Classical and Quantum Mechanics via Lie algebras

[A. Neumaier]

Come on PF members. If Neumaier was right. Others would have figured this out already for more than a century.

How could this have been figured out before 1911, at a time where not even the Schroedinger equation was discovered? The reason why it hasn't been discovered is that those working on the foundations rarely also work on quantum fields, and those who work on the latter usually have more pressing things to do than to indulge in foundational issues. So the interface between foundations and quantum fields has been very little explored.

I'll start with Camboy criticism (A. Neumaier, pls. comment on it):

"I'm sorry - this sounds like nonsense to me. He says only 1 electron in the detector responds because of conservation of energy. What happens when the screen is the inner surface of a hollow sphere a light-year across, and the emitter is a point source dead in the middle emitting a spherical moving quantum field? How is the energy transported across space via the quantum field? Across the whole wave front? In which case, what kind of process involving conservation of energy takes place around the whole surface of the sphere instantaneously when the wave hits the screen? How does this work? if you wish to provide an 'interpretation' one must do more than simply state something happens."

Well?

A quantum field transports the energy in the same way as a classical field, namely by evolution according to the field equations. The energy of a radially expanding field is distributed uniformly.
So an extremely tiny amount of energy arrives at any place of the hollow sphere, integrating over the sphere to the energy of one electron. Thus energy is conserved. The probability of response anywhere is extremely tiny, too, so that uncertainties in the sphere by far dominate the effect, and nothing can be concluded.

 

[A. Neumaier]

I was really intrigued by Neumaier's approach until I read this discussion and what it predicts for this case. Why use buckyballs? Something much simpler: any atomic or molecular beam prepared to interfere in the double slit experiment with deposition on plate that contains none of that atom or molecule. Run it only long enough for sparse deposition, and check for individual atoms consistent with an interference pattern. Shouldn't be hard to do (e.g. silver on glass plate).

I would literally bet a million dollars that the outcome would be consistent with conventional interpretations and falsify Neumaier's.

Note that doing the experiment is far from easy. You need to make sure that
(i) the absorbing surface is completely silver-free,
(ii) one and only one silver atom is emitted by the source,
(iii) The silver field at the absorber had no time to redistibute itself during the procedure it takes to search the absorber for a single silver atom.

 

[Varon]

Sorry, I can't stay silent. The never-ending torrent of such sensationalist ill-informed remarks is getting a bit tedious.

The whole point about interpretations is that every interpretation predicts the same things for any given experimental setup. If they didn't, then interpretations would be experimentally decidable, and those in contradiction with experiment would be discarded. Arnold's interpretation is just that -- an interpretation. It does not contradict experimental results, but rather offers a more rational way of thinking about QM.

And others did "figure it out" (in related forms). Arnold already said elsewhere that his initially naive views about particles in QM were improved considerably after discussions with experts in quantum optics years ago.

If you want to search for a "right" interpretation, first master the most essential and basic interpretation, i.e., "shut up and calculate". Everyone with an interpretation must master "shut up and calculate" first, since that's what decides whether QM is or isn't in contradiction with experiment.

Mainstream Quantum Interpretations are only accepted as valid candidates if they are at least scrutinized by 500 physicists. Neumaier's interpretation just less than ten. That is why I'm inviting others to help scrutinize it. You, Strangerep, is on Neumaier's side. So those who are neutral or can see the logical flaw of Neumaier's such as Pallin pls. elaborate. If at the end of the day, you can't see any theoretical flaws and agree it's a valid interpretation candidate. Then state so in order to make Neumaier's Interpretation part of pop-sci books.

Regarding buckeyballs, atom interferometry, etc, the generic features of the "shut up and calculate" interpretation for a field incident on a double-slit were explained in post #73 of this thread:

https://www.physicsforums.com/showthread.php?p=3171882#post3171882

with an additional bit in post #78.

The more accurate calculations with a relativistic quantum field instead of a classical field do not change the gross features significantly. (Mandel & Wolf give details.)



It's an incident field, and it's already been discussed in the thread I mentioned above. The calculations from Mandel & Wolf indicate the probalistic nature of the predictions.

 

[Varon]

How could this have been figured out before 1911, at a time where not even the Schroedinger equation was discovered? The reason why it hasn't been discovered is that those working on the foundations rarely also work on quantum fields, and those who work on the latter usually have more pressing things to do than to indulge in foundational issues. So the interface between foundations and quantum fields has been very little explored.


