very low).

The shape of the electron field in a beam is given by a solution of the Dirac equation; for a beam it must have an approximately determined momentum and be exponentially damped outside the beam cross section.

The cross section of the beam expands slightly with the distance from the source. For a double slit experiment, both slits must be within the cross section of the beam at the position of the filter containing the slits.

I'm asking this because I'd like to know if the initial electron field emitted from the emitter can become larger than the slits separation when it reach the slits. If it indeed expand, Is this also believed by other physicists, or only you?

These are basic facts of electron optics. (Wikipedia http://en.wikipedia.org/wiki/Electron_optics is not very informative on that, though, you need to consult a book on the subject.)

Schrodinger preferred the pictures of waves representing particles but Lorentz made him realized that waves can spread. How come Schrodinger didn't think in terms of field that naturally spread (if it does)?

He did think in terms of fields. But not in terms of quantum fields as we understand them today. Quantum fields became respectable only around 1948, at a time when Schroedinger was already far beyond hist most creative period.

Note in this message I simply wanted to understand the field extend and behavior of the electron, not the behavior of the wave function. Thanks.

Quantum fields have very little relation to wave functions as treated in QM. The reason is that wave functions in QFT are functions whose arguments are fields, not positions. Very abstract objects.

 

[A. Neumaier]

I'd like to remind readers of this thread that Arnold's original purpose in opening this thread was to seek feedback on the presentation in the book prior to publication. (See opening post.) There's a LOT more in the book than just an interpretation, and much of it could benefit from feedback indicating specific areas which are unclear, or mis-sequenced, etc, etc. I.e., the sort of feedback that helps turn a draft into a publication.

yes. I'd really appreciate this sort of feedback.

By the way, congratulations for having received the science advisor medal!

 

[strangerep]

There's a LOT more in the book than just an interpretation, and much of it
could benefit from feedback indicating specific areas which are unclear, or
mis-sequenced, etc, etc.

[...would appreciate feedback...]

Actually, there one thing which I'd like other people's opinion about...

The book seems to end very suddenly, like encountering a sudden chasm.
There was no epilog chapter that draws together and resummarizes the many
threads in the book. I suspect that's because you were getting tired by that stage,
but it seems to need something like that to polish it off.

By the way, congratulations for having received the science advisor medal!

I found it a bit embarrassing actually, since I'm not in your league.
Let us speak no more of it.

 

[A. Neumaier]

The book seems to end very suddenly, like encountering a sudden chasm.
There was no epilog chapter that draws together and resummarizes the many
threads in the book. I suspect that's because you were getting tired by that stage,
but it seems to need something like that to polish it off.

The course had ended, but a nearly endless subject would have to be continued...

The final book will most likely not end like this.

A lot of stuff is still missing, for example almost everything relating to classical and quantum field theory. Probably I need to give the course a second time, emphasizing the missing things, and have some attentive student to turn it into a good manuscript...

 

[Varon]

Arnold Neumaier book doesn't depend on the QFT interpretation being true, does it? Because if a latest experiment holds, then Neumaier QFT Interpretation is thus refuted. Look at these papers:

http://www.physorg.com/news/2011-06-quantum-physics-photons-two-slit-interferometer.html

http://www.sciencedaily.com/releases...0602143159.htm

http://www.sciencemag.org/content/33.../1170.abstract

It seems to prove that particles indeed choose either left or right slit. Remember Neumaier conjectured is that the field enters both slits and particles don't even exist. The latest experiment refutes Neumaier conjecture.

So before the book is published. Better make it not dependent on the QFT Interpretation being true (which this early is seemingly falsified already).

 

[SpectraCat]

Arnold Neumaier book doesn't depend on the QFT interpretation being true, does it? Because if a latest experiment holds, then Neumaier QFT Interpretation is thus refuted. Look at these papers:

http://www.physorg.com/news/2011-06-quantum-physics-photons-two-slit-interferometer.html

http://www.sciencedaily.com/releases...0602143159.htm

http://www.sciencemag.org/content/33.../1170.abstract

It seems to prove that particles indeed choose either left or right slit. Remember Neumaier conjectured is that the field enters both slits and particles don't even exist. The latest experiment refutes Neumaier conjecture.

So before the book is published. Better make it not dependent on the QFT Interpretation being true (which this early is seemingly falsified already).

