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Classical and Quantum Mechanics via Lie algebras

by A. Neumaier
Tags: algebras, classical, mechanics, quantum
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Varon
#19
May2-11, 07:58 PM
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Quote Quote by Rap View Post
This is an improper question. Only in classical physics can you describe what goes on, because you can make a measurement of what goes on which does not affect the outcome of the experiment. In QM, you cannot, so you cannot know what "goes on". To ask a question for which there is no answer is improper.
But in Neumaier Interpretation, everything is taken into account. It is enhanced quantum-classical hybrid where he can precisely state what happens in between. This is not your typical QM, that is why Neumaier said his model wil someday rock the world and be part of textbook and face out the Copenhagen and other interpretations.
Rap
#20
May2-11, 08:16 PM
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Quote Quote by Varon View Post
But in Neumaier Interpretation, everything is taken into account. It is enhanced quantum-classical hybrid where he can precisely state what happens in between. This is not your typical QM, that is why Neumaier said his model wil someday rock the world and be part of textbook and face out the Copenhagen and other interpretations.
I have not read all of the web page at http://www.mat.univie.ac.at/~neum/ph...ysics-faq.html - should I keep reading this to find what you are saying or do you have another source?
Varon
#21
May2-11, 09:05 PM
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Quote Quote by Rap View Post
I have not read all of the web page at http://www.mat.univie.ac.at/~neum/ph...ysics-faq.html - should I keep reading this to find what you are saying or do you have another source?
Just try to understand Neumaier version of the double slit experiment. Here he can model precisely what happens in between. This is in contrast with orthodox QM where we don't know.
A. Neumaier
#22
May3-11, 02:53 AM
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Quote Quote by Varon View Post
What "outer electrons"? I'm talking about single electron. So when your single electron is emitted. It is a particle before reaching the slits. After it reach the slits. The single electron become delocalized or spread into a field. Now the mystery is how the detector is able to detect single electron again. So don't talk about "outer electrons" in the detector because we are only dealing with a single-electron at a time double slit experiment.
The detector wouldn't be able to respond if it hadn't loosely bound electrons that could be freed when responding to the impinging quantum field formed by your single electron. The response of the detector to the field is a multibody problem, and solving it in the semiclassical approximation gives the desired effect.
A. Neumaier
#23
May3-11, 02:56 AM
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Quote Quote by Rap View Post
I have not read all of the web page at http://www.mat.univie.ac.at/~neum/ph...ysics-faq.html - should I keep reading this to find what you are saying or do you have another source?
See the entry ''The double-slit experiment'' in Chapter A4 of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/ph...tml#doubleSlit
Varon
#24
May3-11, 03:02 AM
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Quote Quote by A. Neumaier View Post
The detector wouldn't be able to respond if it hadn't loosely bound electrons that could be freed when responding to the impinging quantum field formed by your single electron. The response of the detector to the field is a multibody problem, and solving it in the semiclassical approximation gives the desired effect.
Are you saying your interpretation only work for an ensemble of electrons? I want only one electron at a time. What do you mean "The detector wouldn't be able to respond if it hadn't loosely bound electrons that could be freed when responding to the impinging quantum field formed by your single electron." Please rephase it in clearer words. As I understand it. The emitter emits one electron. After it pass thru the slits, it became smeared. Now how does the smeared field converge back into a single electron detected at the screen?
A. Neumaier
#25
May3-11, 03:13 AM
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Quote Quote by Varon View Post
Are you saying your interpretation only work for an ensemble of electrons?
No. I am considering your situation: precisely one elctron moving theough the double slit. But once this electron reaches the detector is meets a host of electrons in the detector. The latter are responsible for the measurable response (since ultimately a current is measured, not the single electron).
Quote Quote by Varon View Post
I want only one electron at a time. What do you mean "The detector wouldn't be able to respond if it hadn't loosely bound electrons that could be freed when responding to the impinging quantum field formed by your single electron." Please rephase it in clearer words. As I understand it. The emitter emits one electron. After it pass thru the slits, it became smeared. Now how does the smeared field converge back into a single electron detected at the screen?
It doesn't. It remains smeared. But one of the electrons in the detector fires and (after magnification) gives rise to a measurable current.. This will happen at exactly one place. Thus it _seems_ that the electron has arrived there, while in fact it has arrived everywhere within its extent.