A quantum field transports the energy in the same way as a classical field, namely by evolution according to the field equations. The energy of a radially expanding field is distributed uniformly.
So an extremely tiny amount of energy arrives at any place of the hollow sphere, integrating over the sphere to the energy of one electron. Thus energy is conserved. The probability of response anywhere is extremely tiny, too, so that uncertainties in the sphere by far dominate the effect, and nothing can be concluded.

Pallin, what can you say about Neumaier's explanation above? If he is right... since you want to bet a million dollars against him... then Neumaier's would be richer by 2.3 million dollars because a Nobel Prize money is about 1.3 million dollars... lol...

Others pls. join scrutinize Neumaier's Interpretation and either support it doesn't violate some known principles or have theoretical flaws or point out the flaws if you can so Neumaier would be aware of them too, and can either improve them or just call it a day.

 

[PAllen]

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. That makes it not just an interpretation (similar to, if you believe some of Deutch's proposals, MWI is testable). Given the difference in prediction, my physical intuition finds the standard prediction much more plausible, enough for me to bet on it. Given this I simply wanted to raise that buckyballs are not needed - just something easy to detect that is not in the receiver.

I would be very interested in strangerep commenting on the prediction difference and the feasibility of an experiment. Strangerep knows this area *much* better than I.

 

[Oudeis Eimi]

Mainstream Quantum Interpretations are only accepted as valid candidates if they are at least scrutinized by 500 physicists. Neumaier's interpretation just less than ten. That is why I'm inviting others to help scrutinize it. You, Strangerep, is on Neumaier's side. So those who are neutral or can see the logical flaw of Neumaier's such as Pallin pls. elaborate. If at the end of the day, you can't see any theoretical flaws and agree it's a valid interpretation candidate. Then state so in order to make Neumaier's Interpretation part of pop-sci books.

Pop-sci!? Why would you want such a thing in the first place?
I thought we were talking REAL science here.

 

[SpectraCat]

Note that doing the experiment is far from easy. You need to make sure that
(i) the absorbing surface is completely silver-free,
(ii) one and only one silver atom is emitted by the source,
(iii) The silver field at the absorber had no time to redistibute itself during the procedure it takes to search the absorber for a single silver atom.

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.

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.

I think these experiments are doable, but would require at least a million dollars worth of equipment to achieve. As interesting as I find Neumaier's proposal, I am sad to say that I don't think there are many experimentalists out there willing to commit those kinds of resources to this project.

 

[Varon]

Pop-sci!? Why would you want such a thing in the first place?
I thought we were talking REAL science here.

Pop-sci means popular science and includes books from Brian Greene, Gribbin, and other pop-sci books. Brian Greene and others have mentioned all existing interpretations but not Neumaier Interpretation. Hence if it's valid, then it should be part of pop-sci books so people would have options that is based on QFT.

 

[Varon]

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.

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.

I think these experiments are doable, but would require at least a million dollars worth of equipment to achieve. As interesting as I find Neumaier's proposal, I am sad to say that I don't think there are many experimentalists out there willing to commit those kinds of resources to this project.

CERN and Fermilab have resource and budgets. I wonder how to introduce Neumaier approach to them. If they can prove Neumaier conjecture... they would get the million dollars back as a Nobel Prize money amounts to 1.3 million dollars. Remember the scientists who were able to prove Einstein Photoelectric effects.. they won a Nobel too.

 

[Varon]

in the thread https://www.physicsforums.com/showthread.php?t=490677&highlight=Neumaier+Interpretation there is an unanswer message from JesseM about Neumaier Interpretation and Bell's Theorem. The last message of it points to this thread so let us continue where it left.

In message #14, Strangerep (lone known supporter of Neumaier Interpretation) states:

"No. States do not consist of "definite outcomes". Although one might like to think of individual events in experiments as definite outcomes, all experiments involve some level of statistical analysis."

