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Classical and Quantum Mechanics via Lie algebras

by A. Neumaier
Tags: algebras, classical, mechanics, quantum
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PAllen
#55
May27-11, 06:11 PM
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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
#56
May27-11, 06:12 PM
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Quote Quote by Varon View Post
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
#57
May27-11, 08:20 PM
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Quote Quote by A. Neumaier View Post
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
#58
May27-11, 09:22 PM
P: 525
Quote Quote by Oudeis Eimi View Post
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
#59
May27-11, 09:29 PM
P: 525
Quote Quote by SpectraCat View Post
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
#60
May28-11, 01:17 AM
P: 525
in the thread http://www.physicsforums.com/showthr...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
#61
May28-11, 07:25 AM
P: 789
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.
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
#62
May28-11, 07:42 AM
P: 525
Quote Quote by Rap View Post
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
#63
May28-11, 10:10 AM
P: 789
Quote Quote by Varon View Post
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
#64
May28-11, 06:51 PM
P: 525
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
#65
May29-11, 02:08 AM
P: 525
Quote Quote by Rap View Post
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
#66
May29-11, 03:32 AM
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Quote Quote by Rap View Post
[...] 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.

Quote Quote by Varon
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
#67
May29-11, 09:32 PM
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Quote Quote by strangerep View Post
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
#68
May30-11, 04:23 AM
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Quote Quote by PAllen View Post
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
#69
May30-11, 12:18 PM
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Quote Quote by PAllen View Post
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
#70
May30-11, 12:33 PM
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Quote Quote by SpectraCat View Post
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 recieve the silver atom with high probability?

Quote Quote by SpectraCat View Post
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
#71
May30-11, 12:39 PM
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Quote Quote by Varon View Post
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
#72
May30-11, 12:45 PM
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Quote Quote by Rap View Post
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.


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