Classical and Quantum Mechanics via Lie algebras


by A. Neumaier
Tags: algebras, classical, mechanics, quantum
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May13-11, 10:36 PM
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Quote Quote by Varon View Post
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
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Quote Quote by Drakkith View Post
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
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May14-11, 01:15 AM
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Quote Quote by A. Neumaier View Post
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?
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May14-11, 12:32 PM
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Quote Quote by SpectraCat View Post
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
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May14-11, 01:31 PM
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Quote Quote by Varon View Post
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.
Quote Quote by Varon View Post
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://www.mat.univie.ac.at/~neum/ph...photodetection ,
and discussed in the thread
http://www.physicsforums.com/showthread.php?t=480072
A. Neumaier
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May14-11, 01:51 PM
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Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
That is the standard interpretation
No. it is your ad hoc invention. The standard interpretations are silent about the situation.
Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
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
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May14-11, 02:40 PM
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Quote Quote by A. Neumaier View Post
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
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May14-11, 03:29 PM
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Quote Quote by SpectraCat View Post
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!
Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
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.
Quote Quote by SpectraCat View Post
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
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May17-11, 02:49 AM
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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
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May17-11, 02:01 PM
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Quote Quote by San K View Post
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
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May26-11, 07:59 PM
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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?
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May26-11, 08:53 PM
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Quote Quote by SpectraCat View Post
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
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May26-11, 10:17 PM
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Quote Quote by PAllen View Post
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
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May27-11, 04:56 AM
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Quote Quote by Varon View Post
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:

http://www.physicsforums.com/showthr...82#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
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May27-11, 07:13 AM
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Quote Quote by Varon View Post
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.
Quote Quote by Varon View Post
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.
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May27-11, 07:21 AM
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Quote Quote by PAllen View Post
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
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May27-11, 05:55 PM
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Quote Quote by strangerep View Post
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:

http://www.physicsforums.com/showthr...82#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
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May27-11, 05:59 PM
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Quote Quote by A. Neumaier View Post
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.


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