Exploring Photon Trajectories in Double Slit Experiments

[Ken G]

Please read the rest of my post carefully before responding .. I explain in detail why the answer is no.

Then go to my question #1 and we'll start there, because charge is a complete red herring to this discussion.

 

[Ken G]

You made me look it up Ken, and it was interesting reading.

"According to the selection rule interpretation, Bohr's correspondence principle is best understood as the statement that each allowed quantum transition between stationary states corresponds to one harmonic component of the classical motion. More precisely, Bohr's selection rule states that the transition from a stationary state n′ to another stationary state n″ is allowed if and only if there exists a τth harmonic in the classical motion of the electron in the initial stationary state; if there is no τth harmonic in the classical motion, then transitions between stationary states whose separation is τ are not allowed quantum mechanically. "

That's very interesting, you can see how classically Bohr liked to think, and how deep was the intuition he gained from it. Too bad he's not posting to this thread! Your quote actually raises an aspect of the correspondence principle I had never seen-- a general and formal way to use the Fourier modes of classical wave equations to impose constraints on quantum laws. I had only ever thought of it in the other direction, that it was a way to derive classical laws from quantum mechanical ones, but of course that does imply constraints on the quantum laws if we already have the working classical theory. Fascinating, thank you.

 

[unusualname]

The correspondence principle is not a law of nature, it's simply a rule for us dumb humans to check that our (quantum mechanical) model of reality is consistent.

The correspondence principle enables us to constrain our models of the microscopic world, simply because these models must (obviously) also describe the macroscopic world we observe in appropriate limits (of large numbers)

However, the correspondence principle says nothing more than that about reality.

Why would anyone resurrect an ancient philosophical principle to attempt to explain modern physics experiments?

Nobody really cares about this out-dated way of thinking anymore, we now have the far more sophisticated decoherence argument to explain macroscopic phenomena.

 

[Ken G]

The correspondence principle is not a law of nature, it simply a rule for us dumb humans to check that our (quantum mechanical) model of reality is consistent.

I'm afraid that's a pretty good definition of a "law of nature." Why you see a distinction there is certainly outside anything that could be called science.

Why would anyone resurrect an ancient philosophical principle to attempt to explain modern physics experiments?

Yeah, like a principle of symmetry among observers. What good physics could that lead to either?

Nobody really cares about this out-dated way of thinking anymore, we now have the far more sophisticated decoherence argument to explain macroscopic phenomena.

Like I said, if you don't understand the correspondence principle, you can't use it to understand various types of quantum phenomena.

 

[unusualname]

^^Not worth replying to directly, to add something interesting, Chaos theory arguably made the correspondence principle useless:

Why We Don't Need Quantum Planetary Dynamics: Decoherence and the Correspondence Principle for Chaotic Systems

 

[SpectraCat]

Then go to my question #1 and we'll start there, because charge is a complete red herring to this discussion.

Well, I would prefer that you read in full my previous discussions of these topics, and address all the points. It's not about charge, it's about MASS. As I have now said several times, it is the wavelike behavior of MASSIVE particles that can never be obtained in the limit of large quantum numbers, because it is precisely that information that is "averaged out" according to the correspondence principle. It's amusing that you think I am the one who has a misunderstanding of the correspondence principle in this respect ... I think exactly the opposite.

Charge is not a red herring in the context in which I used it, which was to explain why you might observe deviations from the quantum mechanical limit if you used high fluxes of electrons to carry out the experiment. However, I agree that it is not relevant to the main issue.

With regard to your "questions" here are my answers:

1) Do you think an electron with no charge would show the same diffraction pattern? Yes or no please.

That is not a valid question without further caveats, so I will supply them. Assuming we could have massive particles with the same mass as the electron, AND we could create monoenergetic beams of them, AND those particles interacted with the ordinary matter of the double slit through the electromagnetic force (i.e. like a neutral atom would), then yes, I would fully expect to see diffraction.

2) Do you think the HUP has an obvious classical analog, which can be used to understand the HUP better, and the existence of this analog is a perfect example of the correspondence principle? Yes or no please.

I already answered this question as best I can in my last post ... my answer is again a qualified yes. The correspondence principle can be appreciated in the context looking at the limit of the Fourier transform of a highly localized wave packet with a broad momentum distribution. That does NOT make the HUP "an example of the correspondence principle", which is the specific statement you made that I objected to. Furthermore, the true understanding of the correspondence principle comes not from this analogy, but rather by looking at the relative magnitudes of the uncertainties as the systems approach macroscopic sizes.

3) Do you think this statement is true: "every quantum theory can be used to spawn a classical theory, that invokes only classical concepts (including no quanta), that will always work in the classical limit of large occupation numbers of that same quantum system, and what's more, it is essentially an accident of history as to which was discovered first, the quantum theory or it's classical analog." Yes or no please.

Of course I agree, that is what the correspondence principle tells us. The issue is that such an treatment CANNOT be generated to describe the diffraction of electrons. You seem to be confusing having high occupation numbers for quantum states of EM-fields (i.e. photons), with having large numbers of monoenergetic electrons. Those two situations are NOT physically analogous. As I said before, if diffraction can be observed for the electrons, then BY DEFINITION they are not in the limit of large quantum numbers. Rather, for the double slit experiment, the observation of diffraction means that the momentum of the electron is sufficiently small that their wavelength is comparable to the width and separation of the slits. Do you disagree that is a requirement for electron diffraction? Do you disagree that electrons which have that property are NOT in the large quantum number limit? Note that the meaningful quantum number in this case refers to the momentum state (or kinetic energy) of the electrons.

Just think about photons, please-- unless you believe that electron diffraction occurs purely due to quantum photon uncertainty effects, but photon diffraction occurs for some other reason! Is that what you think? (I guess that's question #4. You can't learn the correspondence principle without answering those 4 questions.)

Yes that is what I think, as I have explained at length. Of course you can make the trivial observation that the reason that photons and electrons both exhibit diffraction in the double slit is that both have wavelengths that are greater than or equal to the spacing and width of the slits. However, while there is a classical analog of photon diffraction the diffraction of classical EM fields, there is NO classical analog for electron diffraction. If you develop a phenomenological theory from experimental results to try to model and explain electron diffraction, it will necessarily be a quantum one, i.e. one that accounts for the spatial phase of massive particles, and is only valid in the limit where h does not go to zero.

In summary, I am fine with using the correspondence principle to connect diffraction phenomena of quantum photons to classical EM waves. However, as I noted previously, it seems a bit trivial to me ... the reason this works is because the quantum description of the field of the massless photons is essentially the same as the classical EM field .. the only difference is the occupation numbers of the quantum states of the field. For massive particles, the correspondence principle explains why the spatial delocalization of the quantum states can be neglected in the limit of high quantum numbers. Therefore, if you observe an experimental effect that can only be explained by the delocalized nature of quantum particles, it cannot be explained in the classical limit using the correspondence principle. I can't say it more clearly than that, and I can't believe you won't accept that distinction.

 

[yoron]

Now, this might seem simplistic but isn't all classical systems non linear, that is chaotic, when looked over a longer period of time? And the linearity we find is defined from mathematics, not nature?

Isn't it just that we always found reality to be more understandable when confined to a constricted system with clear delimitations? And that it is this chaos theory lift forward, that in open systems you will find chaotic components. To me chaos theory speaks about patterns repeating themselves, unable to backtrack to any origin although being the result of bifurcations creating a 'linear causality chain', even if not traceable coming back at certain intervals? I'm not sure I find it meaningful to put that against the correspondence principle myself?

The correspondence principle as an idea makes a lot of sense, if we want to keep causality. Chaos theory is also about a 'causality' of sorts, just not the old 'linear one'. The correspondence principle could do as well for a non linear reality, as it seems to me?
=

It's a interesting point to make unusualname. I've seen two definitions of classical non-linearity (chaos), and QM recently. One stating that QM contain no chaos. "Let us set the record straight: there is no such thing as quantum chaos. The term “quantum chaos” is a shorthand for the study of quantized systems who’s classical analog exhibits chaotic features. This raises two obvious questions: why does quantum chaos not exist and, since that is the case, why is the study of quantized chaotic systems of interest?" from "A Rough Guide to Quantum Chaos by David Poulin." And then another that seems to explore the possibility of QM containing Chaos. Myself I started to wonder about HUP, versus our classical 'chaos'? That is if you could find a correspondence between them?Quantum Chaos.

 

[Ken G]

^^Not worth replying to directly, to add something interesting, Chaos theory arguably made the correspondence principle useless:

Why We Don't Need Quantum Planetary Dynamics: Decoherence and the Correspondence Principle for Chaotic Systems

Well done digging up another interesting paper for these discussions. That paper is a good entry point into the issues of the correspondence principle as it relates to classical mechanics (Newton's laws). So far we've mostly been talking about the correspondence principle as it relates to classical wave theory, but it's nice to have the other end of the correspondence of wave/particle duality, the duality of correspondences if you will.

From what I've seen of that paper, I feel it lays out a nice foundation for analysis, but it is simply misidentifying what the correspondence principle should mean in chaotic systems-- they interpret the CP as saying that the classical theory and the quantum theory should produce the same trajectory for an initial state, but that's asking too much in view of sensitivity to initial conditions. The more important concern is that the correspondence principle should generate the "same physics" from the classical and quantum theories, which does not require the same trajectory when the trajectory itself has no real physical meaning (the "butterfly effect"). Instead, the "same physics" should simply mean the same statistical tendencies, the same probability distribution of outcomes for any realistic uncertainty in the initial conditions.

In other words, if the quantum theory said "Hyperion will hit the Earth in 2030" and the classical theory said "Hyperion will be ejected from the solar system in 2020", then we'd have a breakdown of the correspondence principle. But neither theory can make predictions like that, and if they both agree that "the chance that Hyperion will hit the Earth by 2030 is 1 part in a quintillion", then we have the correspondence principle working fine.

 

[Ken G]

Thank you for answering my questions, now we can get somewhere:

Assuming we could have massive particles with the same mass as the electron, AND we could create monoenergetic beams of them, AND those particles interacted with the ordinary matter of the double slit through the electromagnetic force (i.e. like a neutral atom would), then yes, I would fully expect to see diffraction.

OK good, we agree there. Now for the next question: do you think that large numbers of these particles passing through the apparatus, still in the collisionless limit, would also diffract and show an interference pattern?

You seem to be confusing having high occupation numbers for quantum states of EM-fields (i.e. photons), with having large numbers of monoenergetic electrons. Those two situations are NOT physically analogous.

Well, I guess my question above will get to the heart of whether or not your claim here is really true.

Rather, for the double slit experiment, the observation of diffraction means that the momentum of the electron is sufficiently small that their wavelength is comparable to the width and separation of the slits. Do you disagree that is a requirement for electron diffraction?

Obviously that is a requirement,a first-year student of classical wave mechanics knows that. It is also irrelevent, the "classical limit" here is the limit of large numbers of particles, not the limit of a large momentum for a single particle. That is the "other side" of the wave/particle duality of correspondences, more appropriate to the Hyperion paper.

Do you disagree that electrons which have that property are NOT in the large quantum number limit? Note that the meaningful quantum number in this case refers to the momentum state (or kinetic energy) of the electrons.

Here's your problem, you have the wrong correspondence in mind! Everything I've said refers, quite clearly, to the correspondence to classical wave mechanics, not the correspondence to classical particle mechanics. Yet your statements here are irrelevant to classical wave mechanics, you are talking about the particle correspondence that turns an electron into a bowling ball. So the problem is now crystal clear: you may have understood one side of the correspondence principle, and think every time you hear it that it is this side, but you have not understood there is another side to that principle, the correspondence of the wave nature of quanta to the classical wave nature of ensembles of quanta.