JesseM answered:

I think you're talking about statistical analysis used in coming up with values of variables for the quantum system itself, but I was talking about the macroscopic "pointer state", like the number that appears on a computer monitor after it runs its statistical analysis program (or the numbers representing raw data before analysis, which may not directly correspond to any quantum observable). That's an element of the physical world too, one which we can directly observe, if Neumaier's interpretation only gives probability distributions for such macro-states rather than definite values, then I would say it isn't a full model of the "one world" we find ourselves in. Again, I'm not requiring that a full model allow such states to be predicted in a deterministic way, it'd be fine if it had a stochastic element which randomly picks one macrostate based on the probability distribution, but as I said this element would have to be a nonlocal one.

Think of it this way: suppose you want to build a simulated universe running on a computer (or collection of computers, see below), and the simulation is supposed to model all the types of macrostates we can directly observe (while it doesn't need to have any model of microstates which we only infer based on macrostates). The model need not predict the results of particular trials of any real-world experiment, but we should be able to create a model of the same type of experiment on our computer(s), with the simulation yielding a series of macroscopic pointer states whose overall statistics should match the results of analogous experiments performed in the real world. If we require that the simulation be a "local" one, then we could imagine a bunch of computers which were each responsible for simulating a small element of space, and on each time-increment the computer should give an output based only on inputs from other computer outputs that lie within its past light cone (this is assuming the laws of physics can be approximated arbitrarily well be a simulation with discrete "pixels" of space and time; if not, you could imagine replacing the finite array of computers with a perfectly continuous array of "functions" at each point in space, which continuously produce outputs at each instant of time based only on inputs from points in their past light cone). And the computers can have stochastic random number generators built in, so if part of their output consisted of a probability distribution, they could also use that probability distribution to randomly select one specific output based on that distribution.

If observable macrostates in a region of space at a particular time are just a function of all the computers' outputs in that region at that time (outputs which may be thought of as "microstates" for specific points in space), then the point here is that no "local" simulation of this type, where the computers have no access to inputs outside their past light cone when generating outputs, can ever give a pattern of macrostates consistent with QM. Even if computers at each point can generate probability distributions in a local way, a stochastic rule for generating specific outcomes based on these probability distributions would have to operate nonlocally, with computers representing points at a spacelike separation coordinate their random choices to make sure they created the correct entanglement correlations. This is just a natural consequence of Bell's theorem. So, I think it's misleading to call Neumaier's interpretion a "local" one, it either fails to model the fact that we see particular outcomes for macroscopic pointer states (which all other interpretations attempt to account for) rather than just probability distributions, or if the model is made to include a stochastic rule for generating a series of particular macrostates, then the rule must operate in a nonlocal fashion.

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?

 

[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?

 

[my_wan]

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.

Yes, well understood and I concur. It is obvious that you are not explicitly trying imply anything outside the standard model, rather just express it from a particular context. I just threw this in as an extension, more or less as an afterthought, to illustrate that the interpretation could potentially run deeper than what you intend convey.

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.

This is where your thinking on the subject appears superior to mine. I was well aware that that once you tried to take the analogies with ontological parts of the field, rather than the field itself, too seriously it runs into very distinct problems. The expectation values in QM are simply NOT the positions and momentums of distinct parts the way they are in classical physics. I was not trying to suggest in the analogy provided held in the particulate sense. Only that in defining a mass particle in terms of a deformable field the apparently localized structure is really no more distinct than a wave is in classical physics. I am still trying to work through the details of precisely how you deal with "field expectations" in an ontological sense. Just because it makes sense in a general way is no garrantee of a lack of incongruencies, but I have nothing to indicate specific incongruencies as yet.

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

Here is one from Phys. Rev. A 54, 1996, "http://www.ino.it/~azavatta/References/PRA54p3489.pdf"".

This phenomena has also been used in "ghost imaging", which allows a camera to take a picture of something the camera cannot see. This is also used in single-pixel detector setups and it is argued by some that this is evidence that it does not depend on non-local quantum correlations.
http://arxiv.org/abs/0812.2633

I am also very curious about this experiment showing interference in uncorrelated separable lights sources, which is given in the context of cross beam experiments mentioned in the paper.
http://arxiv.org/abs/physics/0504166
Though I do not know how much weight to put on these results.

