Classical and Quantum Mechanics via Lie algebras

[A. Neumaier]

I'd like to open a discussion thread for version 2 of the draft of my book ''Classical and Quantum Mechanics via Lie algebras'', available online at http://lanl.arxiv.org/abs/0810.1019 , and for the associated thermal interpretation of quantum mechanics, espoused in the book.

The goal of the thread is to obtain reader's feedback that helps me to improve the presentation while I work towards a version for publication.


Abstract: The book fulfils the didactical purpose of showing that
-- quantum mechanics and classical mechanics are much more similar than can be seen from the usual presentations of the subject;
-- in a very significant sense, theoretical classical and quantum mechanics is nothing but applied Lie algebra;
-- quantum mechanics has a common sense interpretation once one takes the thermodynamical findings of statistical mechanics serious in the foundations.

The content of the book is fully mainstream, covering hundreds of publications by others (301 references, too numerous to include them into this opening post), including many references to basic experiments. However, the selection and presentation of the material is very different from what one can find elsewhere.

The importance of the topic is obvious. With exception of the thermal interpretation, nothing is new about the scientific content. The presentation of the book is in intelligible English, complemented by LaTeX (some of it only intelligible by intelligent readers). With exception of historical evidence (and perhaps oversights), everything is defined or derived with mathematical rigor. The empirical equivalence of the presented material to standard mechanics is manifest, and almost the whole body of experimental physics supports the theory presented. [If this paragraph sounds a bit crackpottish - I am required to state all these things in order to conform to the submission rules.]


The thermal interpretation of quantum mechanics was presented first last year in a lecture whose slides (Slide 23-34 define the interpretative core) are available at http://arnold-neumaier.at/ms/optslides.pdf , which in turn is based on insights from Sections 8.4 and 10.3-10.5 of version 2 (or Sections 5.4 and 7.3-7.5 of version 1) of the above book.A short exposition is given in the entry ''Foundations independent of measurements'' of Chapter of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#found0 . See also the following PF posts:

https://www.physicsforums.com/showthread.php?p=3246436#post3246436
https://www.physicsforums.com/showthread.php?p=3187039#post3187039
https://www.physicsforums.com/showthread.php?p=3193747#post3193747

 

[qsa]

how does the thermal arise for a single electron.

 

[A. Neumaier]

how does the thermal arise for a single electron.

The thermal interpretation does not only apply to thermal states; it is completely general.

I suggest that you begin by reading the slides http://arnold-neumaier.at/ms/optslides.pdf
where the interpretation is explained for a single photon. The electron is essentially the same, except for the different state space.

 

[A. Neumaier]

This post contains replies to posts 1-7 from https://www.physicsforums.com/showthread.php?t=490677
I'll comment on the later posts at another time.

can you pls create a more layman friendly introduction to it like describing in detail how it explains buckyball made up of 430 atoms that can still interfere with itself?

One major idea being put forth by Neumaier is that fields are now primary and particles are just momentum of the fields. So particle concept is now outdated and there is no sense of thinking of the double slit experiment as particle that moves in between the emitter and detector but more like field interacting in between (perhaps like Feynman interaction vortexes). If that is true, then the buckyball composing of 430 atoms can be considered as field too.. but does it make sense to think in terms of 430 atom buckyball field??

If a beam of buckyballs is coherently prepared so that it shows interference effects (which is not easy at all - typical buckyball beams are not coherent)
then its quantum field oscillates in a wave manner.

A Neumaier is clearly a very erudite and impressive scholar, but his interpretation is unlikely to be correct as modern experiments urge a fundamental probabilistic character to Nature which his interpretation is not in agreement with.

Why not?

He is a genius clinging to old school deterministic ideas about nature

The thermal interpretation explains the conditions under which a stochastic interpretation of QM is valid, the conditions under which a determinstic interpretation is valid, and the conditions under which neither is valid.
See Chapter 10.3-5 of version 2 of the draft of my book.

No other interpretation can do that.

And also I'm not sure he should be allowed to promote such a non peer reviewed philosophy so strongly on these forums.

about 10 of my over 1300 contributions to PF mention the thermal interpretation. Everything else is orthodox physics.

the interpretation stuff is really not scientific

Before making such unsupported negative comments you should first read and understand what my interpretation consists of.