This disconnect is severe, and means you need to reread the entire discussion with the correct correspondence in mind. But it was a useful mistake to make-- it draws out the fact that there are these two very separate types of correspondence, a duality of correspndences, which I hadn't been on the lookout for or I might have caught it sooner. When you answer my italicized question above, you will see this other correspondence that you have been missing, and that will open the door to a whole new world of using classical analogs to help understand two-slit quantum experiments for particles with mass-- as you apparently already knew could be done with particles without mass.

 

[SpectraCat]

Man, you really pick and choose the points in my posts that you want to respond to, don't you? I would really appreciate it if you would address the other points that have gone unaddressed ... I will try to summarize them below after I have dealt with your latest post.

Thank you for answering my questions, now we can get somewhere:
OK good, we agree there. Now for the next question: do you think that large numbers of these particles passing through the apparatus, still in the collisionless limit, would also diffract and show an interference pattern?

Of course (assuming they width of the energy distribution is sufficiently narrow that they can be described as monoenergetic) ... what would that change? There is no classical limit or correspondence principle at work there .. you just have more quantum particles going through the slits, so you build up the interference pattern faster than you would have when there were fewer particles. The appearance of interference fringes still depends on the quantum delocalization of the particles due to the HUP, as I have said from the beginning. As such, it cannot be described as classical.

Now I have a question for you ... let's switch back to electrons, so we are talking about a physically real case again ... by passing large numbers of particles through, you claim we are somehow studying the system in the limit of large quantum numbers. Please explain, in as much detail as possible, which quantum numbers are different (i.e. "in the large limit") between the one-by-one case we agree is clearly quantum, and the "large numbers of electrons" that you claim somehow bring us to the limit of the correspondence principle? Until you can answer that question, we can't make any progress here.

Well, I guess my question above will get to the heart of whether or not your claim here is really true.

Well, not so much your question as my own.

Obviously that is a requirement,a first-year student of classical wave mechanics knows that. It is also irrelevent, the "classical limit" here is the limit of large numbers of particles, not the limit of a large momentum for a single particle. That is the "other side" of the wave/particle duality of correspondences, more appropriate to the Hyperion paper.Here's your problem, you have the wrong correspondence in mind! Everything I've said refers, quite clearly, to the correspondence to classical wave mechanics, not the correspondence to classical particle mechanics. Yet your statements here are irrelevant to classical wave mechanics, you are talking about the particle correspondence that turns an electron into a bowling ball.

With all due respect, that last bit is utter nonsense. As I have explained repeatedly, and you have never addressed even once (except to contradict it without explanation), there is no classical limit in which massive particles behave like waves. That you would think there is, or even could be, indicates that you have a deep-seated misunderstanding of the quantum mechanical principles that you suppose yourself to be educating others about. This gets at one of the points that you have never addressed, namely how the Schrodinger equation somehow magically morphs into a classical wave equation in the classical limit, when the two equations don't even have the same mathematical form:

Here is the Schrodinger equation:

$$i\hbar\frac{d}{dt}\Psi\left(\vec{r},t\right)=-\frac{\hbar^2}{2m}\nabla^2 \Psi\left(\vec{r},t\right) + V\left(\vec{r}\right)\Psi\left(\vec{r},t\right)$$

Here is the classical wave equation:

$$\frac{d^2}{dt^2}u\left(\vec{r},t\right)= c^2\nabla^2u\left(\vec{r},t\right)$$

Note that the Schrodinger equation involves the first time derivative of the wave function, while the classical wave equation involves the second time derivative of the scalar function representing the waveform. Please explain to me how to get from one to the other in the classical limit that you claim is valid.

So the problem is now crystal clear: you may have understood one side of the correspondence principle, and think every time you hear it that it is this side, but you have not understood there is another side to that principle, the correspondence of the wave nature of quanta to the classical wave nature of ensembles of quanta.

That seems like more nonsense ... there is no classical wave nature to ensembles of quanta for massive particles. I grow tired of this .. from what I know about physics, your claim that there is some classical limit in which massive particles have wave-character is bizarre in the extreme, and is certainly not in the mainstream. Please provide a reference for the claim you are making. Normally I would have asked for it sooner, but you have shown that you know what you are talking about in other arenas, so I figured I'd eventually figure out what you are talking about here.

This disconnect is severe, and means you need to reread the entire discussion with the correct correspondence in mind. But it was a useful mistake to make-- it draws out the fact that there are these two very separate types of correspondence, a duality of correspndences, which I hadn't been on the lookout for or I might have caught it sooner. When you answer my italicized question above, you will see this other correspondence that you have been missing, and that will open the door to a whole new world of using classical analogs to help understand two-slit quantum experiments for particles with mass-- as you apparently already knew could be done with particles without mass.

Your patronizing attitude becomes tiresome. You have provided not a shred of evidence a and only vague justifications for why the correspondence you purport to exist actually does. I asked for an equation, it was not given. I provided detailed explanations of why the idea that massive particles can display wave-like properties in the classical limit makes no sense in light of the HUP (or the de Broglie equation, for that matter) .. those points remain unaddressed, except for your bizarre dismissal of the HUP as "an example of the correspondence principle". Once more I will ask you to explain why you think a phenomenon that depends exclusively on the quantum delocalization of massive particles can possibly persist in the classical limit? You have never once answered that question with a declarative statement of your thoughts on the topic .. you have only asked me more questions. I have answered your questions, now please answer mine.

 

[DevilsAvocado]

If you think that obvious point is in any way relevant to what I said, it is hopeless that you will understand what I did say (which is that many quantum phenomena can be better understood by noticing their classical analogs). Indeed, I've mentioned several classical analogs in this thread, I explained how they could have been arrived at even without knowing that we are dealing with quanta (like two-slit diffraction patterns), and still you cling to the empty claim that this somehow doesn't make sense.

What’s empty and what doesn’t make any sense is, as far as I can see, still under debate in this thread.

Maybe you can answer this: just what do you think is inherently "quantum" in a two-slit diffraction pattern? I'm all ears.

I’ll do that in this post, no worries mate. In the meantime, I’ll provide a little dish of https://www.physicsforums.com/showpost.php?p=3366381&postcount=110" to chew on:

"So we can say that we cannot classically explain why the pattern is built up from dots (that's the *inherently 'quantum'* part)"​

(emphasis mine)

Meanwhile, I'll just have to hope that someone else was lurking in this thread, someone who actually did wish to understand the correspondence principle, and who might glean the importance of these words: every quantum theory spawns a classical theory that has to work in the classical limit. That's what "classical analog" means, for those watching at home.

And this is why I’m still pursuing this thread, because this latest confusing "classical twist" will undoubtedly misguide any "layman at home".

For a start – you’re contradicting yourself:

(emphasis mine)

*every* quantum theory spawns a classical theory that has to work in the classical limit. That's what "classical analog" means, for those watching at home.

Note I never said "there is no such thing as a quantum effect that has no classical analog." What I did say is "*many* quantum effects do have classical analogs that we take advantage of all the time, especially when testing quantum mechanics, yet many people seem to be unaware of this fact."

I do hope you understand difference between "every" and "many"??
(And please don’t tell me that there are "quantum effects" that "we take advantage of", without a corresponding "quantum theory".)

This kind of confusing gabble will undoubtedly misguide any "layman at home".

I don’t know why you use this vague language of double negation; "I never said “there is no such thing as a quantum effect that has no classical analog.”"...??

I have no idea why you 'beat around the bush' like this, but I’ll help you spelling it out in simple understandable English: You are saying that – YES *there are* quantum effects that have *no* classical analog.

Good, now when we come this far, could you just mention ONE quantum effect that have no classical analog (to cancel out the 'beating around the bushes' accusation), pleeeeeeeease??

To be fair to the "layman at home", don’t you think it would be suitable to explain more in detail what the Correspondence principle really is? That it’s not a law of nature? That it’s not without controversies among physicist, including the founding fathers of QM like Sommerfeld, Pauli, and Heisenberg? That it was formulated by Niels Bohr in 1920, at the time of the old quantum theory, and that it originates from as early as 1913, when Bohr was developing his model of the atom (which we now know is incomplete).

Yes, the Correspondence principle was a cornerstone in Bohr's philosophical interpretation of quantum mechanics - the Copenhagen interpretation, yet there are three (3) different interpretations of the Correspondence principle - the frequency interpretation, the intensity interpretation and the selection rule interpretation.

And as I said, the Correspondence principle was mistrusted by Arnold Sommerfeld, Wolfgang Pauli and Werner Heisenberg:

Bohr has discovered in his principle of correspondence a magic wand (which he himself calls a formal principle), which allows us immediately to make use of the results of the classical wave theory in the quantum theory. (Sommereld [1919] 1923, p. 275)

The magic of the correspondence principle has proved itself generally through the selection rules of the quantum numbers, in the series and band spectra… Nonetheless I cannot view it as ultimately satisfying on account of its mixing of quantum-theoretical and classical viewpoints. (Sommerfeld 1924, p. 1048; quoted also in Seth 2008, p. 345).

I personally do not believe, however, that the correspondence principle will lead to a foundation of the rule… For weak men, who need the crutch of the idea of unambiguously defined electron orbits and mechanical models, the rule can be grounded as follows: ‘If more than one electron have the same quantum numbers in strong fields, they would have the same orbits and would therefore collide… The justification of the exclusion of the above-mentioned cases in the H-atom by pointing to the collision with the nucleus has never pleased me much. It would be much more satisfying if we could understand directly on the grounds of a more general quantum mechanics (one that deviates from classical mechanics). (Pauli to Bohr December 31st, 1924; quoted in Heilbron 1983, p. 306 and Serwer 1977, p. 236)

It is true that an ingenious combination of arguments based on the correspondence principle can make the quantum theory of matter together with a classical theory of radiation furnish quantitative values for the transition probabilities… Such a formulation of the radiation problem is far from satisfactory, however, and easily leads to false conclusions. (Heisenberg 1930, p. 82)​

One should also add that in 1920, no one knew about Bell's inequality and EPR-Bell test experiments, which is completely impossible to find any classical analogy for, unless some crackpot is claiming that non-locality and/or non-realism is indeed "Classical Properties" (and now we are talking LARGE quantum numbers!).

Everyone knows that in EPR-Bell 1 + 1 = 3 and that this is not a classical number.

I really don't know what you are talking about, to clarify the situation, please write down the classical formulation of wave mechanics that predicts the diffraction of "large ensembles of electrons".

(emphasis mine)

First you need a classical measurable. Electron energy flux density will suffice (we could use electron number flux, but my point is that we never need to think of these things as particles at all to "understand" diffraction). Now you need a wave theory. Huygen's principle works fine. Let's simplify life and just get a theory that works for electrons of a given energy (which here means a given ratio of energy flux to mass flux). The wave equation with the v of that population of electrons will work fine, where v is found from timing experiments. Now we need a concept of frequency because it's a wave theory, and here we can leave the frequency as a free parameter that the interference experiment will determine. The wave equation describes the speed of signal propagation, Huygen's principle tells us how to handle the sources and the slits, and the frequency parameter gives us the interference we need. Every one of these is a 100% classical concept, remember that we are pretending we don't even know we have particles here. Now we put them together to calculate the energy fluxes everywhere subject to the free frequency parameter, compare to experiments, and poof, both the frequency parameter drops out, and the fact that we have what we would call a correct theory for electron diffraction, and all classical.

I have to agree with SpectraCat, I don't know what you are talking about?? How could we pretend there are no particles and at same time claim "poof" we have "electron diffraction, and all classical"?? I’m sorry Ken G, this is nuts, totally nuts.

But okay, I’ll be a nice guy and pretend that you are also just a nice guy who wants to help laymen to understand that QM is not weird or mystical at all, and most of the time we do find analogies in our classical world that works perfectly well – nothing to 'worry' about. Okay?