WRONG WRONG WRONG WRONG WRONG! Please stop making declarative statements about this stuff when you don't know what you are talking about. You are NOT an expert on this subject, so please read what the articles actually say, and then read what has been said about this experiment on other threads and make sure you understand it before posting. If you don't understand, please ask questions until you do understand.

 

[Oudeis Eimi]

Arnold Neumaier book doesn't depend on the QFT interpretation being true, does it? Because if a latest experiment holds, then Neumaier QFT Interpretation is thus refuted. Look at these papers:

http://www.physorg.com/news/2011-06-quantum-physics-photons-two-slit-interferometer.html

http://www.sciencedaily.com/releases...0602143159.htm

http://www.sciencemag.org/content/33.../1170.abstract

It seems to prove that particles indeed choose either left or right slit. Remember Neumaier conjectured is that the field enters both slits and particles don't even exist. The latest experiment refutes Neumaier conjecture.

So before the book is published. Better make it not dependent on the QFT Interpretation being true (which this early is seemingly falsified already).

*** EDIT
* My original reply came though as being more confrontational than I intended.
* I toned it down a bit to better reflect what I meant, rather than what I wrote.
***

Varon, those results - which you clearly DO NOT understand, despite what you might think - are in completely accord with standard quantum mechanics. They don't falsify any interpretation.

There isn't such a thing as the 'QFT interpretation'. QFT is the mainstream, currently most fundamental formulation of quantum mechanics (I'm considering string theory and LQG as non-mainstream here). Neumaier's 'thermal interpretation' gives the fields described by QFT an ontological status, rather than considering them a computation tool (as some people do), but it's otherwise not as radical an interpretation as you seem to believe. You continue to make these posts in such unjustified, haughty tone, about things you know little about.

If you *really* want to learn physics, drop the pop-sci and open a textbook. Begin with a good general physics text. You have years of study ahead of you before you'll have the basic groundings for discussing QM.

 

[A. Neumaier]

Arnold Neumaier book doesn't depend on the QFT interpretation being true, does it?

Most of my book is independent of any interpretation, in the same way as an ordinary QM textbook. Therefore one can use it in a shut-up-and-calculate fashion. But it is also written in a way to make the analogy between the quantum world an the classical world as apparent as possible, resulting naturally in the thermal representation.

When the latter is applied to quantum fields, it yields the results discussed in this and related threads. But actually the current version of the book contains almost no field theory, as I haven't had the time yet to present the latter coherently.

 

[gpran]

I came to know about this concept of ‘Thermal Interpretation’ from the thread ‘Quantum Interpretation Poll (2011)’. I am writing this to get clarification about some of the basic concepts.

1) Please see the slide show: http://arnold-neumaier.at/ms/optslides.pdf. It mentions that the intensity of the beam is S0 = ψ*ψ. Does it mean that ψ*ψ gives classical intensity of the beam and not probability? I believe that probability is of statistical nature whereas intensity is real. May be, it is suggested that probability of finding a particle is more if intensity of beam is greater in a particular location. This is acceptable where we have large number of particles but what about a single particle?
2) The Schrödinger equation is obtained in the paper through a mathematical exercise. Can we say that the equation has been derived and not presented as a postulate? Is it because we are assuming a classical beam of particles for the derivation?
3) What is exact picture of a particle? If you suggest that a particle is like a beam or wavepacket then it is equally confusing or abstract. If a charged particle electron is like a beam then does it mean that the mass and charge are spread throughout the space? If there are two particles then the two beams may mix with each other leading to a bigger particle. For neutral particles like photons this is acceptable but for charged particles like electron this may not be acceptable. In widely accepted Q.M. interpretation, ψ is not real and therefore addition does not lead to a bigger particle.
4) I presume that there is no problem of wavefunction collapse in this approach. Is it because the theory assumes a classical beam of particles/photons?

I may be asking these basic questions because I have not really understood what is said in the slides. My problem is that I am trying to compare every statement made in the slides with the traditional interpretations taught in the textbooks. I feel that a short note/chart about the concept giving the differences with the presently accepted interpretations may help. I request help from anybody who is working on this theory.

