Classical and Quantum Mechanics via Lie algebras

[Varon]

No, but that a highly delocalized buckyball (not just any buckyball, but the kind prepared in a buckyball interference experiment) appears at a single place when checked with
a microscope.

No. I only need to be able to explain experimentally verified facts.

I don't know, and since there is no way to check any attempted explanation, I need not know.

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.

In other words. There are really no particles? So in the photoelectric experiment, what makes each electron eject from the material? Or compton scattering?

 

[Drakkith]

In other words. There are really no particles? So in the photoelectric experiment, what makes each electron eject from the material? Or compton scattering?

The energy contained in an electron or photon. Just because they might not be a particle doesn't mean that the energy isn't quantized still.

 

[Varon]

The energy contained in an electron or photon. Just because they might not be a particle doesn't mean that the energy isn't quantized still.

So you agree with the explanation of Neumaier on the double slit experiment where the electron detected is not the original one sent but just one of the million existing electrons in the detector that is simply triggered (as detailed in this thead)?

So finally the double slit experiment mystery is finally solved after 80 years??

 

[SpectraCat]

No, but that a highly delocalized buckyball (not just any buckyball, but the kind prepared in a buckyball interference experiment) appears at a single place when checked with a microscope.

I do not know if such an experiment *has* been done, but it is certainly feasible, and I would be willing to bet a considerable sum that the particles detected appear in only one place. What else could happen? What would be the nature of a "delocalized particle stuck to a surface"? Interference via the double-slit is not magic .. if doesn't make the particles into something else, it just creates a very delicate coherent superposition of the quantum trajectories. The interaction of the molecule with the surface is certainly strong enough to disrupt that delicate superposition, resolving the molecule at a single location. That is the standard interpretation and it is far more consistent and believable (at least to me) than your suggestion that there is somehow another form of "smeared out" molecule that can survive interaction with a detector and remain in its smeared out form. There is absolutely no evidence that heavy atoms and molecules interacting with surfaces behave in any fashion other than "particle-like".

No. I only need to be able to explain experimentally verified facts.

I don't know, and since there is no way to check any attempted explanation, I need not know.

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.

The rest of that strikes me as pure sophistry. At best, your model suffers from just as large a problem as standard QM. In standard QM, there is the measurement problem .. it is not understood precisely how coherent quantum states are "collapsed" (or whatever term you prefer) at the time of measurement such that single eigenvalues are measured. In your case, you posit that particles undergoing interference in a double slit experiment arrive at the detector and do not collapse, but rather remain "smeared out", and cause a response of the detector that is proportional to the intensity of the interfering "field" (it's somewhat clear what the field is in the case of a photon, and perhaps even an electron, but much less so in the case of a heavy particle like a buckyball). You admit you have no idea how the "smeared out" particles that passed through the double slit get back to their more localized, particle-like form, which in the case of heavy atoms and molecules, is how they are normally observed in experiments.

So what has been gained by adopting your model rather than standard QM?

 

[San K]

That seems incomplete. First of all, it is not a simple matter of a detector registering an electronic "click" ... the actual buckyball molecule impinges on the detector .. its landing position can be measured .. for example if you cooled the detector to very low temperature, and then ran an STM over the surface, you would see the buckyball localized in one place. You could also measure an interference pattern in similar fashion by by running the experiment multiple times.

So, in order for your theory to be consistent, it seems like you need to explain how the wave representing the buckyball can hit the detector "all at once", but then end up with a buckyball localized in just one discrete position. Your proposed explanation is plausible for electrons or photons because they are detected "destructively", but massive particles can be measured in other ways ... how can your theory account for this.

Ya...or to take SpectraCat's argument further...lets build a "primitive" detector (no carrying of signal via electrons)...such that...every time the bucky ball impinges on the detector...its leaves a tiny mark...

kinda like paint-balls but not exactly...i..e there are no electron (from the detector side) involved here...how would Neu's hypothesis explain the patterns of molecules on such a primitive detector...?

or let's make it even simpler...instead of detector we have a white sheet of paper...coated with some chemical...that...reacts with the bucky ball to create a tiny black dot...

after say a million/billion molecules have passed through the slits and touched the detector...we would see a (interference/non-interference pattern depending upon our setup) a pattern...is there a way to explain this via Neu's hypothesis?

 

[A. Neumaier]

In other words. There are really no particles?

Particles are semiclassical approximations for field phenomena concentrated along narrow beams. It is not very different from water - which is in particle form if a tab is dripping but not if the water flows in a river.

The particle concept loses its meaning when applied outside its domain of applicability. Trying to keep the concept then leads to all sorts of weird things.

So in the photoelectric experiment, what makes each electron eject from the material?