Let’s look at the Double Slit Experiment in way that I know you’ll like:

http://www.youtube.com/watch?v=ZXyxnxnWAAQ&hd=1
https://www.youtube.com/watch?v=ZXyxnxnWAAQ

A hardcore 'QM-Weirdo-Mystifier' would now say: – OMG! OMG! Look at that totally weird QM laser stuff! Totally AWESOME man! Out of this world man! NO ONE could never ever explain this in classical terms!

And then Ken G, you come in the picture and calm things down by showing this video:


https://www.youtube.com/watch?v=-8a61G8Hvi0

And then you say: – See? There’s absolutely nothing strange about this... It’s just ordinary wave mechanics, completely explainable in everyday classical physics!

This is perfectly cool by me, and probably a good thing to teach the public the wave part of QM.

The problem begins when you use all kind of weird arguments to avoid the other crucial particle part of QM, and it all becomes very strange since you are using Niels Bohr in this odd campaign – the same man who is very well known for his basic QM principle of http://en.wikipedia.org/wiki/Complementarity_(physics)" , i.e. the wave–particle duality...??

I think it’s sad, because my first impression was you did have a lot of usable knowledge, which for sure could be used in a better way than this.

Finally, back to you initial question – What’s inherently "quantum" in a two-slit diffraction pattern?

Well, besides having you answering the question yourself, I would add the obvious – it’s of course the quantum itself! Call it what you like; energy package, particle, electron or whatever – but we all know what it is, it’s not the wave(function), it’s that other "stuff" that makes all the difference in the world! If there were no quanta in Quantum Mechanics, it would of course have been called "Wave Mechanics" instead...

And now, if you still want to demystify the Double Slit experiment with only waves, you have to put in a high pressure washer instead, and hope the water would magically split before the slits, and then magically start interfere with itself after the slits, to finally reenter into a concentrated beam just before hitting the detector to make ONE concentrated mark, not a splash all over the place.

That’s what I call real water-wave-magic! Totally AWESOME man!

If Niels Bohr in 1920 would have had access to Dr. Tonomura’s video of single electrons in the Double Slit experiment (that I showed in https://www.physicsforums.com/showpost.php?p=3366035&postcount=107"), I’m sure he would had reformulated the Correspondence principle – but he hadn’t.

There is no way to make these facts go away – every single electron-detection is visible – even if there are millions of electrons in the experiment.

Inherently quantum two-slit diffraction pattern

Before ending this long post; I have a question for you – Do you believe that Local Realism is still feasible? Yes or no please, there is no way to be a bit pregnant.

 

[Ken G]

Man, you really pick and choose the points in my posts that you want to respond to, don't you? /quote]Actually, I find that in situations where you feel essentially everything I'm saying is wrong, and I feel essentially everything I'm saying is right, it serves to find one clear case where you are saying I'm wrong and I can demonstrate that I'm right. The neutron diffraction experiment is exactly that, so let's see how that plays out, and the rest should follow.

Of course (assuming they width of the energy distribution is sufficiently narrow that they can be described as monoenergetic) ...

OK, this is good, we've established:
I) A neutron diffraction experiment gets the same diffraction pattern if it's done with one neutron at a time, or a vast ensemble of neutrons, so long as we stay in the collisionless limit where neutrons are not bouncing off each other.

That's actually all I'm going to need.

There is no classical limit or correspondence principle at work there .. you just have more quantum particles going through the slits, so you build up the interference pattern faster than you would have when there were fewer particles.

Actually, you do have a classical limit here, you do have a correspondence principle here, and this is the entire point I'm making. First you need a classical observable. Energy flux will do nicely. So hold up your classical detector into this vast ensemble of neutrons and measure the energy flux at various places. You get the diffraction pattern we both agree on.

Now pretend you are a student, given that detecting apparatus, but you have no idea what is being sent from the emitter, it could be particles or sound waves or phlogiston, you have no idea. Your job is to be a scientist, and develop a theory that can predict what will happan if you modify the geometry of the slits. I'm serious, this would be a wonderful exercise in how science works. So you notice you have a pattern that looks like interference, so you say "aha, I think a wave theory might work here." I'm serious, this is exactly how it was done in many situations. You play with the equations, and sure enough, you develop a wave theory that beautifully predicts what will happen when you modify the slit geometry. You say, "I understand the physics here, we have a wave coming out of the emitter, I'll call it a nound wave. It has a characteristic wavelength I can set as a free parameter to make the pattern work, and that parameter stays the same when I alter the slits, and my predictions work too. Then I swapped my classical energy detector for a classical momentum detector, and sure enough, I found a fixed ratio between energy and momentum fluxes, which I'm going to call (half) the speed of the wave. This also stays constant when I alter the geometry of the slits. I'm doing great, I have a wave with known speed and wavelength, so also known frequency, and my theory predicts the energy and momentum fluxes for any slit geometry. I have a classical wave theory, please give me my coveted scientific award.

Now please note several things:
1) the student did all this without knowing that there were any particles involved here at all, let alone neutrons, and
2) the classical wave theory the student arrived at is exactly what you get if you take the Schroedinger equation in the limit of large occupation numbers (yes for monoenergetic neutrons, and as I say long ago, that particle energy could also be a controlled variable and the classical wave theory would work just great, would find a different wave speed for each mono-energy, just as I said-- the classical theory generated by the quantum mechanics of a particle with mass has a dispersion relation built into it).
3) Facts 1 and 2 are called "the correspondence principle".
4) Sometimes by accident of history, the quantum theory comes first, sometimes the classical theory comes first, it just depends on the particle. But whichever theory comes first, they are connected by the correspondence principle.

The appearance of interference fringes still depends on the quantum delocalization of the particles due to the HUP, as I have said from the beginning. As such, it cannot be described as classical.

I just told you how it would be completely described as classical. If this still hasn't clicked, ask yourself this: what if my hypothetical student experiment had actually been carried out in the year 1900? Bingo, we would have exactly an interference pattern that would be explained as classical. Whether some predicted experimental outcome can be called classical or not is not an ontological stance, it is purely answered by what type of theory predicted it, and many results, like interference fringes, can be predicted by either classical or quantum theories. As I just showed.

That sums up what I've been saying. There's really no need to go through every objection you've raised, what I've just shown makes it all crystal clear. Most of the time you were using a different type of correspondence principle anyway, not the classical limit that turns a quantum into a wave, but the classical limit that turns a quantum into a bowling ball. So all that can be ignored as a category error, and it's better to just focus on the above, because the whole nature of the disagreement is spelled out right there.

Now I have a question for you ... let's switch back to electrons, so we are talking about a physically real case again

(ahem, neutrons are physically real)

... by passing large numbers of particles through, you claim we are somehow studying the system in the limit of large quantum numbers.

Correction, large occupation numbers, as I said. "Large quantum numbers" is a rather ambiguous phrase, you are misinterpreting its meaning here.

Please explain, in as much detail as possible, which quantum numbers are different (i.e. "in the large limit") between the one-by-one case we agree is clearly quantum, and the "large numbers of electrons" that you claim somehow bring us to the limit of the correspondence principle?

The occupation numbers of the modes. This is exactly why you are not understanding.

Until you can answer that question, we can't make any progress here.

I've answered it half a dozen times already, just scan for the phrases "occupation number" and "classical wave."

With all due respect, that last bit is utter nonsense. As I have explained repeatedly, and you have never addressed even once (except to contradict it without explanation), there is no classical limit in which massive particles behave like waves.

With all due respect, that's complete nonsense, and let's hope our common ground point (I), and the experiment I just described in great detail, makes that crystal clear.

That you would think there is, or even could be, indicates that you have a deep-seated misunderstanding of the quantum mechanical principles that you suppose yourself to be educating others about.

Now we have exposed just how ridiculous that claim is!

 

[Ken G]

In the meantime, I’ll provide a little dish of https://www.physicsforums.com/showpost.php?p=3366381&postcount=110" to chew on:

"So we can say that we cannot classically explain why the pattern is built up from dots (that's the *inherently 'quantum'* part)"​

(emphasis mine)

Emphasize it all you want, it's completely correct, and contradicts nothing I've said. The things I am saying are fully self-consistent, I can't even yet tell why you think they're not.

For a start – you’re contradicting yourself:

Sorry, no help there-- citing those two perfectly correct and perfectly non-contradicting statements does not help me see what misconception is leading you to think they contradict each other.

I do hope you understand difference between "every" and "many"??

Sorry, still no help, because I do know the difference between those two words, and I still have no idea what contradiction you are imagining. Seriously, I don't--- those statements are both correct, neither contradicts the other, and the words "every" and "many" were used in completely correct ways. I suppose if you lift the words out of their sentences, they do seem like contradictory words, but I'm afraid lifting them out of their very different sentences doesn't help me find the contradiction you imagine here.

You are saying that – YES *there are* quantum effects that have *no* classical analog.

Excellent, then you did understand me, despite the double negative. I knew you could handle it. In fact, I spelled out a quantum effect that has no classical analog-- the way spots accumulate on a detector when we turn the flux down. Oh yes, you quoted that point just above, how helpful. Now what is your problem with these true facts? I'm stilil missing the contradiction you imagine, I think you must be making a logical error.

To be fair to the "layman at home", don’t you think it would be suitable to explain more in detail what the Correspondence principle really is? That it’s not a law of nature?

Welll I'm not sure what your personal definition of what a law of nature is, but it is perfectly irrelevant. I explained at great detail what the correspondence principle is, it is the statement that all quantum theories must be consistent with a classical theory in the classical limit, and the classical theory can be derived from the quantum theory if you don't already have the classical theory, and if you do already have the classical theory but not the quantum theory, it imposes constraints on what the quantum theory can do. Whether or not you personally call that a law of nature is of no concern to me, it is what it is. Are you offering a counterexample to it, or do you just think the "layman" at home should be kept ignorant of this principle?

One should also add that in 1920, no one knew about Bell's inequality and EPR-Bell test experiments, which is completely impossible to find any classical analogy for, unless some crackpot is claiming that non-locality and/or non-realism is indeed "Classical Properties" (and now we are talking LARGE quantum numbers!).

Apparently your argument here is once again that because you can find quantum phenomena with no classical analog (which I already gave an example of myself), it refutes my claim that many quantum phenomena do have classical analogs and it can be quite informative to understand them. I just can't follow that reasoning, it sounds like wrong logic to me.

I have to agree with SpectraCat, I don't know what you are talking about??

Then read my last post to SpectraCat, I think it should be pretty clearly laid out. Are you as confused as he is about the difference between a "large quantum number" like a huge energy for a single particle, and a "large quantum number" like a huge occupation number for the number of particles in a given domain of phase space? Let me clarify. A classical wave theory is linear, so we have the concept of modes. We also have a concept of energy in the modes. Via the h parameter, this converts to a quantum-number concept of the number of quantums of excitation of the mode. In the classical theory, you don't know these are particles, so you just call them energy in the mode. But if the number of quanta in the mode is large, then you have a classical limit, and if it is small, then you are in the quantum domain. The correspondence principle constrains the behavior of the two theories in these two limits.

In particular, it says that everything that happens in the classical limit must happen in the aggregated limit of many repetitions in the quantum domain, but you can have things that happen in the quantum domain that "average out" and do not appear in the classical domain. All the same, much of the quantum behavior does survive to the classical domain, and when it does, we have ready access to classical intuitions. This is a Good Thing. So now you understand what I have been saying over and over.

And then you say: – See? There’s absolutely nothing strange about this... It’s just ordinary wave mechanics, completely explainable in everyday classical physics!

This is perfectly cool by me, and probably a good thing to teach the public the wave part of QM.

Excellent, so what are you going on about? Those two statements more or less summarize everything I've been trying to accomplish, that you have been fighting, with faulty logic and vast misconstruals of what I said. When you actually quoted what I did say above, there was no contradiction at all, yet you still claimed there was because of two different-sounding words you could lift out of the sentence. That is just not even close to a logical argument.