 

[my_wan]

Now I think I have a more complete picture of your interpretation. I went back to some of your earlier work. Primarily:
http://lanl.arxiv.org/abs/quant-ph/0303047"

You place no judgment at all on the noncommutativity of QM, other than as an empirical fact, and conceptually work with the "expectation values" as fluid properties in the classical thermodynamic sense. Thus Hilbert space remains a separate construct in an ontological sense with no specific ontological status assigned directly to it. That certainly does escape many classical issues while still maintaining a direct and unmodified formal transition from one to the other. The difficulty it appears then is making the point when people are so accustomed to assigning distinct empirical properties to distinct points in space.

How do you deal with the conservation issue with wave cancellations? In effect it boils down to, if two quantum waves overlap so as to cancel what happened to the energy associated with those waves? If they simply become non-existent there appears to be a conservation violation. Dirac got around this by simply assuming particles could only self-interact, hence they did not really disappear.

This self-interaction hypothesis is, however, dubious.
http://arxiv.org/abs/quant-ph/0312026" .

 

[Ken G]

I'm only just beginning to be introduced to the thermal approach, but what I've seen so far shows promise. On another thread, I was grappling with the question of how we should regard "what a classical apparatus knows about itself", in a sense. The usual interpretation is that the projection onto the measuring device is a mixed state, and further, that a mixed state is "in a definite state we just don't know which." Then when we look, it merely confirms what was true before we looked. Although this runs into no problems in experience, it does not seem to be strictly true to our own theory-- our own theory tells us that a mixed state is just a mixed state, and not a definite state that we just don't know which. The latter conjures the concept of a probability distribution, but the former seems more inherently "fuzzy" to me. It seems your language offers the possibility of putting that difference on a firmer basis.

If you consider the subtext of what I'm saying, I suggesting that maybe you can take your idea even farther: out of the nebulous quantum realm, where "anything goes" pretty much, and into the well-worn classical realm, where surely there are no new surprises. But the status of a "mixed state" was always a bit nebulous in the classical realm too-- we say that the air in this room, treated classically, is in a definite state "we just don't know which one", but how do we really know that this is what the classical theory asserted? There is no instrument or perceptive agent anywhere that has the power to tell the definite state of the air in the room, so on what basis did we claim there was such a state?

On the other hand, if I shuffle a deck of cards, I might struggle with wondering if every card is in a definite micostate of internal particles, but I don't have difficulty asserting that the order of the cards is definite, even before the cards are looked at. This conforms to our tests, because we can objectively determine the order of the cards. So does the concept of "resolution" come up here too, is the status of a deck of cards really something different, from an information theory standpoint, than the microstate of the air in this room? Was there fuzziness in classical physics that we just never noticed?

 

[A. Neumaier]

I'm only just beginning to be introduced to the thermal approach, but what I've seen so far shows promise. On another thread, I was grappling with the question of how we should regard "what a classical apparatus knows about itself", in a sense. The usual interpretation is that the projection onto the measuring device is a mixed state, and further, that a mixed state is "in a definite state we just don't know which."

In the thermal interpretation, the classical properties are manifest as the expectations of the field operators. This matches naturally with a hydrodynamical description of classical matter. Thus the problem of identifying the classical properties simply vanishes. Statistical mechnaics guarantes that the fields are measurable in a coarse-grained sense, because of being in a mixed (thermal) state.

There is no instrument or perceptive agent anywhere that has the power to tell the definite state of the air in the room, so on what basis did we claim there was such a state?

One doesn't need a fully precise description, since the obsefvation of a field is itself necessarily coarse-grained. It is enough that the description matches the actually possible resolution. In the thermal interpretation, this is guaranteed by the standard results from statistical mechnaics.

 

[A. Neumaier]

Now I think I have a more complete picture of your interpretation. I went back to some of your earlier work. Primarily:
http://lanl.arxiv.org/abs/quant-ph/0303047"

You place no judgment at all on the noncommutativity of QM, other than as an empirical fact, and conceptually work with the "expectation values" as fluid properties in the classical thermodynamic sense. Thus Hilbert space remains a separate construct in an ontological sense with no specific ontological status assigned directly to it. That certainly does escape many classical issues while still maintaining a direct and unmodified formal transition from one to the other. The difficulty it appears then is making the point when people are so accustomed to assigning distinct empirical properties to distinct points in space.

In quantum field theory, expectations of the field operators also apply to any point in space, and indeed one gets from the thermal interpretation very naturally the hydrodynamical description of classical matter, with definite properties at every point. Thus there is no such difficulty, once one thinks in terms of quantum fields.