Arnold, can you please write a Wikipedia article about it and give the basics

I write here, and leave Wikipedia to those active there.

as your articles are so vague and disorganized.

I suggest that you begin by reading the slides http://arnold-neumaier.at/ms/optslides.pdf
where the interpretation is explained. They contain the material of a well-organized lecture in which nothing is left vague.

Neumaier gives example of beam of photon. But a beam of photon has real wave, whereas electron wave is just probability wave. So one can't argue whether before observation, a beam of photon is there or not. It has real wave. Whereas matter waves are not actual waves.

Coherent electron waves are as real as coherent photon waves, as the many interference experiments show. In QFT they are actual waves in the most real sense of the word.

Feynman mentions in his book "The Strange Story of Light and Matter" about reflections of light. He said that in reflections in a glass, 4% of the photons are always deflected. How do the photons know how to be 4% Feynman asks. What I want to know is, can reflections be done with matter wave too like electron wave such that you can also see 4% of electron being deflected?

Electron fields are not so different from photon fields as you might think. There is a whole discipline of physics called electron optics http://en.wikipedia.org/wiki/Electron_optics where the optical properties of electrons are studied in close analogy to the optical properties of light.

would the field operators at a given point in spacetime give the probabilities or expectation values for the outcome of some measurement at that point?

The field operator evaluated at a point x in space-time defines the probability distribution of the magnitude of the quantum field at that point. But field operators are only distributions, not ordinary functions, which means that only smeared values of the field make sense. What is measurable is usually the expectation value of the field smeared over the region in space time determined by the active part of the detector and the duration of the measurement.

Neumaier goes on to say that expectation values are the basic elements of his interpretation:

Yes. In the thermal interpretation, _all_ measurements are interpreted as measurements of expectation values.

But if he wants to avoid collapse, how does he go from expectation values to actual measured values of microscopic systems? (or macroscopic 'pointer states' associated with those measurements)

Here is the main difference to the traditional interpretations.
The thermal interpretation doesn't change anything in the theory. What is changed is _only_ the interpretation of measurements. All measurements are primarily measurements of the macroscopic object that is actually inspected when measuring something.

To be valid, any inference about the value of some microscopic object must be
(ideally) backed up by an argument that the microscopic object influences the macroscopic object in a way that the observed macroscopic behavior results.

 

[strangerep]

In the thermal interpretation, _all_ measurements are interpreted as measurements of expectation values.

Leaving aside the interpretation, and looking instead at how you formulate QM,
starting with an algebra of observables, then states and relying on a list of
axiomatic (Whittle-style) properties of expectations, I'm wondering whether one
can indeed account for all features of QM that way...

Consider the Cauchy (or Breit-Wigner) distribution that gives the probability
distribution of the lifetime of unstable particles. The usual expectation, variance,
etc, are undefined for that distribution but it's clearly an important part of quantum
physics. How then do you get a Breit-Wigner distribution if you've started the
theory from expectations?

 

[A. Neumaier]

Leaving aside the interpretation, and looking instead at how you formulate QM,
starting with an algebra of observables, then states and relying on a list of
axiomatic (Whittle-style) properties of expectations, I'm wondering whether one
can indeed account for all features of QM that way...

Consider the Cauchy (or Breit-Wigner) distribution that gives the probability
distribution of the lifetime of unstable particles. The usual expectation, variance,
etc, are undefined for that distribution but it's clearly an important part of quantum
physics. How then do you get a Breit-Wigner distribution if you've started the
theory from expectations?

Only _bounded_ quantities _must_ have an expectation. For unbounded quantities the expectation need not exist. Thus (as in C^*-algebras), one can always go to the exponentials e^{is A} of a self-adjoint but unbounded quantity. in probability theory, the function defined by the expectations f(s):=<e^{isa}> is called the characteristic function of A. it completely characterizes the distribution of functions of A, and is the right thing to study in case of cauchy-distributed A.

 

[A. Neumaier]

This post contains replies to posts 1-7 from https://www.physicsforums.com/showthread.php?t=490677
I'll comment on the later posts at another time.