If a water wave reaches a dam with a hole in it, the water will come out solely through this hole although the wave reached the dam everywhere. A detector is (in a vague way) similar to such a dam with a large number of holes, of which only one per electron can respond because of conservation of energy.
Varon
#26
May3-11, 03:26 AM
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Quote Quote by A. Neumaier View Post
No. I am considering your situation: precisely one elctron moving theough the double slit. But once this electron reaches the detector is meets a host of electrons in the detector. The latter are responsible for the measurable response (since ultimately a current is measured, not the single electron).

It doesn't. It remains smeared. But one of the electrons in the detector fires and (after magnification) gives rise to a measurable current.. This will happen at exactly one place. Thus it _seems_ that the electron has arrived there, while in fact it has arrived everywhere within its extent.

If a water wave reaches a dam with a hole in it, the water will come out solely through this hole although the wave reached the dam everywhere. A detector is (in a vague way) similar to such a dam with a large number of holes, of which only one per electron can respond because of conservation of energy.
But your theory doesn't explain one electron at a day double slit experiment or in instance where only one buckyball is sent out in a year. It still interferes with itself. Because after 20 years. The 20 buckyball would still form interference patterns added up one year at a time.
Hence your model may not tally with reality.
A. Neumaier
#27
May3-11, 03:35 AM
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Quote Quote by Varon View Post
But your theory doesn't explain one electron at a day double slit experiment or in instance where only one buckyball is sent out in a year. It still interferes with itself. Because after 20 years. The 20 buckyball would still form interference patterns added up one year at a time.
Hence your model may not tally with reality.
Each electron capable of responding has a response rate proportional to the intensity of the incident field. This is enough to correctly account for the interference pattern. No memory is necessary to achieve that.

If you send one buckyball a year in a coherent fashion (I doubt that one can prepare this, but suppose one could) then at positions of destructive interference the response rate would be zero while at positions of constructive interference, the resonse rate would be zero except once a year where it would be maximal. Thus it is most likely that the yearly recorded event comes from an electron sitting at a point of constructive interference. After 20 years, one would see the pattern emerging.
Varon
#28
May12-11, 08:09 PM
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Quote Quote by A. Neumaier View Post
Each electron capable of responding has a response rate proportional to the intensity of the incident field. This is enough to correctly account for the interference pattern. No memory is necessary to achieve that.

If you send one buckyball a year in a coherent fashion (I doubt that one can prepare this, but suppose one could) then at positions of destructive interference the response rate would be zero while at positions of constructive interference, the resonse rate would be zero except once a year where it would be maximal. Thus it is most likely that the yearly recorded event comes from an electron sitting at a point of constructive interference. After 20 years, one would see the pattern emerging.
Something that puzzles me greatly.

First of all. How many electrons do typical detectors have? Let's say there are a thousand. How can the uniform quantum wave after the slits trigger just one of the electrons in the detectors and not others. How can the principle of energy conservation cause it? Pls. elaborate. Thanks.
SpectraCat
#29
May12-11, 08:20 PM
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Quote Quote by A. Neumaier View Post
Each electron capable of responding has a response rate proportional to the intensity of the incident field. This is enough to correctly account for the interference pattern. No memory is necessary to achieve that.

If you send one buckyball a year in a coherent fashion (I doubt that one can prepare this, but suppose one could) then at positions of destructive interference the response rate would be zero while at positions of constructive interference, the resonse rate would be zero except once a year where it would be maximal. Thus it is most likely that the yearly recorded event comes from an electron sitting at a point of constructive interference. After 20 years, one would see the pattern emerging.
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.
A. Neumaier
#30
May13-11, 04:44 AM
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Quote Quote by Varon View Post
Something that puzzles me greatly.