How do you deal with the conservation issue with wave cancellations?

The situation is not really different from that with a classical Maxwell field, where waves can destructively interfere.

 

[Ken G]

In the thermal interpretation, the classical properties are manifest as the expectations of the field operators. This matches naturally with a hydrodynamical description of classical matter. Thus the problem of identifying the classical properties simply vanishes. Statistical mechnaics guarantes that the fields are measurable in a coarse-grained sense, because of being in a mixed (thermal) state.

Yes, that is an attractive feature. Some people are left unsatisfied by that, they want an ontology that is crisp, but then they face questions that cannot be answered satisfactorily. Your approach loosens the ontology, but the questions evaporate. I call that a good trade, but others seem to prefer to keep the questions instead. That way all they have to do is sweep the questions under the rug and they have the best of all possible worlds, though it is something of a mild self-delusion I would say.

It is enough that the description matches the actually possible resolution.

And that's the heart of it right there-- when is that enough, and when is it not enough. To me, it raises the same issue that the Copenhagen interpretation raises: which is paramount, our ontologies or our epistemologies? Are we trying to know what is, or are we trying to fit our images of what is to what we can know? It sounds like you are siding with Copenhagen and taking that latter approach, and that is one of the things I like about your approach. You also seem to be more specific about things that Copenhagen is willing to leave uncharacterized.

 

[Ken G]

The situation is not really different from that with a classical Maxwell field, where waves can destructively interfere.

It's interesting that you say this, because on several other threads about weak measurements and Bohm interpretations and so on, I've been trying hard to draw the parallels between the quantum and classical pictures. I'm finding many people are unwilling to consider those kinds of parallels-- I even had one person tell me I was embarrassing myself by trying to point them out! There's a kind of myth that "quantum is quantum and classical is classical and never the twain shall meet." I'm not sure where that thinking comes from, it seems to completely ignore the correspondence principle, but maybe it's because educators have had to stress "quantum weirdness" in order to get students interested in that nether world. If so, they may have succeeded too well!

 

[rodsika]

Dear Ken, can't you see anything wrong with the thermal interpretation. Dr.
Neumaier was basically claiming that when a 430 atom molecule in the form of
buckyball was sent to the double slit. The slits literally slit the
buckyball into hundreds or thousands of pieces and spatter them across the
detector. And since a detector is consist of millions of electrons. One of these
get triggered and we erroneously thought this one triggered was the location of
the original buckyball when it was just a part of it. This was possible because
according to him, the buckyball being emitted was not a particle to start with
but a field which is undefined. As a more distinct example in case you haven't
grasped the basic of this interpretation. It's like if you sent a cow to the
double slit. It slits the cow into dozens of pieces. When say the kidney hits one of the existing electrons in the detector. We thought the cow is located in that electron
detector position. Dr. Neumaier reasoning this was possible was because the cow
was a field to start with. Now with all our experimental might. Can't we test
this outrageous claim of Dr. Neumaier, or recalling all your knowledge as full
fledge physicist.. can you think of a way to*scrutinize it.*If you meet your
fellow physicists in the lab. Please ask if they can think of a way to test Dr.
Neumaier conjecture and whether there wasn't already existing test(s) that might
have already refuted it that we might not be aware of.. such as a test that
established the particle nature of matter in an absolute way. Thank you.

 

[Ken G]

Dear Ken, can't you see anything wrong with the thermal interpretation. Dr.
Neumaier was basically claiming that when a 430 atom molecule in the form of
buckyball was sent to the double slit. The slits literally slit the
buckyball into hundreds or thousands of pieces and spatter them across the
detector. And since a detector is consist of millions of electrons. One of these
get triggered and we erroneously thought this one triggered was the location of
the original buckyball when it was just a part of it. This was possible because
according to him, the buckyball being emitted was not a particle to start with
but a field which is undefined.

It might be putting words in his mouth, but if I trust that your rendition is accurate, I would say that I do see that as a potentially valid picture, even if a bit bizarre at first look.