The problem begins when you use all kind of weird arguments to avoid the other crucial particle part of QM, and it all becomes very strange since you are using Niels Bohr in this odd campaign – the same man who is very well known for his basic QM principle of http://en.wikipedia.org/wiki/Complementarity_(physics)" , i.e. the wave–particle duality...??

Complementarity, as I pointed out above several times, is an absolutely wonderful example of exactly what I'm talking about-- the value of understanding classical analogs. I'm going to guess you've heard of Fourier transforms and their use in analyzing classical wave systems? Very instructive, very useful intuition, all extremely classical, and all very useful for understanding complementarity. Everyone knows this, actually, and the similar concepts that appear almost daily to sound engineers and radio astronomers are not quantum mechanics. A typical sound engineer probably never even learns quantum mechanics, they don't need to know a "phonon" from a hole in the wall, expressly because they work in the classical limit (of occupation number, once again-- I'm not sure you're getting that). Yet they could much more easily understand complementarity than someone without that classical experience. Do you reject that simple claim? Remember, it is the crux of what I have been saying, as is a matter of black-and-white record above, so to reject my point above, you must reject this claim now. Do you, or don't you?

The irony here is that the quantum weirdness associated with the complementarity principle is not the mundane constraint connecting the localizabilty and bandwidth of a wave packet, it is the weirdness that particles experience this same constraint. So this constraint is not a purely quantum phenomenon, but it only seems weird when it is a quantum phenomenon! Which is my entire point here, actually, so thank you for bringing up such a perfect confirming example of my thesis, though you strangely see it as a refutation.

I think it’s sad, because my first impression was you did have a lot of usable knowledge, which for sure could be used in a better way than this.

Well here's the thing: anything can seem wrong when you don't understand it. The danger is in concluding it's actually wrong, when in fact you just don't understand it.

Well, besides having you answering the question yourself, I would add the obvious – it’s of course the quantum itself!

Well this only exposes what I already know, you still have no idea what I've been saying. Let me clarify with these questions: do we see two-slit patterns in contexts other than quantum mechanics? Is there value in understanding that? Is that an example of a classical analog helping us understand a quantum phenomenon? Is this a perfect example of the correspondence principle (with respect to occupation numbers)? When you understand that the answer to every one of those questions is a definitive "yes", then you will finally, finally, understand what I am really saying, and not what you have been telling yourself this whole time what I was saying.

If there were no quanta in Quantum Mechanics, it would of course have been called "Wave Mechanics" instead...

This is the kind of perfectly obvious statement that just leaves me scratching my head about why you think it is the least bit relevant to the actual argument I've presented. At no time have you had the slightest idea what that argument was, so all your objections are just completely irrelevant, even the ones with correct logic like this last remark.

And now, if you still want to demystify the Double Slit experiment with only waves, you have to put in a high pressure washer instead, and hope the water would magically split before the slits, and then magically start interfere with itself after the slits, to finally reenter into a concentrated beam just before hitting the detector to make ONE concentrated mark, not a splash all over the place.

Nope, still not the least bit of relevance to my actual argument. I might blame myself, except I think I've been perfectly clear. I think the actual blame falls mostly on the fact that you still don't get that I have been talking about the classical analogs you get when you go to high occupation numbers of the quanta in each relevant patch of phase space. Maybe if you get that, you can go back through what I've said, and start to see what I actually said instead of this absurd distortion you keep reflecting.

If Niels Bohr in 1920 would have had access to Dr. Tonomura’s video of single electrons in the Double Slit experiment (that I showed in https://www.physicsforums.com/showpost.php?p=3366035&postcount=107"), I’m sure he would had reformulated the Correspondence principle – but he hadn’t. (my bold)

Now that is just patently absurd! You don't think Nils Bohr knew everything in that video? Did he ever recant the correspondence principle? Let's look at a simple syllogism here:
1) Niels Bohr was not an idiot.
2) Niels Bohr died in 1962.
3) Niels Bohr formulated the correspondence princple, and adhered strictly to some version of it his whole life
4) Electron diffraction earned Thomson and Davisson the Nobel Prize for Physics in 1937
5) Niels Bohr knew that one electron at a time would make individual spots
6) Niels Bohr knew that the correspondence principle predicted repetition of the spots would reveal the pattern that Thomson and Davisson got the Nobel Prize for, indeed that is exactly the purpose of the correspondence principle to be able to predict that (do you understand that yet?)
6) Your claim just made Niels Bohr roll over in his grave. Fortunately, I'm here to point that out, with this little syllogism, so maybe he can get some rest.

Before ending this long post; I have a question for you – Do you believe that Local Realism is still feasible? Yes or no please, there is no way to be a bit pregnant.

Ah, the entanglement issue. I can only imagine you brought it up because you are still folllowing the faulty logic that if someone says quantum phenomena always spawn classical theories that mimic enough of the behavior to be useful to know about, then any example of quantum phenomena that don't have classical analogs somehow refutes that. No, that is just plain bad logic.

 

[Cthugha]

The more important concern is that the correspondence principle should generate the "same physics" from the classical and quantum theories, which does not require the same trajectory when the trajectory itself has no real physical meaning (the "butterfly effect"). Instead, the "same physics" should simply mean the same statistical tendencies, the same probability distribution of outcomes for any realistic uncertainty in the initial conditions.

The problem with this line of reasoning is that for any real system the probability distributions as predicted by quantum mechanics and the distributions expected from classical arguments differ. There is no real system where these two can be STRICTLY identical up to all orders, not even for a laser beam.

 

[DevilsAvocado]

... Before ending this long post; I have a question for you – Do you believe that Local Realism is still feasible? Yes or no please, there is no way to be a bit pregnant.

Ah, the entanglement issue. I can only imagine you brought it up because you are still folllowing the faulty logic ...

I can see that you are very good in imagining things, but sorry – you’re wrong again. I brought it up to finally find out if you’re a real crackpot, or if all this is just a giant misunderstanding that makes it look like this.

But I have to tell you, the way you’re avoiding this simple question does not look promising. How hard can it be?

Therefore: Yes or no please?

 

[SpectraCat]

Man, you really pick and choose the points in my posts that you want to respond to, don't you?

Actually, I find that in situations where you feel essentially everything I'm saying is wrong, and I feel essentially everything I'm saying is right, it serves to find one clear case where you are saying I'm wrong and I can demonstrate that I'm right.

The problem is that the points you ignore are the ones that show why you are wrong. For example, you have yet to provide an equation for your supposed classical theory of electron diffraction. You also have not explained how you can obtain a classical wave equation by taking the classical limit of the Schrodinger equation. Finally, you have not explained how a classical theory can preserve or predict the spatial delocalization that gives rise to the experimentally observed diffraction of massive bodies .. of course that is because it cannot, since spatial delocalization of massive bodies is a feature that is exclusive to (if not definitive of) quantum theories.

The neutron diffraction experiment is exactly that, so let's see how that plays out, and the rest should follow.OK, this is good, we've established:

*Sigh* .. the problem is that you some idea what you are talking about, but you have, as I already pointed out, deep-seated misunderstandings about quantum mechanics. In addition, your posts strongly suggest that you are not an expert in science, although you may be an expert in another field, like philosophy or history of science. The fact that you would continually confuse photons, and electrons is evidence of that, as is the fact that you are apparently incapable of writing down an equation or providing a mathematical derivation to back up your reasoning. Finally, a scientist would realize that the fastest way to end an argument like this is to provide a literature reference for their claims. I can do that, because every single text on quantum mechanics will back up what I am saying. I have asked you to do the same for your claim that one can formulate a classical theory of electron diffraction, and it seems you cannot. That would mean that all of your musings in that regard constitute a personal theory, and such theories are not allowed to be discussed on these forums. To clear that up, please provide the reference I have asked for.

I have done this before to no effect, and I will try one more time ... here are the detailed refutations of your latest arguments.

I) A neutron diffraction experiment gets the same diffraction pattern if it's done with one neutron at a time, or a vast ensemble of neutrons, so long as we stay in the collisionless limit where neutrons are not bouncing off each other.

This is the first time that neutrons have been raised on this thread. Where did you get the idea that we are talking about neutrons? The hypothetical particles that we agreed to discuss are uncharged particles with the same mass as an electron, and therefore are not neutrons. It is the repeated confusion of significant details like this which suggest that you are not a scientist. Neutrons also diffract, but they do so differently than electrons, due to their larger mass and different interactions with matter.

That's actually all I'm going to need.

Actually, you do have a classical limit here, you do have a correspondence principle here, and this is the entire point I'm making. First you need a classical observable. Energy flux will do nicely. So hold up your classical detector into this vast ensemble of neutrons and measure the energy flux at various places. You get the diffraction pattern we both agree on.

Now pretend you are a student, given that detecting apparatus, but you have no idea what is being sent from the emitter, it could be particles or sound waves or phlogiston, you have no idea. Your job is to be a scientist, and develop a theory that can predict what will happan if you modify the geometry of the slits. I'm serious, this would be a wonderful exercise in how science works. So you notice you have a pattern that looks like interference, so you say "aha, I think a wave theory might work here." I'm serious, this is exactly how it was done in many situations. You play with the equations, and sure enough, you develop a wave theory that beautifully predicts what will happen when you modify the slit geometry. You say, "I understand the physics here, we have a wave coming out of the emitter, I'll call it a nound wave. It has a characteristic wavelength I can set as a free parameter to make the pattern work, and that parameter stays the same when I alter the slits, and my predictions work too. Then I swapped my classical energy detector for a classical momentum detector, and sure enough, I found a fixed ratio between energy and momentum fluxes, which I'm going to call (half) the speed of the wave. This also stays constant when I alter the geometry of the slits. I'm doing great, I have a wave with known speed and wavelength, so also known frequency, and my theory predicts the energy and momentum fluxes for any slit geometry. I have a classical wave theory, please give me my coveted scientific award.

Now please note several things:
1) the student did all this without knowing that there were any particles involved here at all, let alone neutrons, and
2) the classical wave theory the student arrived at is exactly what you get if you take the Schroedinger equation in the limit of large occupation numbers (yes for monoenergetic neutrons, and as I say long ago, that particle energy could also be a controlled variable and the classical wave theory would work just great, would find a different wave speed for each mono-energy, just as I said-- the classical theory generated by the quantum mechanics of a particle with mass has a dispersion relation built into it).
3) Facts 1 and 2 are called "the correspondence principle".
4) Sometimes by accident of history, the quantum theory comes first, sometimes the classical theory comes first, it just depends on the particle. But whichever theory comes first, they are connected by the correspondence principle.
I just told you how it would be completely described as classical. If this still hasn't clicked, ask yourself this: what if my hypothetical student experiment had actually been carried out in the year 1900? Bingo, we would have exactly an interference pattern that would be explained as classical. Whether some predicted experimental outcome can be called classical or not is not an ontological stance, it is purely answered by what type of theory predicted it, and many results, like interference fringes, can be predicted by either classical or quantum theories. As I just showed.

No, you only think you showed it. There are several significant problems with the analysis above, and I deal with several of them in more detail below. First off, the process you describe does not lead to a classical theory at all, it leads to a phenomenological model, which is could be either quantum nor classical. The "quantum" or "classical" nature would depend on the assumptions made during the development of the model. If such a model involved assumptions based on classical mechanics, then it would be later discovered to be "wrong", because it would fail to predict other physical phenomena (most notably the discrete nature of the "mass flux" of the "nound" wave). An analogous example would be the Bohr model of the atom, which was "wrong" because it assumed classical orbits for the electrons. So, the phenomenological theory developed in way you describe would either be discarded as incorrect (or perhaps incomplete), or scientists would continue to investigate until the eventual discovery of de Broglie hypothesis (to explain the wave nature of the "mass flux" .. to use your term), and thus to the development quantum mechanics (assuming it had not yet been discovered). This is because there is no classical basis for massive bodies to have wave-character, after all, that is the seminal difference between quantum and classical theories, and as I have said all along, it is grounded in the HUP.