First of all. How many electrons do typical detectors have? Let's say there are a thousand.
Its more like 10^20.
Quote Quote by Varon View Post
How can the uniform quantum wave after the slits trigger just one of the electrons in the detectors and not others. How can the principle of energy conservation cause it? Pls. elaborate. Thanks.
Each electron feels just the piece of the quantum wave reaching it. The electron responds by random ionization, with a rate proportional to the intensity. It takes the energy from its surrounding.

The detector as a whole receives the energy everywhere, also with a rate proportional to the intensity. This energy is redistributed (fast, but with a speed slower than that of light) through the whole detector, roughly according to hydrodynamic laws.

Thus there is no violation of conservation of energy.
A. Neumaier
#31
May13-11, 04:46 AM
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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.
Could you please give a reference to such an experiment, from which you know that this is what actually happens?
Varon
#32
May13-11, 05:09 AM
P: 525
Quote Quote by A. Neumaier View Post
Its more like 10^20.

Each electron feels just the piece of the quantum wave reaching it. The electron responds by random ionization, with a rate proportional to the intensity. It takes the energy from its surrounding.

The detector as a whole receives the energy everywhere, also with a rate proportional to the intensity. This energy is redistributed (fast, but with a speed slower than that of light) through the whole detector, roughly according to hydrodynamic laws.

Thus there is no violation of conservation of energy.
But in one-electron (or photon or buckyball) at a time double slit experiment, how does the wave after the slits select only one electron among the 10^20 in the detector?
SpectraCat
#33
May13-11, 07:10 AM
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Quote Quote by A. Neumaier View Post
Could you please give a reference to such an experiment, from which you know that this is what actually happens?
Which part? That massive particles can be deposited on surfaces and imaged using scanning probe microscopy techniques? That is a matter of established fact, and a simple google search will turn up lots of references .. I'll bet there's even one for buckyball somewhere. My idea about lowering the temperature was simply a suggestion so that one can be sure that the particle has not diffused along the surface from its original point of impact.

But that's all just a distraction ... in order for your theory to be complete, you need to explain what happens in the case of massive particles that can be detected non-destructively. Well .. really you need to explain what happens in the case of electrons too .. you say the electron that undergoes interference arrives in a "smeared out wave" and is detected "everywhere", and that the electron that registered a "click" is not the original electron, but one that existed inside the detector. So what happens to the "smeared out" electron that underwent interference? Does it stay "smeared out" forever? If not, how and when is it reconstituted in to the more familiar "non-smeared out" form?

I just chose to ask you about massive particles because it is easier to appreciate the issue.
A. Neumaier
#34
May13-11, 08:21 AM
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Quote Quote by Varon View Post
But in one-electron (or photon or buckyball) at a time double slit experiment, how does the wave after the slits select only one electron among the 10^20 in the detector?
The wave selects nothing. 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.
A. Neumaier
#35
May13-11, 08:30 AM
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Quote Quote by SpectraCat View Post
Which part? That massive particles can be deposited on surfaces and imaged using scanning probe microscopy techniques?
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.
Quote Quote by SpectraCat View Post
in order for your theory to be complete, you need to explain what happens in the case of massive particles that can be detected non-destructively.
No. I only need to be able to explain experimentally verified facts.
Quote Quote by SpectraCat View Post
Well .. really you need to explain what happens in the case of electrons too .. you say the electron that undergoes interference arrives in a "smeared out wave" and is detected "everywhere", and that the electron that registered a "click" is not the original electron, but one that existed inside the detector. So what happens to the "smeared out" electron that underwent interference? Does it stay "smeared out" forever? If not, how and when is it reconstituted in to the more familiar "non-smeared out" form?
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.
Varon
#36
May13-11, 10:28 PM
P: 525
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.

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?


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