This post contains replies to the remaining posts from https://www.physicsforums.com/showthread.php?t=490677

But Neumaier says that his interpretation "acknowledges that there is only one world", and that it "is consistent with assigning a well-defined (though largely unknown) state to the whole universe", shouldn't that mean the interpretation has to give more than just a collection of probabilities for different states at different points in spacetime, since in our "one world" we see "states" consisting of definite outcomes rather than just probabilities?

We see definite outcomes whenever we look at a system large enough that the assumptions of statistical mechanics apply. In particular, this holds for all the things that are _actually_ measured, such as pointers of instruments, colors of pixels on a screen, developped photographic plates, sounds in a Geiger counter,
currents in a photodetector.

We _infer_ from these raw measurements properties of systems that we cannot ''read'' directly, and the inference is as good or as bad as the causal link provided by quantum mechanical theory in the respective case.

But there are plenty of cases where var(A) would be large even for macroscopic systems, like the state of macroscopic "pointers" which show the results of experiments on quantum particles

Yes. This implies that the macroscopic pointer gives only unreliable information about the quantum particle, unless many repeated measurements are made under sufficiently idenitcal conditions.

Do you guys agree that the Ensemble Interpretation (a requirement for Neumaier Interpretation) is already falsified?

The thermal interpretation does not _require_ the ensemble interpretation.
Instead, it gives the conditions under which an ensemble interpretation is valid.
See Section 10.3 of my book.

I presume that the Ensemble Interpretation is the same as the Statistical Interpretation?

Yes.

Both these can't handle single system. But Neumaier Interpretation (actually not an Interpretation but just a QFT way of looking at it or from a QFT point of view) can handle single system. Why is that Neumaier's can handle single system while the Ensemble and Statistical can't since they are identical? What are the differences?

The difference is that I discard the so-called eigenvalue-eigenstate link,
and give the quantum expectation a different interpretation. See Sections 10.3-10.5 of my book.

if Neumaier's interpretation only gives probability distributions for such macro-states rather than definite values,

It gives definite values to macroobservables of macrostate, within some tiny uncertainly level.

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

A valid simulation must be as nonlocal as QM itself.

So, I think it's misleading to call Neumaier's interpretion a "local" one

It isn't local; I nowhere claimed that. The thermal interpretation shares all nonlocal features with orthodox quantum mechanics.

 

[qsa]

The thermal interpretation does not only apply to thermal states; it is completely general.

I suggest that you begin by reading the slides http://arnold-neumaier.at/ms/optslides.pdf
where the interpretation is explained for a single photon. The electron is essentially the same, except for the different state space.

Thanks. I still have more questions but let me ask you this. I understand you that you claim that the wavefunction and its derived probability is not real in standard QM interpretation, it is just a mashinary to interpret experiments. But, in QFT and QM any time we want to calculate something (like energy) we take the whole wavefunction into account which to me it says that all aspects of wavefunction (at least the probabilities) is real and it exists at the same time. Am I saying things correctly?

 

[Rap]

Quote from chapter A5 section 1 -

"Note that a measurement does not need a conscious observer.
A measurement is any permanent record of an event, whether or not
anyone has seen it. Thus the terabytes of collision data collected
by CERN are measurements, although most of them have never been
looked at by anybody."

Consider a "Schroedinger's cat" scenario - the particles generating the tracks and the "permanent record" are inside an isolated box - How is the "permanent record" described by a scientist outside the box? I expect it would be a mixed state, but does this mixed state constitute a measurement?

 

[A. Neumaier]

I understand you that you claim that the wavefunction and its derived probability is not real in standard QM interpretation, it is just a mashinery to interpret experiments. But, in QFT and QM any time we want to calculate something (like energy) we take the whole wavefunction into account which to me it says that all aspects of wavefunction (at least the probabilities) is real and it exists at the same time.

In the standard interpretation probabilities are not observables, but propensities for observing something.
This makes the standard ontology quite weird.

In the thermal interpretation (as in real life), many expectations are measurable (to some limited degree of accuracy), and so are many probabilities (as expectations of projectors). Thus these are real in the thermal interpretation, making things much more intelligible.