We do agree on one thing, and that is that any scientist (student or otherwise) conducting such experiments in the early 1900's would be worthy of a Prize!

That sums up what I've been saying. There's really no need to go through every objection you've raised, what I've just shown makes it all crystal clear. Most of the time you were using a different type of correspondence principle anyway, not the classical limit that turns a quantum into a wave, but the classical limit that turns a quantum into a bowling ball. So all that can be ignored as a category error, and it's better to just focus on the above, because the whole nature of the disagreement is spelled out right there.

That's just wrong ... I have been using precisely the same definition of the correspondence principle as you have, the difference is that I have been applying it correctly and drawing physically correct conclusions, while you have not.

(ahem, neutrons are physically real)

Ahem, we weren't talking about neutrons.

Correction, large occupation numbers, as I said. "Large quantum numbers" is a rather ambiguous phrase, you are misinterpreting its meaning here.

No, that is not correct, and this may be the crux of your misunderstanding. The correspondence principle doesn't say anything about "occupation numbers" .. it talks about quantum numbers .. let's not confuse the issue with different terms. The quantum numbers for the states of the quantum photon field are sometimes called occupation numbers. However, there is no analogous quantity for the quantum states of a massive system ... you cannot build up a classical "field" from the quantum descriptions of electrons (or neutrons) in the same way. For one thing, photons are bosons, so there is no limit on the number of photons that can be added to a single quantum state. Electrons (and neutrons) are fermions, and such there can be no more than one particle per quantum state, so the idea of "occupation numbers", as applied to photons, doesn't make any sense. Furthermore, as I pointed out previously, in order for massive particles to diffract, the quantum numbers for their momentum states must not be in the "limit of large numbers". If they were, then the de Broglie wavelength would be small with respect to the size of the slit, and there would be no diffraction. With regard to your model for developing a phenomenological theory of electron diffraction, it is this feature of the experiments, the fact that the diffraction pattern depended on the momentum of the "mass flux", that would lead to the discovery of the de Broglie hypothesis, and therefore to quantum mechanics.

The occupation numbers of the modes. This is exactly why you are not understanding.

That's not an acceptable answer, because it is not at all clear which "modes" are you talking about? Please provide a complete description in terms of quantum mechanics. As I described above, the idea of multiple particles building up in the same "mode", as occurs with photons, is fundamentally impossible due to the Pauli exclusion principle.

I've answered it half a dozen times already, just scan for the phrases "occupation number" and "classical wave."

Yes, and each time you have been wrong. Repeating yourself doesn't make it any less wrong. Furthermore, you have never provided the requested quantum mechanical explanation for your answer, for the case of massive particles that we have been discussing.

With all due respect, that's complete nonsense, and let's hope our common ground point (I), and the experiment I just described in great detail, makes that crystal clear.

Well, calling it nonsense doesn't make it nonsense, and my statement is completely within the mainstream of physics. So, what it made crystal clear is that you have, as I said, a deep-seated misunderstanding of quantum mechanics.

Now we have exposed just how ridiculous that claim is!

No, quite the contrary .. your post showed how well-justified that claim is. What is ridiculous is that you would claim that classical theories could explain the very features of the physical world that led to the discovery of quantum mechanics! I really have to insist that you provide some sort of literature reference to back up your preposterous claim.

 

[Ken G]

The problem with this line of reasoning is that for any real system the probability distributions as predicted by quantum mechanics and the distributions expected from classical arguments differ. There is no real system where these two can be STRICTLY identical up to all orders, not even for a laser beam.

That is indeed a problem-- if the probability distributions are different. I wonder why chaos does that? What breaks the connection between the commutators and the Poisson bracket?

 

[Ken G]

I
Therefore: Yes or no please?

You want my opinion on local realism? I'm mor of an expert than Bell you think? I have no opinion different from the standard expectation that entanglement cannot be described by local realism.

My turn. Do you understand the difference between a classical limit that turns a particle into a bowling ball (say an ultra-high energy cosmic ray), and the one that turns a photon into a laser beam? I claim this is still your fundamental mistake in interpreting everything I've said.

 

[Ken G]

The problem is that the points you ignore are the ones that show why you are wrong. For example, you have yet to provide an equation for your supposed classical theory of electron diffraction.

Take the Schroedinger equation, and take h->0 while interpreting every h/m as a constant equal to 2*v*lambda, where I explained how to get v and lambda in the experiment I described (that you still have not commented on, oddly).

You also have not explained how you can obtain a classical wave equation by taking the classical limit of the Schrodinger equation.

I thought it was clear from the description I gave, but now it should be clearer still. The only wrinkle is having d/dt instead of d^2/dt^2, an interesting issue that might be worth discussion when you finally understand what I'm saying.

Finally, you have not explained how a classical theory can preserve or predict the spatial delocalization that gives rise to the experimentally observed diffraction of massive bodies .. of course that is because it cannot, since spatial delocalization of massive bodies is a feature that is exclusive to (if not definitive of) quantum theories.

I never made the slightest claim that this was possible. Are you another one of these people who can't tell the difference between the logic of "classical analogs are often easy to find and useful when you can" and "there always has to be a classical analog of everything or what I'm saying is wrong." Read those two phrases as many times as it takes.

The fact that you would continually confuse photons, and electrons is evidence of that, as is the fact that you are apparently incapable of writing down an equation or providing a mathematical derivation to back up your reasoning.

Incorrect, I simply don't see the fundamental difference there that you do. They both diffract, after all, and diffraction is what we are talking about.

Finally, a scientist would realize that the fastest way to end an argument like this is to provide a literature reference for their claims.

I'm still waiting to find out if you have the slightest idea what I'm saying about occupation numbers rather than energy per particle. You have not made one single remark that indicates you appreciate that difference.

I can do that, because every single text on quantum mechanics will back up what I am saying.

You still haven't even understood what I'm saying, as I keep pointing out. Why have you not commented on the student experiment I described? Do you think a reference you can find will contradict what I said there?

I have asked you to do the same for your claim that one can formulate a classical theory of electron diffraction, and it seems you cannot.

Wrong again.

This is the first time that neutrons have been raised on this thread. Where did you get the idea that we are talking about neutrons?

Are you serious? We were talking about chargeless electrons. You need a road map?

The hypothetical particles that we agreed to discuss are uncharged particles with the same mass as an electron, and therefore are not neutrons.

So now you think the mass of electron being what it is is decisive to your argument? I'm afraid that's ridiculous.

It is the repeated confusion of significant details like this which suggest that you are not a scientist.

No, it shows I know the difference from when the numerical value of the mass matters, and when it cannot. This is your "refutation" of my argument?

Neutrons also diffract, but they do so differently than electrons, due to their larger mass and different interactions with matter.

You think they diffract differently in a way that is not contained in the v and lambda parameters that I carefully described? Please elaborate.

If such a model involved assumptions based on classical mechanics, then it would be later discovered to be "wrong", because it would fail to predict other physical phenomena (most notably the discrete nature of the "mass flux" of the "nound" wave).

That's just silly. I explained a classical approach to getting a wave theory, it makes no difference if classical mechanics is in the background somewhere (as for sound waves) or if it isn't (as for neutron diffraction).

That's just wrong ... I have been using precisely the same definition of the correspondence principle as you have, the difference is that I have been applying it correctly and drawing physically correct conclusions, while you have not.

You still see no significance in the difference between one particle with lots of energy, and a huge ensemble of particles with low energy? Not one of your remarks is germane to that distinction,

No, that is not correct, and this may be the crux of your misunderstanding. The correspondence principle doesn't say anything about "occupation numbers" .. it talks about quantum numbers .. let's not confuse the issue with different terms. The quantum numbers for the states of the quantum photon field are sometimes called occupation numbers. However, there is no analogous quantity for the quantum states of a massive system ... you cannot build up a classical "field" from the quantum descriptions of electrons (or neutrons) in the same way. For one thing, photons are bosons, so there is no limit on the number of photons that can be added to a single quantum state. Electrons (and neutrons) are fermions, and such there can be no more than one particle per quantum state, so the idea of "occupation numbers", as applied to photons, doesn't make any sense.

I gave a prescription for finding the classical theory, both experimentally and theoretically. And by Bohr's logic, it must agree with the quantum theory. I'd call that a pretty obvious example of the correspondence principle, and I've been quite clear that is what I have been talking about all along.

Furthermore, as I pointed out previously, in order for massive particles to diffract, the quantum numbers for their momentum states must not be in the "limit of large numbers".

And I pointed out I'm well aware of that. That was the whole "particle turning into a bowling ball" business. You just read past that?

That's not an acceptable answer, because it is not at all clear which "modes" are you talking about?

Modes are sectors in phase space. All we need is enough occupation in each to generate a classical theory, via coarse-graining. Like all classical wave theories.

Let me conclude. You still think Bohr would change the correspondence principle if he knew about neutron diffraction? What aspect of it do you think he didn't know about?

 

[Cthugha]

That is indeed a problem-- if the probability distributions are different. I wonder why chaos does that? What breaks the connection between the commutators and the Poisson bracket?

Oh, sorry for the misunderstanding. I was not referring zo chaos. In fact I do not know enough about chaos to make claims about it. The probability distributions already differ for simple systems like a common laser beam. Maybe this is easier to visualize in an extended explanation. In laser beams the fact that the measurement of a photon destroys it, is countered by the intrinsic noise properties of the laser beam such that the detection of a photon does not alter the statistical tendency to detect another one which is the classical limit that a measurement does not change the measured state. Mathematically speaking this means that for a light field of mean photon number $$\langle n \rangle$$ and momentary fluctuations $$\Delta n$$ you want the expectation value
$$\frac{\langle n (n-1) \rangle}{\langle n \rangle^2}=\frac{\langle (\langle n \rangle +\Delta n) (\langle n \rangle + \Delta n -1) \rangle}{\langle n \rangle^2}$$ to be equal to one.

It turns out that the above reduces to
$$1-\frac{1}{\langle n \rangle} +\frac{\langle \Delta n\rangle^2}{\langle n \rangle^2}$$
which is one if $$\langle \Delta n\rangle^2 =\langle n\rangle$$
or in other words it is true if the probability distribution shows the same variance as a Poissonian distribution.

Now you can repeat that game and check what is the requirement for the quantum and classical distributions to coincide if you detect three instead of two photons. You will now find that it is necessary that the skewness of the quantum distribution is the same as that of a Poissonian distribution. For four photons the kurtosis must match and so on and so on. If you want to detect some arbitrary number of photons the distribution must be equal to a Poissonian one up the order that corresponds to the number of photons. To get full correspondence between the distributions this must hold up to arbitrary order. However any real system will have some limited (but probably extremely large) number of emitters and can therefore not fulfill this condition in some order. At this point the quantum and classical distributions and predictions start to differ. Usually this order will be on the same order as the mean photon number in a beam.

Of course one could call that nitpicking, but for example in optics any formulation of the correspondence principle will only hold for large photon numbers and also only for orders of the probability distribution that are small compared to that mean photon number. Of course not many people are interested in the, say 67th order of a distribution, but one should keep in mind that there are differences somewhere.

 

[Ken G]

Mathematically speaking this means that for a light field of mean photon number $$\langle n \rangle$$ and momentary fluctuations $$\Delta n$$ you want the expectation value
$$\frac{\langle n (n-1) \rangle}{\langle n \rangle^2}=\frac{\langle (\langle n \rangle +\Delta n) (\langle n \rangle + \Delta n -1) \rangle}{\langle n \rangle^2}$$ to be equal to one.