 

[A. Neumaier]

1) Please see the slide show: http://arnold-neumaier.at/ms/optslides.pdf. It mentions that the intensity of the beam is S0 = ψ*ψ. Does it mean that ψ*ψ gives classical intensity of the beam and not probability? I believe that probability is of statistical nature whereas intensity is real. May be, it is suggested that probability of finding a particle is more if intensity of beam is greater in a particular location. This is acceptable where we have large number of particles but what about a single particle?

Everything in Section 1 is classical physics. Neither particles nor probabilities are involved, only the electromagnetic field.

You may read as background Chapters 2 and 6 of the book by Mandel & Wolf. (It has quantum optics in its title but the first 8 chapters are purely classical.)

Section 1 demonstrates that a simple quantum system, which is usually described in terms of particles and probabilities (and associated interpretation problems), can as well be described by a classical field (and was in fact so described, almost 50 years before Planck first suggested quantization), without losing anything in predictive value.

The remainder of the paper extends this equivalence to everything that can be done with a single photon.

However, entangled multiphoton states cannot be described by the classical electromagnetic field. But the thermal interpretation can be extended - though this is yet to be written up.

2) The Schrödinger equation is obtained in the paper through a mathematical exercise. Can we say that the equation has been derived and not presented as a postulate? Is it because we are assuming a classical beam of particles for the derivation?

The derivation shows that with the assumptions and approximations made, the Schroedinger equation holds in the classical setting. Therefore it is derived, not assumed.

Assumed was only classical physics.

3) What is exact picture of a particle?

There is no exact picture of a particle, just as there is no exact picture of a cloud.

A particle is a localized field concentration that consistently behaves like a classical point at the length scales probed. Its boundary is a bit fuzzy but the fuzziness doesn't matter since it is below the scale of resolution of the description.

If you suggest that a particle is like a beam or wavepacket then it is equally confusing or abstract.

Confusing is to think particles are well-defined points. Real particles, no matter of which size, are extended objects with fuzzy boundaries. Point particles are unreal abstractions of real particles, obtained by deliberately ignoring detail in order to gain simplicity of the description.

In celestial mechanics, where the particle picture originated, stars and planets are particles. Where does the star or planet begin and end? One cannot tell - the atmosphere just gets thinner and thiner as one goes outward, and at some point its density is so small that one doesn't care anymore. Thus stars and planets are ill-defined as exact objects, but they are well-defined as a point for most practical purposes. Except for the planet Earth, which is too close to us observers to treat it as a point particle. Therefore we use a field description of the earth: At each point we know the composition and density of the materials.

In the quantum realm things are fully analogous. As long as we don't consider length scales comparable to its size, an atom or elementary particle behaves like a point - it is a particle. But once shorter scales become relevant (going through a narrow slit, say), the particle description becomes inappropriate and one needs more detail - provided by the field description,.

If a charged particle electron is like a beam then does it mean that the mass and charge are spread throughout the space?

Yes. Just as the mass of the particle Earth considered in celestial mechanics is spread out throughout the space.

If there are two particles then the two beams may mix with each other leading to a bigger particle.

Not usually. They will pass each other, and occasionally, particles in the beams will scatter. It is uncommon that particles from different beams stick together.

4) I presume that there is no problem of wavefunction collapse in this approach. Is it because the theory assumes a classical beam of particles/photons?

No. The thermal interpretation is an interpretation of quantum systems, described by the usual shut-up-and-calculate attitute, but giving intuitive words so that one can open one's mouth without talking nonsense.

Collapse exists in a much-used approximation, namely to precisely the extent it is derivable from the standard methods of nonequilibrium statistical mechanics.

The thermal interpretation affects not the collapse but the way one interprets measurements. Measured directly are _not_ eigenvalues of operators, only expectations of macroscopic quantum fields.

But everything one can say about a microscopic system is obtained by inference from the way the microscopic system interacts with the observing macroscopic system according to the standard Rules of Quantum Mechanics and statistical mechanics.

I may be asking these basic questions because I have not really understood what is said in the slides. My problem is that I am trying to compare every statement made in the slides with the traditional interpretations taught in the textbooks. I feel that a short note/chart about the concept giving the differences with the presently accepted interpretations may help. I request help from anybody who is working on this theory.

Since different people have very different questions about the thermal interpretation I can prepare such a note only after I have enough feedback from readers about what needs which sort of explanation. This is the main purpose of this discussion thread. (Well, for my whole book, not just for the thermal interpretation, though the latter seems to attract most of the interest here.)