 

[A. Neumaier]

Quote from chapter A5 section 1 -

"Note that a measurement does not need a conscious observer.
A measurement is any permanent record of an event, whether or not
anyone has seen it. Thus the terabytes of collision data collected
by CERN are measurements, although most of them have never been
looked at by anybody."

Consider a "Schroedinger's cat" scenario - the particles generating the tracks and the "permanent record" are inside an isolated box - How is the "permanent record" described by a scientist outside the box? I expect it would be a mixed state, but does this mixed state constitute a measurement?

A permanent record is typically a macroscopic state in local equilibrium, changing so slowly that the techniques of statistical mechanics are applicable.

Whether it constitutes a measurement depends on one's definition of a measurement. The thermal interpretation has the huge advantage that one doesn't need to know what a measurement is, and still has a perfectly valid interpretation. Measurement is a difficult subject, so it should not figure in the foundations.

 

[Phrak]

Abstract:[/B] The book fulfils the didactical purpose of showing that
-- quantum mechanics and classical mechanics are much more similar than can be seen from the usual presentations of the subject;
-- in a very significant sense, theoretical classical and quantum mechanics is nothing but applied Lie algebra;
-- quantum mechanics has a common sense interpretation once one takes the thermodynamical findings of statistical mechanics serious in the foundations.

I have positve criticism of your abstract in presentation. Consider me just a reader, trying to understand and see if I am interested in reading further.

didactical

I'm a physicist not a philosopher, so I need some added reminder or hint about what didactic means.

-- quantum mechanics and classical mechanics are much more similar than can be seen from the usual presentations of the subject;

Give an example with motivational argument to show similarity. Get rid of the (--) and use standard English.

-- in a very significant sense, theoretical classical and quantum mechanics is [sic.: are] nothing but applied Lie algebra;

Again, show by comparison of the usage of Lie algebra's in classical and quantum physics to motivate comparison.

-- quantum mechanics has a common sense interpretation once one takes the thermodynamical findings of statistical mechanics serious in the foundations.

This one is a giant step. You need more motivation for making this claim within your abstract. Give a few more details and defer it to the main body of the text using a phrase such as "as will be demonstarted". This should be a good half of your abstract.

I hope this helps on the frontier of written communication.

 

[A. Neumaier]

I'm a physicist not a philosopher, so I need some added reminder or hint about what didactic means.

http://en.wikipedia.org/wiki/Didactic_method

Give an example with motivational argument to show similarity.

This is done leisurely in Chapter 1 of the book, and comes across at many other places in the book. The abstract is not intended to make looking at the actual text. superfluous. It just summarizes what someone can expect to get out from reading the book.

Again, show by comparison of the usage of Lie algebra's in classical and quantum physics to motivate comparison.

In a nutshell:
Poisson brackets define Lie algebras. Commutators define Lie algebras.

But to appreciate how far this goes, you need to study the book, not the abstract. It will be worth your time.

This one is a giant step. You need more motivation for making this claim. Give a few more details and defer it to the main body of the text using a phrase such as "as will be demonstrated". This should be a good half of your abstract.

The main body of the text is the whole book. Innovations on old subjects can usually not be described in a few paragraphs. Please criticize the book (or the FAQ, or the lecture quoted), not the abstract.

 

[A. Neumaier]

An electron behaves as a particle only in situations where an approximate semiclassical description is applicable. This is _not_ the case for a tightly bound electron such as in an ordinary atom or molecule, but it is often the case for an electron in a beam, when one doesn't aske too detailed questions. (Electron beams in full generality are treated in electron optics, where the Dirac equation is treated as a classical field.)

Depending on the preparation, you may regard it as a particle before it passes the screen, but afterwards no longer - passing the screen turns the electron into a delocalized object - the more delocalized the further away from the slits.

Indeed. There is no quantum mystery.

Not as a fundamental quantum law. But the Born rule has limited validity, which can be discussed in the framework of the thermal interpretation.

Talking about it hear is the first part of spreading it. I am gathering experience in how people respond and what must be said to make the case. For publishing it, the Scientific American is not the right place - this is a journal for expaining things to the interested public, not for describing new results to the scientific community.

But sooner or later, my thermal interpretation will be published - a full, convincing account of it is not written in a few pages, but takes time.