First of all, I want to thank you for bringing your expertise to bear on this issue. But I'm not sure we are talking about exactly the same thing here, and I wish to learn more. I would have said that to have a correspondence principle, we do not need that expression to be exactly one, that would imply the two theories are identically the same in regard to expectation values at all orders. We only need the difference between that expression, and 1, to vanish uniformly as n gets large, for some given question we are asking (perhaps a given order of the probability distribution). That's what I would mean by "in the classical limit" for the purposes of that specific question. You are saying that no classical theory can be identical to a quantum theory to all orders, which I would expect to be true but isn't what should be considered a refutation of the correspondence principle. Granted, just exactly how we should frame the correspondence principle is very much at issue, and the discussion will likely lead to expansion of this idea.

Of course one could call that nitpicking, but for example in optics any formulation of the correspondence principle will only hold for large photon numbers and also only for orders of the probability distribution that are small compared to that mean photon number.

Ah, that's the interesting point, you are saying that what is meant by the "classical limit" depends on what aspect of the probability distribution you are interested in. Point taken, but to me, that's just a clarification of the meaning of the classical limit, not a refutation of the correspondence principle. Generally speaking, a classical limit is not interested in arbitrarily high orders of the probability distribution, but you're right that it very much depends on what question we are asking.

Of course not many people are interested in the, say 67th order of a distribution, but one should keep in mind that there are differences somewhere.

Yes, I am perfectly willing to assert that no classical theory can be exactly the same as a quantum theory. Indeed, it is likely that such high orders of the probability distribution are exactly the kinds of considerations you'd need to get "spots" appear on the detector. Above I said that the appearance of spots is a fundamentally quantum phenomenon. This is natural, because that is what motivates the characterization as a "quantum" in the first place. So my prevailing point here is that we should give unto Caeser what is Caeser's (the fundamentally quantum phenomena like spots), but we should not give unto Caeser what is not rightfully his (the diffraction pattern). Certainly we view the quantum theory as the more fundamental, that also does not refute the CP-- the CP only says that a classical theory can answer the classical questions, and I've added to that that this is actually a useful thing to do to help us understand the more fundamental quantum theory. That sums up exactly what I'm saying here.

Let me summarize even more clearly, for it has been a long exchange and much of the disagreements have stemmed from the simple fact that I was not understood, which as we all know can waste a lot of bandwidth! I'm identifying what we might call a "classical theory", which uses classical notions like real-valued functions in space and time and classically aggregated measurements like energy and momentum fluxes, to predict the outcomes of experiments involving large ensembles of occupation numbers, which I stressed includes a concept of large enough phase-space density to be addressed by classical notions (though others on the thread have interpreted stictly as "large quantum numbers", but I'm saying that can also be viewed as a large occupation number of elementary excitations of some kind of internal quantized mode, though that is not the kind of limit I have been describing above). An important point about the classical theory is that is must never invoke a quantum of any kind, because that is the distinguishing element from a quantum theory, and the quantum theory uses different measurements like spots and coincidence counts (and internal degrees of freedom like spin, but we don't need to get into spin here, it's just another example of a realm of quantum topics that sometimes have useful classical analogs and sometimes don't).

OK, given this, what I'm fundamentally saying is that the correspondence principle asserts a logical consistency between quantum and classical theories, such that the projection of the quantum theory onto the classical measurables must generate a classical theory that could have itself described those measurables in the classical limit. Also, if we already have a working classical theory on those measurables, then any more fundamental quantum theory must have a structure that, when taken to the classical limit, is consistent with the classical theory. That is just precisely how I characterized "the correspondence principle" above, and I think pretty well encapsulates the logical content of what Bohr had in mind. So in this light, we see that if the quantum theory ever disagreed with the classical theory in the classical limit, we could not say "that's quantum for you", we'd be forced to say "one or the other of these theories must be replaced."

Then I made a few claims about this logical connection. I said that it is just an accident of history in each particular context whether the quantum theory or the classical theory was discovered first. We all know that classical theories are not thrown out, because they still work fine in the classical domain. In particular, photon diffraction was first studied as a classical phenomenon, and electron and neutron diffraction were first studied as a quantum phenomenon. Others on this thread seemed to think this has fundamentally something to do with their masses, but my point is that there is no reason we can't imagine the classical work first being done on electron and neutron diffraction, and the quantum work first being done on photons-- it actually has nothing at all to do with their masses, it's just how history went. Given all this, the real over-arching point is, classical analogs are very useful to keep track of, even in quantum theories, and many people seem to over-stress the "weirdness" of topics that are actually not considered weird in the classical theory-- so the true "quantum weirdness" is not that the phenomena show up in a theory, it's simply that we did not expect them to show up in a quantum theory, owing to certain prejudices we have about how quanta "should" behave based on our experiences with bowling balls.

Now that I've summarized what I have been saying above, I'm quite interested in your take. I think it is fair to say that none of the above detractors of this idea ever understood that this is what I was saying, so essentially none of their objections were relevant, though some interesting points did come up and I expect some more will too.

 

[SpectraCat]

Take the Schroedinger equation, and take h->0 while interpreting every h/m as a constant equal to 2*v*lambda, where I explained how to get v and lambda in the experiment I described (that you still have not commented on, oddly).

Again, that's not a proof, a demonstration, or an equation .. it's just a mathematically vague recipe. Furthermore, to me it sure looks like if I follow your recipe, I will end up in the limit of lambda=0, which I agree is the correct classical limit, but of course there would be no diffraction in that limit. If you mean something else, then please write down the mathematical derivation you describe, along with the result that you claim can describe electron (or neutron) diffraction in the classical limit. Or provide a reference that supports your claims.

I haven't commented much on the experiment you describe, because it isn't very helpful to the discussion as you have described it. You have given vague ideas which assume the existence of measurement techniques where it is not at all clear that such techniques exist. For example, you just assume that the speed of the "waves" will be clear to the experimenter ... really? How will they get that information? In order to measure the speed of the waves, you need to be able to resolve the peaks and valleys of the waveform. How is that done in your experiment? How do you propose to measure the momentum of the "classical waves"? You also talk about measuring the energy flux .. how will that be done? The lack of those details makes the description you have provided basically useless .. you just assume that all of the quantities you need can be clearly defined and measured "in the classical limit", when it is not at all clear how that can be done without using devices that are based on understanding the underlying quantum mechanical principles in play. The only facet of this experiment that is at all clear is that an interference pattern *could* be observed under the right source conditions (i.e. monoenergetic beam, with the energy selected such that the wavelength of the particles is of the same order as the slit width), but that relies on a quantum mechanical description of the diffraction phenomena (i.e. that the massive particles have a wavelength).

I thought it was clear from the description I gave, but now it should be clearer still. The only wrinkle is having d/dt instead of d^2/dt^2, an interesting issue that might be worth discussion when you finally understand what I'm saying.

Good lord .. you think that's a *wrinkle*? That's like saying that the distinction between velocity and acceleration is a *wrinkle*. The significance of the different orders of the time derivative is fundamental .. it means that quantum probability distributions have time-evolutions that are analogous to diffusion, rather than wave-propagation. This is not a *wrinkle* that can somehow be finessed away.

I never made the slightest claim that this was possible. Are you another one of these people who can't tell the difference between the logic of "classical analogs are often easy to find and useful when you can" and "there always has to be a classical analog of everything or what I'm saying is wrong." Read those two phrases as many times as it takes.

You certainly did claim that it was possible ... your claim that you can explain electron diffraction "in the classical limit" is identical to my statement. That is the fundamental misunderstanding that persist in proffering on this thread, and it is getting very tiresome. You are not making claims that are supported by mainstream physics .. I doubt anyone is following this right now, but this thread will be maintained as a permanent record for as long as PF exists, and it is important that your incorrect statements about the correspondence principle and quantum mechanics are not allowed to stand.

Incorrect, I simply don't see the fundamental difference there that you do. They both diffract, after all, and diffraction is what we are talking about.

Right .. *you don't see the difference*, even though it does exist, and it is important. That is the source of your misunderstanding, as I identified umpteen posts ago.

I'm still waiting to find out if you have the slightest idea what I'm saying about occupation numbers rather than energy per particle. You have not made one single remark that indicates you appreciate that difference.

[I put the section below in bold, because you appear to have missed it in my previous comments]

I already explained why "occupation numbers" don't make any sense for massive particles in the sense you are using them. There are no "occupation numbers" that pertain to particle number for massive particles, except in the case of exotic matter like BEC's which are not under discussion here. The only "occupation numbers" for massive particles are quantum numbers, which index the amount of energy (or momentum [EDIT] or other properties like angular momentum that are not directly relevant to this dicussion) carried by the particles, in the sense that they tell you [EDIT][STRIKE]how many[/STRIKE] which (and how many) quantum states are populated. That is why there is no other "version" of the correspondence principle that works in the manner you have described for massive particles.

In addition, I also gave another fundamental reason why occupation numbers are nonsensical for the particles we have been talking about (electrons and neutrons), since those particles are fermions, and thus are prohibited from occupying the same quantum states. Are you unfamiliar with the Pauli exclusion principle? Assuming you are not, please define "occupation numbers" for electrons (or neutrons) in a manner that is consistent with the PEP.

You still haven't even understood what I'm saying, as I keep pointing out. Why have you not commented on the student experiment I described? Do you think a reference you can find will contradict what I said there?

Well, you haven't said anything well-defined yet about that experiment, so it's hard to refute or support your claims.

Are you serious? We were talking about chargeless electrons. You need a road map?
So now you think the mass of electron being what it is is decisive to your argument? I'm afraid that's ridiculous.
No, it shows I know the difference from when the numerical value of the mass matters, and when it cannot. This is your "refutation" of my argument?

You think they diffract differently in a way that is not contained in the v and lambda parameters that I carefully described? Please elaborate.

Yes, they certainly do .. neutrons do not interact with matter in the same way as electrons do, and this has nothing to do with their wavelength of speed. Neutrons pass through matter much more readily than electrons do, thus you could not design a double slit for neutrons in the same way as for electrons. But that was not my main point, my main point is that you are injecting unnecessary confusion into the discussion by continually switching around the definitions of that particles we have been discussing. I can keep up with it (although it is irritating to have to do so), but a less experienced reader might get lost. That is why I have had to take the time to point out and correct every time you change the definitions of particles in your descriptions. The distinctions *are* important, even though you have not realized that yet.

That's just silly. I explained a classical approach to getting a wave theory, it makes no difference if classical mechanics is in the background somewhere (as for sound waves) or if it isn't (as for neutron diffraction).

Yes, it does ... the theory is only classical if obeys the assumptions of classical physics. As I pointed out before, the process you describe does NOT result in a classical theory .. it only results in a phenomenological model. For it to evolve into a classical theory, it would need to be consistent with the rest of classical physics, and also have predictive power about experiments carried out with "neutron fluxes" (or whatever you want to call them) under different experimental conditions. As I have also pointed out, investigation of the diffraction phenomenon we have been discussing would necessarily lead to the discovery of quantum mechanics, thus the phenomenological model you have proposed (assuming it would even be possible in the manner you describe), would ultimately result in a quantum theory. In fact, this is not so different from how quantum mechanics was developed in the first place, except for the (not insignificant) fact that the theory preceded the experiments in several important cases.

You still see no significance in the difference between one particle with lots of energy, and a huge ensemble of particles with low energy? Not one of your remarks is germane to that distinction,

I see EVERY significance in that distinction .. it is YOU who appear to be saying that an equivalence can be drawn between the two cases via your *misapplication* of the correspondence principle. Think about what you just wrote ... then think about the photoelectric effect ... do you see why I am bringing this up?

I gave a prescription for finding the classical theory, both experimentally and theoretically. And by Bohr's logic, it must agree with the quantum theory. I'd call that a pretty obvious example of the correspondence principle, and I've been quite clear that is what I have been talking about all along.