Ultimately I'll write a properly published paper on the subject, giving a reasonably complete view of the thermal interpretation.

At present, simply ask about everything that you don't understand, and I'll do my best to explain.

 

[my_wan]

I am busy studying Arnold's work. I have not commented here because Arnold wants feedback from those having difficulty with his interpretation and I am quiet accustomed to thinking about QM in very similar terms. Though Arnold has certainly thought about it in many ways I have not. Perhaps me throwing in a perspective might help, maybe. Otherwise it can be refuted or ignored.

By the way, this thermal interpretation also extends to gravity. Such as outlined by Brustein and Hadad in "http://arxiv.org/abs/0903.0823" ", JHEP 1104:029,2011, describing gravity as an entropic force. I suspect that the connection may run much deeper than mere interpretation can fully justify.

It seems to me that most of the confusion is primarily generated by various levels of conflation between theory and interpretation, which are woefully different beast. The remainder appear to be mostly trying to visualize a mass particle as a group of particles traveling through an otherwise empty space. Even a classical wave cannot be described this way, as there are no distinct set of particles traversing a gas to convey sound. Thinking of a mass particle as a distinct group of parts is equally bogus in this thermodynamic interpretation.

To get the interpretive picture forget the particles and look at the definition of a Hilbert space. Now simply assume this Hilbert space is ontologically real and extends throughout all space like air extends throughout an atmosphere. Now consider the wave function, but instead of defining it as a probability think of it as a variational density change in Hilbert space. Much like sound is a variational density change in a gas. At times the density variations can be highly localized. Much like a classical soliton can. In such cases we can refer to that soliton a distinct entity, just like we refer to a tornado as a distinct entity even though fundamentally it is not, and is not even defined by a distinct set molecules. Likewise for a mass particle in this interpretation. Then when you create a situation with many such particles interacting, density variations (not probabilities), which particle is which becomes an ill defined concept. Like asking which wave is which on a choppy ocean. The difference is the medium in this case is defined by an ontologically real Hilbert space with somewhat different properties than a classical medium. Only it still shares the same basic thermodynamics under the degrees of freedom provided by the Hilbert space. Perhaps, maybe for some, that will give some basic context under which to conceptualize the interpretation. Arnold can take exception to any point he sees fit, and/or consider the general reaction to it.

Arnold, have you looked at the phenomena of "ghost interference"? This fits well into this interpretation and might possibly provide a way to measure the energy associated with the total wavefunction itself. This would allow us to study conservation laws as it applies to the wavefunction as a whole. Of course it also provides an interpretation of virtual particle production and associated momentum fluctuations, interaction free measurements, etc.

I cannot claim this is a perfectly valid interpretation, but nothing I have seen refutes it and that is all that is required so long as it is characterized simply as an interpretation. In fact, given that it is empirically predicated on a standard Hilbert space, it is essentially by definition very difficult to refute.

 

[A. Neumaier]

I am busy studying Arnold's work. I have not commented here because Arnold wants feedback from those having difficulty with his interpretation and I am quiet accustomed to thinking about QM in very similar terms.

Actually I am interested in all sorts of feedback that helps me to give a better exposition of everything I did in this direction.

By the way, this thermal interpretation also extends to gravity. Such as outlined by Brustein and Hadad in "http://arxiv.org/abs/0903.0823" ", JHEP 1104:029,2011, describing gravity as an entropic force. I suspect that the connection may run much deeper than mere interpretation can fully justify.

Yes. It may well turn out that gravitation is a pure thermodynamic effect. But in my book and lectures I am sticking to the most solidly accepted part of quantum mechanics, to avoid any unnecessary friction.

To get the interpretive picture forget the particles and look at the definition of a Hilbert space. Now simply assume this Hilbert space is ontologically real and extends throughout all space like air extends throughout an atmosphere.

This was Schroedinger's idea, but turned out to be not realizable as the dimensions are vastly different. In the thermal interpretation, the ontological status of beables is given to the field expectations, which are true fields in spacetime rather than objects in a high-dimensional space. This is the improvement upon Schroedinger and the reason why everything works neatly and intuitively.

Arnold, have you looked at the phenomena of "ghost interference"?

I never heard of this term. Could you please provide a reference?