If I understand the perspective, he might say that the buckeyball isn't really a buckeyball in the first place, it is a field that we have labeled a buckeyball because when we have lots of it we have lots of buckeyballs, and when we get just one, we assume there was already one there, but we don't really know what was already there, it's just kind of an assumption on our part. We assert its existence and find no contradiction, but that's not the same as saying we know it existed, if there isn't really anything there called a "real buckeyball" in the first place. To be honest, I'm rather sympathetic to that approach, because I like keeping careful track of what we know versus what we are just assuming we know.

It's like if you sent a cow to the
double slit. It slits the cow into dozens of pieces. When say the kidney hits one of the existing electrons in the detector. We thought the cow is located in that electron
detector position.

That doesn't sound like a fair characterization, because a kidney is a distinguishably different piece of a cow, whereas the "buckeyball field" he is talking about doesn't have distinguishably different parts like that (we are not actually breaking the bonds in there, after all).

Please ask if they can think of a way to test Dr.
Neumaier conjecture and whether there wasn't already existing test(s) that might
have already refuted it that we might not be aware of.. such as a test that
established the particle nature of matter in an absolute way.

I'm pretty sure Dr. Neumaier's approach is designed to make all the same predictions as more typical modes of thought, so we already know it's not going to be testable. Instead, the question is, does this mindset make certain troubling questions go away, or does it build a picture of "what is" that we find repugnant in some way? I'm afraid questions like that are always going to be matters of personal taste, but I do see a certain plausibility in the idea that there really is no such thing as "a cow." A better ontology might assert the existence of fields of attributes of various systems or combinations of systems that when you put them altogether you end up with something we recognize as a cow by virtue of gross similarities of behavior and appearance to our mental image of what a cow is.

 

[rodsika]

It might be putting words in his mouth, but if I trust that your rendition is accurate, I would say that I do see that as a potentially valid picture, even if a bit bizarre at first look.

If I understand the perspective, he might say that the buckeyball isn't really a buckeyball in the first place, it is a field that we have labeled a buckeyball because when we have lots of it we have lots of buckeyballs, and when we get just one, we assume there was already one there, but we don't really know what was already there, it's just kind of an assumption on our part. We assert its existence and find no contradiction, but that's not the same as saying we know it existed, if there isn't really anything there called a "real buckeyball" in the first place. To be honest, I'm rather sympathetic to that approach, because I like keeping careful track of what we know versus what we are just assuming we know.
That doesn't sound like a fair characterization, because a kidney is a distinguishably different piece of a cow, whereas the "buckeyball field" he is talking about doesn't have distinguishably different parts like that (we are not actually breaking the bonds in there, after all).

I'm pretty sure Dr. Neumaier's approach is designed to make all the same predictions as more typical modes of thought, so we already know it's not going to be testable. Instead, the question is, does this mindset make certain troubling questions go away, or does it build a picture of "what is" that we find repugnant in some way? I'm afraid questions like that are always going to be matters of personal taste, but I do see a certain plausibility in the idea that there really is no such thing as "a cow." A better ontology might assert the existence of fields of attributes of various systems or combinations of systems that when you put them altogether you end up with something we recognize as a cow by virtue of gross similarities of behavior and appearance to our mental image of what a cow is.

No we are not talking about an Ensemble. But a single buckyball at a time double
slit experiment. Dr. Neumaier said that after the buckyball was emitted. The
slits slit the field to various fragments and these hit the detector in all
regions. Since his field is literal with left and middle and right portion
maintained. After it passes thru the slits. The left field would focus on the
left, middle field on middle and right field on the right although diffraction
and interference would also produce constructive and destructive inteference.
Let's analyze just using single buckyball experiment.. let's forget ensemble as
we are scrutinizing what happens in single buckyball emission and detection. If
there is a test that can show a single buckyball still found at the detector.
Then this would refute Dr. Neumaier conjecture. Can you think of a test or other
experiment setup which doesn't use electrons as detection elements? Again Dr.
Neumaier arguments was that a detector is composed of millions of electrons as
detection elements. So a smeared splattered field can trigger just one of them
because after the one was triggered, it would use up all available energies in
the detection circuits with the rest of the electrons in passive mode unable to
fire. So if you can think of a way that we can detect the buckyball or photon
without using electrons. Then his conjecture can be put to experiment test and
be falsifiable. If Dr. Neumaier is right. Then the measurement problem was
solved and we can mention this in all physics textbook from hereon and he become
immortalized in the Physics Hall of Fame in the company of Einstein and Bohr.