That's nonsensical post-rationalization. You yourself have said that there are quantum phenomena and theories that have no classical analogs. What you have yet to realize is that diffraction phenomena for massive particles is an important example of that case.

And I pointed out I'm well aware of that. That was the whole "particle turning into a bowling ball" business. You just read past that?

I don't know what to say .. you say you are aware of it, but then you demonstrate that you don't understand it's significance. That's why I keep bringing it up .. to try to get you to realize that it is the fundamental distinction you have been missing, and the reason why you cannot draw parallels between photon diffraction and electron diffraction in the manner you have been attempting to do.

Modes are sectors in phase space. All we need is enough occupation in each to generate a classical theory, via coarse-graining. Like all classical wave theories.

Ok, I'll try this in your jargon ... what does it mean to increase the "occupation" for "sectors in phase space" for massive bodies? It does NOT have the same physical significance as increasing occupation for quantum field modes in the case of photons. There is no quantum number for massive particles corresponding to "occupation of sectors in phase space", so increasing the "occupation numbers" of such "modes" does not bring you into the limit where the correspondence principle applies.

Let me conclude. You still think Bohr would change the correspondence principle if he knew about neutron diffraction? What aspect of it do you think he didn't know about?

Where did that question come from? Of course he wouldn't .. as I have said, there is no issue with the correspondence principle .. it just can't be applied to get a classical theory of neutron diffraction. Bohr would never have claimed that it could. Actually, perhaps I now see where another facet of your misunderstanding stems from. What the correspondence principle actually says, is that classical physical theories emerge naturally from quantum theories in the limit of large quantum numbers. It does not say the reverse, which is the way you have been phrasing it. You have repeatedly said that the correspondence principle maintains that "every quantum theory spawns a classical theory that has to work in the classical limit", which is simply incorrect. There is a quantum theory of electron spin, what is the equivalent classical theory? There is a quantum theory for the photoelectric effect, what is the equivalent classical theory? There is a quantum theory for electron tunneling, what is the equivalent classical theory? There are no equivalent classical theories for those phenomena, because they are purely quantum phenomena. The same is true for electron diffraction, or diffraction of any other massive particles.

Anyway, I have wasted far too much time on this discussion, and I have allowed you to distract me from my far more interesting discussion with other PF members about the title issue of this thread. This will be my last post on the matter until you start providing better justifications for your claims, either in the form of detailed mathematical derivations, or literature references to support your statements. I would also again caution you about the PF rules against using these forums to put forth your personal theories about physics.

 

[Ken G]

You certainly did claim that it was possible ... your claim that you can explain electron diffraction "in the classical limit" is identical to my statement.

This seems to be the crux of the issue-- whether or not someone with no knowledge of quantum mechanics and no invoking of any quantum particle could have explained electron (or neutron to avoid the charge issue) diffraction with a purely classical wave theory. You claim that would not have been possible, I claim that it would have been possible. Your argument requires that the mass of the particle be the thing that would make it impossible, because we certainly know it was possible with photons. Can we agree this is the crux of the disagreement? The rest is getting too long to wade through (I should comment, it was DevilsAvocado who made the claim about Bohr, not you, I mistakenly crossed those arguments but apparently I am not facing such a "unified front" of counterargument since you three don't always agree with each other about the correspondence principle).

I doubt anyone is following this right now, but this thread will be maintained as a permanent record for as long as PF exists, and it is important that your incorrect statements about the correspondence principle and quantum mechanics are not allowed to stand.

I'm awaiting Cthugha's take on whether or not the mass of a particle makes it impossible to create a working classical theory of its diffraction, which is the crux of our disagrement. I find your argument there totally unconvincing.

[I put the section below in bold, because you appear to have missed it in my previous comments]

I already explained why "occupation numbers" don't make any sense for massive particles in the sense you are using them. There are no "occupation numbers" that pertain to particle number for massive particles, except in the case of exotic matter like BEC's which are not under discussion here. The only "occupation numbers" for massive particles are quantum numbers, which index the amount of energy (or momentum [EDIT] or other properties like angular momentum that are not directly relevant to this dicussion) carried by the particles, in the sense that they tell you [EDIT][STRIKE]how many[/STRIKE] which (and how many) quantum states are populated. That is why there is no other "version" of the correspondence principle that works in the manner you have described for massive particles.

I did miss this statement in your earlier remarks, and yes, this is the crux of the issue-- is there a "classical limit" that refers to occupation number, which in the classical limit is a concept of "phase space density." So we must ask ourselves, does the correspondence principle apply to a concept of a classical limit in phase-space density? You say emphatically no, I say yes, this is one of the most important places we find the correspondence principle. As I am well aware of the Pauli exclusion principle, the occupation number I refer to (as I mentioned) is a classical limit in the occupation in physically resolvable (coarse-grained) cells in phase space. So is there, or is there not, a "classical limit" in phase-space density, and is this relevant to the correspondence principle?

I point out that if the answer to that is "yes there is such a classical limit", then essentially every single thing you have said in this entire thread is irrelevant to anything I am talking about, which is just exactly my contention here.

 

[SpectraCat]

This seems to be the crux of the issue-- whether or not someone with no knowledge of quantum mechanics and no invoking of any quantum particle could have explained electron (or neutron to avoid the charge issue) diffraction with a purely classical wave theory. You claim that would not have been possible, I claim that it would have been possible. Your argument requires that the mass of the particle be the thing that would make it impossible, because we certainly know it was possible with photons. Can we agree this is the crux of the disagreement? The rest is getting too long to wade through (I should comment, it was DevilsAvocado who made the claim about Bohr, not you, I mistakenly crossed those arguments but apparently I am not facing such a "unified front" of counterargument since you three don't always agree with each other about the correspondence principle).

I'm awaiting Cthugha's take on whether or not the mass of a particle makes it impossible to create a working classical theory of its diffraction, which is the crux of our disagrement. I find your argument there totally unconvincing.
I did miss this statement in your earlier remarks, and yes, this is the crux of the issue-- is there a "classical limit" that refers to occupation number, which in the classical limit is a concept of "phase space density." So we must ask ourselves, does the correspondence principle apply to a concept of a classical limit in phase-space density? You say emphatically no, I say yes, this is one of the most important places we find the correspondence principle. As I am well aware of the Pauli exclusion principle, the occupation number I refer to (as I mentioned) is a classical limit in the occupation in physically resolvable (coarse-grained) cells in phase space. So is there, or is there not, a "classical limit" in phase-space density, and is this relevant to the correspondence principle?

I point out that if the answer to that is "yes there is such a classical limit", then essentially every single thing you have said in this entire thread is irrelevant to anything I am talking about, which is just exactly my contention here.

Ok .. that was actually very useful for narrowing down the source of our disagreement, so I will make one more post in response to this point. With regard to your latest question, of course there is no classical limit on the phase space density. Think about what you are asking for ... you are asking for phase space to be *quantized*? How can that arise in a classical context? In phase space, each configuration of the system corresponds to a point in phase space, which is continuous in every dimension, hence since there are an infinite number of points in any finite region of phase space, the classical phase space density can increase to infinity.

To come at it from another angle ... what do you think the HUP *is*? It is the *quantum* limit on the phase space density, which classical theories tell us is infinitely divisible. That is why Planck's constant is sometimes said (generally in pop physics books) to specify "the fundamental graininess of space-time". This is what I have been saying all along. If you try to develop a theory along classical lines that involves phenomena occurring where this limit on the phase space density matters, then you will UNAVOIDABLY end up developing a quantum mechanical theory ... or else an incorrect theory, I suppose.

If you won't believe me, perhaps you will believe another PF Science Advisor, Bill_K, who says precisely the same thing on https://www.physicsforums.com/showthread.php?t=489484" (it is the 3rd link that comes up if you google "phase space density quantum mechanics").

Here is another result from google searching: http://www.ysfine.com/home/book91.html

Finally, here is a wikipedia link that also supports what I am saying: http://en.wikipedia.org/wiki/Wigner_quasi-probability_distribution#Relation_to_classical_mechanics.

 

[Ken G]

Ok .. that was actually very useful for narrowing down the source of our disagreement, so I will make one more post in response to this point. With regard to your latest question, of course there is no classical limit on the phase space density. Think about what you are asking for ... you are asking for phase space to be *quantized*?

Not quite, I'm asking it to be coarse-grained. That's a perfectly routine concept in hydrodynamics. Even plasma physics has a concept of "occupation number", in some sense-- the number of particles in the DeBye sphere. It is natural for a distribution of particles to have some natural scale, such that when you get many particles in that scale, you have a kind of thermodynamic limit. Part of the problem is terms like "classical"-- what does that really mean, that the Greeks did it, that Newton did it, that it isn't quantum mechanics? All I mean by the term is that you start to see physics where you do not need to know there are any particles there. Much like the equations of MHD plasma physics or thermodynamics or hydrodynamics, all things I would call "classical theories" simply because none of the equations of the theory invoke particles. Deriving certain terms in the equations can invoke microphysics, but these can also be set experimentally, as I described in the "student experiment" I was talking about.

How can that arise in a classical context? In phase space, each configuration of the system corresponds to a point in phase space, which is continuous in every dimension, hence since there are an infinite number of points in any finite region of phase space, the classical phase space density can increase to infinity.

I hope I've made it clear that a "fluid average" in the reduced phase space used in both fluid and wave mechanics (where you are essentially manipulating moments rather than particles) is actually quite routine, not a problem.

To come at it from another angle ... what do you think the HUP *is*?

It is the quantum origin of the reason that classical wave mechanics works. That's your answer in "correspondence principle language."

If you try to develop a theory along classical lines that involves phenomena occurring where this limit on the phase space density matters, then you will UNAVOIDABLY end up developing a quantum mechanical theory ... or else an incorrect theory, I suppose.

And that has nothing to do with what I'm talking about, as I've said, because I am talking about the classical limit of that same quantum mechanical theory.

If you won't believe me, perhaps you will believe another PF Science Advisor, Bill_K, who says precisely the same thing on https://www.physicsforums.com/showthread.php?t=489484" (it is the 3rd link that comes up if you google "phase space density quantum mechanics").

What you are not getting is that the issue here is not that I don't believe you, indeed I already know almost everything you say. It is that it is not relevant to what I'm saying. How do turn "what you're saying is not understanding what I'm saying" into "I don't believe you"?

Finally, here is a wikipedia link that also supports what I am saying: http://en.wikipedia.org/wiki/Wigner_quasi-probability_distribution#Relation_to_classical_mechanics.

None of the links you gave adjudicate our discussion in any way, they only adjudicate wrong things that you think I am saying, that I have repeated over and over I am not saying. For one thing, I understand the HUP just fine. Wigner distributions I don't know much about, but from what I can see, they completely support what I am saying-- that there is value in considering classical analogs to quantum mechanics, not because it's the same thing, but because it can be instructive to do so, and can help dissipate some of the "quantum weirdness" by understanding things in a more classical way.

 

[Ken G]

Here are some more papers about applying the correspondence principle in phase space:

http://iopscience.iop.org/1367-2630/11/1/013014/fulltext#nj293180s2
On the correspondence principle: implications from a study of the nonlinear dynamics of a macroscopic quantum device

abstract:
The recovery of classical nonlinear and chaotic dynamics from quantum systems has long been a subject of interest. Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing. In this paper, we discuss the quantum to classical crossover of a superconducting quantum interference device (SQUID) ring. Such devices comprise a thick superconducting loop enclosing a Josephson weak link and are currently strong candidates for many applications in quantum technologies. The weak link brings with it a nonlinearity such that semiclassical models of this system can exhibit nonlinear and chaotic dynamics. For many similar systems an application of the correspondence principle together with the inclusion of environmental degrees of freedom through a quantum trajectories approach can be used to effectively recover classical dynamics. Here we show (i) that the standard expression of the correspondence principle is incompatible with the ring Hamiltonian and we present a more pragmatic and general expression which finds application here and (ii) that practical limitations to circuit parameters of the SQUID ring prevent arbitrarily accurate recovery of classical nonlinear dynamics.

and

http://onlinelibrary.wiley.com/doi/10.1002/9783527610853.ch27/summary
The Bohr-Heisenberg Correspondence Principle Viewed from Phase Space

abstract:
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can be successfully used far away from the classical limit considered by Bohr and Heisenberg.