Its the same principle as in the double slit experiment. This is explained in the entry ''The photoelectric effect'' in Chapter A4 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#photodetection ,
and discussed in the thread
https://www.physicsforums.com/showthread.php?t=480072

 

[A. Neumaier]

I do not know if such an experiment *has* been done, but it is certainly feasible, and I would be willing to bet a considerable sum that the particles detected appear in only one place.

Well - this makes my interpretation testable to some extent. (Though, as with other tests of foundations, there will always be loopholes if something doesn't come out as expected.) Maybe someone will test it one day.

What else could happen? What would be the nature of a "delocalized particle stuck to a surface"?

This question is only strange if you think in terms of particles. But buckyballs actually form a field - with particle being localized features of the field.

The analogous question of what happens if a delocalized drop of water (in the form of a faint mist) reaches a detector. It just stays there delocalized and is virtually unmeasurable at the resolution of typical water drops. There is no conceptual problem.
The quantum case is essentially the same.

Interference via the double-slit is not magic .. if doesn't make the particles into something else, it just creates a very delicate coherent superposition of the quantum trajectories.

There is a field both before and after the slit; so the fundamental field description (in terms of the standard model) doesn't suffer any discontinuity or magic.

On the other hand, after the slits, there are no particles in any meaningful sense. Only an empty label ''particle'' without any discernible meaning persists.

The interaction of the molecule with the surface is certainly strong enough to disrupt that delicate superposition, resolving the molecule at a single location.

You imagine that this is the case, but to give it the label ''certainly'', you need to provide a proof for your assertion, which you can't give. Thus what you say is pure speculation.

That is the standard interpretation

No. it is your ad hoc invention. The standard interpretations are silent about the situation.

and it is far more consistent and believable (at least to me) than your suggestion that there is somehow another form of "smeared out" molecule that can survive interaction with a detector and remain in its smeared out form.

Well, the field description was not invented by me but is standard. I only take it more serious than others.

There is absolutely no evidence that heavy atoms and molecules interacting with surfaces behave in any fashion other than "particle-like".

There is no evidence at all about the behavior of single delocalized heavy molecules. You can't claim the lack of evidence as something favoring your point of view.

In your case, you posit that particles undergoing interference in a double slit experiment arrive at the detector and do not collapse, but rather remain "smeared out", and cause a response of the detector that is proportional to the intensity of the interfering "field" (it's somewhat clear what the field is in the case of a photon, and perhaps even an electron, but much less so in the case of a heavy particle like a buckyball).

It is completely clear for a long time to anyone knowing the literature. You may look at the paper by

W. Sandhas,
Definition and existence of multichannel scattering states,
Comm. Math. Phys. 3 (1966), 358--374.

to see how fields for bound states are constructed rigorously in the nonrelativistic case (sufficient for buckyballs). The relativistic case is similar, and figures under the heading of Haag-Ruelle scattering theory.

 

[SpectraCat]

Well - this makes my interpretation testable to some extent. (Though, as with other tests of foundations, there will always be loopholes if something doesn't come out as expected.) Maybe someone will test it one day.

This question is only strange if you think in terms of particles. But buckyballs actually form a field - with particle being localized features of the field.

The analogous question of what happens if a delocalized drop of water (in the form of a faint mist) reaches a detector. It just stays there delocalized and is virtually unmeasurable at the resolution of typical water drops. There is no conceptual problem.
The quantum case is essentially the same.

There is a field both before and after the slit; so the fundamental field description (in terms of the standard model) doesn't suffer any discontinuity or magic.

On the other hand, after the slits, there are no particles in any meaningful sense. Only an empty label ''particle'' without any discernible meaning persists.

You imagine that this is the case, but to give it the label ''certainly'', you need to provide a proof for your assertion, which you can't give. Thus what you say is pure speculation.

No. it is your ad hoc invention. The standard interpretations are silent about the situation.

Well, the field description was not invented by me but is standard. I only take it more serious than others.

There is no evidence at all about the behavior of single delocalized heavy molecules. You can't claim the lack of evidence as something favoring your point of view.

It is completely clear for a long time to anyone knowing the literature. You may look at the paper by

W. Sandhas,
Definition and existence of multichannel scattering states,
Comm. Math. Phys. 3 (1966), 358--374.

to see how fields for bound states are constructed rigorously in the nonrelativistic case (sufficient for buckyballs). The relativistic case is similar, and figures under the heading of Haag-Ruelle scattering theory.

I will read the paper that you mentioned when I have the time. That still all seems like obfuscation and sophistry to me. There is only one specific point that I take exception to:

I said: "The interaction of the molecule with the surface is certainly strong enough to disrupt that delicate superposition, resolving the molecule at a single location. That is the standard interpretation and it is far more consistent and believable (at least to me) than your suggestion that there is somehow another form of "smeared out" molecule that can survive interaction with a detector and remain in its smeared out form."