And in 10 years time, it will be the consensus of the scientific community, since unlike with all other interpretations, there is nothing weird about the thermal interpretation.

Let us focus on the double slit experiment as Feymann said it's the main mystery. If it's solved, the entire quantum mystery solved.

I can't understand what you meant by "passing the screen turns the electron into a delocalized object". You said the electron is a particle before it passes the screen. Since it is already a particle, how can it turned into a delocalized particle at the screen?

The electron is always a quantum field. The quantum field can be regarded to describe a particle if and only if the field has a nonzero expectation only in a region small compared to the whole system considered. Thus we may say that the field is a particle as long as this condition is satisfied. Because of the dispersion of the field caused by the slits, this condition stops to be satisfied almost immediately after the field (with support large enough to cover both slits) passed the double slit. Thus it is no longer justified to talk about a particle.

The situation is similar as with a sphere of glass. If you throw it, you may regard it as a particle. But if it hits an obstacle and fragmentizes, it is no longer localized enogh to deserve the name of a particle.

Let's go from the beginner in the emission. So the electron is emitted. You believed it travels as particle? But where does it pass, the left or right slit? And what caused the interferences in the screen. Standard explanation says it interferes with itself because it is a wave after it is emitted.. and only become a particle at the detection screen. Pls. elaborate what happened to your electron after emission.. before it reaches the slits.. after it exits the slits and after detection in the screen.

The field passes the doulbe slit in a fashion similar as a water wave would do, except with quantum corrections.

 

[Varon]

The electron is always a quantum field. The quantum field can be regarded to describe a particle if and only if the field has a nonzero expectation only in a region small compared to the whole system considered. Thus we may say that the field is a particle as long as this condition is satisfied. Because of the dispersion of the field caused by the slits, this condition stops to be satisfied almost immediately after the field (with support large enough to cover both slits) passed the double slit. Thus it is no longer justified to talk about a particle.

The situation is similar as with a sphere of glass. If you throw it, you may regard it as a particle. But if it hits an obstacle and fragmentizes, it is no longer localized enogh to deserve the name of a particle.

The field passes the doulbe slit in a fashion similar as a water wave would do, except with quantum corrections.

Interesting. But how come the detector detects one electron and not the fragmentized parts (after passing thru the slits)?

 

[A. Neumaier]

Interesting. But how come the detector detects one electron and not the fragmentized parts (after passing thru the slits)?

The quantum field does not fragmentize like a broken glass sphere. It just expands into a superposition of two spherical waves. The outer electrons of the detector respond to the incident quantum field by an approximate Poisson process with rate proportional to the incident density. This accounts correctly for the simple statistics obtained for an ordinary electron beam. See post #4 of this thread, and the longer discussion of the case of photons in
https://www.physicsforums.com/showthread.php?p=3187039#post3187039
and in the thread
https://www.physicsforums.com/showthread.php?t=480072

 

[Varon]

The quantum field does not fragmentize like a broken glass sphere. It just expands into a superposition of two spherical waves. The outer electrons of the detector respond to the incident quantum field by an approximate Poisson process with rate proportional to the incident density. This accounts correctly for the simple statistics obtained for an ordinary electron beam. See post #4 of this thread, and the longer discussion of the case of photons in
https://www.physicsforums.com/showthread.php?p=3187039#post3187039
and in the thread
https://www.physicsforums.com/showthread.php?t=480072

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. Pls. explain what goes on between the slits and the detector and how the detector only detects one electron. My example is not the same as your electron beam and statistics for the ensemble. I'm referring to a single electron emission and detection.

 

[Rap]

Pls. explain what goes on between the slits and the detector

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.

 

[Varon]

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]

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://arnold-neumaier.at/physfaq/physics-faq.html - should I keep reading this to find what you are saying or do you have another source?

 

[Varon]

I have not read all of the web page at http://arnold-neumaier.at/physfaq/physics-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]

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]

I have not read all of the web page at http://arnold-neumaier.at/physfaq/physics-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://arnold-neumaier.at/physfaq/physics-faq.html#doubleSlit

 

[Varon]

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]

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).

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]

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]

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]

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]

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]

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.

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]

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]

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]

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 into 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]

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]

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.

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.

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 into 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]

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.