You said: "You imagine that this is the case, but to give it the label ''certainly'', you need to provide a proof for your assertion, which you can't give. Thus what you say is pure speculation."

and

"No. it is your ad hoc invention. The standard interpretations are silent about the situation."

Is that really true? Because I am certain that standard QM says that measurements of observables can only yield eigenvalues. Thus for a position measurement, as is carried out by the detector, we should observe a well-resolved position, rather than the superposition of position states reflected by your "smeared out" version. This is often called the measurement problem, and is sometimes interpreted as "wavefunction collapse" ... I think all of that is pretty "standard" and is certainly not "my ad hoc invention".

Also, I again ask you, where is the experimental evidence of massive particles existing in the sort of "smeared out" state you describe while interacting with a macroscopic surface? A simple google search will provide hundreds of examples of images of well-localized versions of massive particles interacting with macroscopic techniques. There is even a famous one where IBM spelled out their corporate logo with single atoms (I think it was using Xenon on gold).

 

[A. Neumaier]

You said: "You imagine that this is the case, but to give it the label ''certainly'', you need to provide a proof for your assertion, which you can't give. Thus what you say is pure speculation."

and

"No. it is your ad hoc invention. The standard interpretations are silent about the situation."

Is that really true?

Well - give the proof, then!

Because I am certain that standard QM says that measurements of observables can only yield eigenvalues.

This is far from true:
- measurements of half lives, spectral frequencies, or of the anomalous magnetic moment of the electrons are not eigenvalues of observables in any relevant sense.
- standard QM is silent about anything unobserved. But nobody has performed your experiment.
- the projective measurements that you have in mind are applicable only to discrete observables whose spectrum is known in advance. Not to the position of a particle.
- what constitutes a measurement of the position of a particle is not even well-defined.

Thus for a position measurement, as is carried out by the detector, we should observe a well-resolved position,

A position measurement of an atom by an electron microscope is a complex process that produces a picture from which an uncertain position is deduced. The picture can be arbitrarily fuzzy, and reveals a definite shape only if a particle is indeed localized.

Also, I again ask you, where is the experimental evidence of massive particles existing in the sort of "smeared out" state you describe while interacting with a macroscopic surface?

Electrons are massive and are always delocalized in ordinary matter, unless they are free and move in a well-collimated beam.

Regarding heavier particles, I count the interference experiments for buckyballs as such evidence.

 

[San K]

A bucky ball if went in wave from, would have more than a single quanta of energy.

Thus when it hits the screen, per Neu's hypothesis, we should see a couple of electrons (out of the billions) being triggered and not just one.

Thus if we go with the dam with one hole analogy, a couple of electrons would come out of the hole.

 

[A. Neumaier]

A bucky ball if went in wave from, would have more than a single quanta of energy.

No. If a single buckyball reaches the slit, it will be a delocalized single-buckyball state afterwards. Mass conservation (valid for a nonrelativistic particle such as a buckyball) implies that it cannot bring more mass than that of a single buckyball to the screen.

(How much energy it brings depends on its momentum, hence on the preparation. Thus what was argued before by both sides about energy should have in fact been argued about mass.)

 

[Varon]

Come on PF members. If Neumaier was right. Others would have figured this out already for more than a century. Why only he figured this out. I hope other critics can put hole in his theory. If it is really wrong. Let's not let it drag on and make it disturb us who search for the right interpretation. 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?

 

[PAllen]

I do not know if such an experiment *has* been done, but it is certainly feasible, and I would be willing to bet a considerable sum that the particles detected appear in only one place. What else could happen? What would be the nature of a "delocalized particle stuck to a surface"? Interference via the double-slit is not magic .. if doesn't make the particles into something else, it just creates a very delicate coherent superposition of the quantum trajectories. The interaction of the molecule with the surface is certainly strong enough to disrupt that delicate superposition, resolving the molecule at a single location. That is the standard interpretation and it is far more consistent and believable (at least to me) than your suggestion that there is somehow another form of "smeared out" molecule that can survive interaction with a detector and remain in its smeared out form. There is absolutely no evidence that heavy atoms and molecules interacting with surfaces behave in any fashion other than "particle-like".

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.

 

[Varon]

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.

How do we do this experiment? Has anyone tried it? If Neumaier wins. He gets a Nobel. Although he may argue that the atom or molecule wave becomes splash all over the detector.. which happens to form interference pattern too. Hope Neumaier can comment what would be the predicted output.

 

[strangerep]

Come on PF members. If Neumaier was right. Others would have figured this out already for more than a century. Why only he figured this out. I hope other critics can put hole in his theory. If it is really wrong. Let's not let it drag on and make it disturb us who search for the right interpretation.

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.

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.)

Although he may argue that the atom or molecule wave becomes splash all over the detector.. which happens to form interference pattern too. Hope Neumaier can comment what would be the predicted output.

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.

 

[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.