These underscore the value of classical analogs, though again we find that there are some problems in getting quantum chaos to agree with classical chaos. I interpret that as being because generally the classical limit is successful at recovering lower-order structures (like diffraction patterns) rather than high-order structures (like spots), and this fact is confounded by the sensitivity to initial conditions found in chaotic systems. The main objection we saw above seemed to center on the idea that diffraction patterns had to be inherently quantum effects when seen in particles with mass, but not in particles with no mass, and to be quite honest, I still haven't the slightest idea why those detractors believed that, so I can't really comment on it further.

 

[DevilsAvocado]

You want my opinion on local realism? I'm mor of an expert than Bell you think? I have no opinion different from the standard expectation that entanglement cannot be described by local realism.

GREAT – an expert – wow!

I was real worried there for awhile... on the other hand, the rest of your posts doesn’t directly save your a*s when it comes to crackpotery.

One of your major preposterous claims: "Every quantum theory spawns a classical theory that has to work in the classical limit"

Now, I do hope you realize that Local Realism is a significant feature of classical mechanics? And that you’ve just admitted that quantum mechanics rejects this principle due to the theory of distant quantum entanglements...

Get the picture?

I guess you know who Erwin Schrödinger is, and what the Schrödinger equation mean to QM??

Erwin Schrödinger coin the word Verschränkung (translated by himself as Entanglement): "to describe the correlations between two particles that interact and then separate, as in the EPR experiment", and in the paper defining and discussing the notion of "entanglement" he recognized the importance of the concept, and stated:

"I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."​

There’s not much to add after this, is it...?

*The* characteristic trait of quantum mechanics, the one that enforces its *entire departure* from classical lines of thought.

I hope you realize that you have to run over both Erwin Schrödinger, and the most fundamental concept in the theory of QM, to still make any claim of this cranky delusion of yours: "Every quantum theory spawns a classical theory that has to work in the classical limit"

The theory of quantum entanglement does not work at all in any "classical limit", and it proves that Local Realism, a significant feature of classical mechanics, does not work in QM theory, interpretations or any performed experiment this far. The theory of QM + Bell's inequality + thousands of Bell test experiments has once and for all proven that the concept of Local Realism cannot be applied to QM, period.

Unless you widely expand your cranky thoughts and make "enough-to-get-permanently-banned" statements that – YOU are right and QM is wrong – you lose buddy!

Welll I'm not sure what your personal definition of what a law of nature is, but it is perfectly irrelevant. I explained at great detail what the correspondence principle is, it is the statement that all quantum theories must be consistent with a classical theory in the classical limit, and the classical theory can be derived from the quantum theory if you don't already have the classical theory, and if you do already have the classical theory but not the quantum theory, it imposes constraints on what the quantum theory can do. Whether or not you personally call that a law of nature is of no concern to me, it is what it is. Are you offering a counterexample to it, or do you just think the "layman" at home should be kept ignorant of this principle?

I would absolutely recommend any layman to generally completely ignore all of your homemade nonsense regarding the "law of nature", and particularly your distorted an twisted lies about Niels Bohr and the Correspondence principle, because your 'homemade version' is all false from the beginning, period.

You are the worst kind when it comes to crackpotery. Clever enough to fool any layman, and even some professionals (to begin with), and dishonest enough to not clearly spell it out what you’re really aiming for, and then accusing people who "don’t understand" for being dumb and not clever enough to see this "beautiful theory of yours" – when the whole point is to type as much nonsense as possible to create complete confusion – of course delicately mixed with your personal crackpot "theory". As long as you’re able to dump these cranky ideas of yours – is everything is fine.

You start with this very 'friendly attitude' of being on a 'voluntary quest' of 'helping' poor laymen to more easily understand the "wonders of QM" by making classical analogies. And in the spirit of this wonderful quest you state – "many quantum effects do have classical analogs" – which sounds pretty harmless. And of course, you do not explain for the poor and dumb layman that "analogies" and scientific proofs are two completely different things.

Then you move one step further and state – "every quantum theory spawns a classical theory" – which start to sound like a proof of something, but you (deliberately) 'fail' to explain exactly what this mean, and how it works, and last but not least – you are just mumbling a lot of words without any references and equations to backup this 'revolutionary' thesis of yours.

The next step is to conclude the "obvious" – (your version of) the correspondence principle is a law of nature!

Wow! This is crackpotery in the higher dimension! Watch and learn folks, Ken G might soon be permanently banned...

Now, when users like SpectraCat tries to debate these claims of yours, you jump swift and easy between these different "levels of complete nonsense" to create even more confusion. Sometime you’re just trying "to help laymen understand", next you have something fundamental to say about quantum theory, and shortly after that you have a philosophical "law of nature", without any math whatsoever. The nearest any of kind of "proof" we ever get, is your brilliant circus trick to pretend and then – "poof" – everything works!

This is 'hilarious'.

No wonder SpectraCat gives up. This can’t be discussed in ordinary terms – because there is nothing to discuss, and you utilize every smokescreens available to hide this fact.

You’re crackpot, educated, but still a crackpot.

Things get real nasty when you, without hesitating, enter the next level in "crackpot heaven", and provide clear signs of developing a 'theory' of your own??

Granted, just exactly how we should frame the correspondence principle is very much at issue, and the discussion will likely lead to expansion of this idea.

"How we should frame the correspondence principle"? "lead to expansion of this idea"?

And after this PF Guidelines violation, comes GRAND FINALE:

So in this light, we see that if the quantum theory ever disagreed with the classical theory in the classical limit, we could not say "that's quantum for you", we'd be forced to say "one or the other of these theories must be replaced."

WTF is this?

You must seriously overestimate your 'fiddling artistry'... We all know that you have been deep fishing for some totally crazy version of "Classical QM", and now you spell it right out in the open??!?

READ https://www.physicsforums.com/showthread.php?t=414380" FOR GOD’S SAKE!

Now that is just patently absurd! You don't think Nils Bohr knew everything in that video? Did he ever recant the correspondence principle? Let's look at a simple syllogism here:
1) Niels Bohr was not an idiot.
2) Niels Bohr died in 1962.
3) Niels Bohr formulated the correspondence princple, and adhered strictly to some version of it his whole life
4) Electron diffraction earned Thomson and Davisson the Nobel Prize for Physics in 1937
5) Niels Bohr knew that one electron at a time would make individual spots
6) Niels Bohr knew that the correspondence principle predicted repetition of the spots would reveal the pattern that Thomson and Davisson got the Nobel Prize for, indeed that is exactly the purpose of the correspondence principle to be able to predict that (do you understand that yet?)
6) Your claim just made Niels Bohr roll over in his grave. Fortunately, I'm here to point that out, with this little syllogism, so maybe he can get some rest.

Well, patently absurd is not a bad summarization of the BS you produced in this thread lately, no bad at all. We all know very well that Niels Bohr wasn’t an idiot, he was a genius. Sadly, this characterization is more uncertain when it comes to others in this discussion.

Niels Bohr and Albert Einstein were the two monumental giants of their time, both very bright and genius. But they were not "Gods" – they were humans and both made mistakes (as all humans do). They will always be remembered in the history of science.

I have given you pretty harsh critics in this post, and that partly because I now know that you are deliberately exploiting and twisting the great work of Niels Bohr – for your own purpose.

Shame on you

There’s no secret that the 'experimental environment' was limited at the time; mainly scattering experiments like the Compton-Simon and Stern-Gerlach experiments in which the measurement result was established by ascertaining the direction in which a particle or a photon had been scattered. Furthermore, there where important transitions from the Old quantum theory to Quantum mechanics, and last but not least; Einstein challenged Bohr constantly since he was 'unsatisfied' with the path on which QM had taken after 1925. The famous Bohr–Einstein debates lasted for several decades and culminated in 1935 with the EPR paradox, which forced Bohr to reformulate his Correspondence principle. The philosophical (or epistemological) debate between Bohr & Einstein was never settled. In 1955 the world lost one of the greatest geniuses of all time, Albert Einstein, and in 1962 the other scientific giant Niels Bohr died. None of them ever knew that the EPR paradox could be solved mathematically and proved experimentally, since Bell's inequality was published first in 1964 by John Stewart Bell.

Niels Bohr & Albert Einstein in 1925

In point 3 you show that you know there has been more than one version of the Correspondence principle. The truth is there have been three (3!) versions:

• Correspondence in the Old quantum theory
• Weak form of the correspondence principle
• Strong form of the correspondence principle

Correspondence in the Old quantum theory was applied during the developing stages of quantum physics preceding the conception of quantum mechanics (i.e. before 1925); it implies that in dealing with quantized systems classical relations are preserved as much as possible. Note that the correspondence approach in the Old quantum theory has given rise to the http://en.wikipedia.org/wiki/BKS_theory" which turned out to be in disagreement with experiment, and therefore was a blind alley in the development of quantum physics. Also note that BKS sticks to a classical wave description of the electromagnetic field, which failed.

Weak form of the correspondence principle implies the expectation that if quantum mechanics is applied to larger and larger objects the quantum mechanical description finally will coincide with that of classical mechanics, it coincides with the belief that classical mechanics is the 'classical limit' of quantum mechanics (h → 0). I.e. this is the version that YOU for some nutty reason refer to as the last and valid version...? WHY??

Strong form of the correspondence principle is switching from the 'relation with classical mechanics' to the 'relation with the measurement arrangement'. Compared to earlier versions the notion of 'correspondence' changed in several ways:

1. Does not rely on the 'classical limit of quantum mechanics'.
   
2. Is stressing the 'importance of the experimental arrangement' in establishing the physical meaning of a 'quantum mechanical observable'.
   
3. Is pointing to the difference between quantum mechanics and classical mechanics rather than to their similarity, the difference being established by the notion of 'incompatibility of quantum mechanical observables'.

The final conclusion of all this cranky excess is that the one who will make Niels Bohr, not only roll over in his grave, but also throw up at the same time is YOU, Ken G.

To sum it up for any layman still lurking in this thread:

 

[DevilsAvocado]

We do agree on one thing, and that is that any scientist (student or otherwise) conducting such experiments in the early 1900's would be worthy of a Prize!

(Now I know who will get my vote on next PF Best Humor Award. You are worthy of that Prize!)

I would also again caution you about the PF rules against using these forums to put forth your personal theories about physics.

... if this continue there’s definitely need for action ...

 

[Ken G]

I was real worried there for awhile... on the other hand, the rest of your posts doesn’t directly save your a*s when it comes to crackpotery.

This comment is a waste of bandwidth, as it is pure rhetoric with zero logical content.

Now, I do hope you realize that Local Realism is a significant feature of classical mechanics? And that you’ve just admitted that quantum mechanics rejects this principle due to the theory of distant quantum entanglements...

I'm afraid this is very poor logic on your part, because the correspondence principle certainly allows local realism to appear in the classical limit, and you have not argued that it doesn't, which is an obvious logical requirement of your argument. I trust you can see that, it's quite simple really. Or can you now tell us a quantum theory that does not obey local realism in the classical limit? I think you might get a Nobel prize if you can show that a classical limit of a quantum theory can disobey local realism, because then we can all stop wasting our time with difficult quantum experiments and coincidence counting, because from now on we can get violations of local realism in classical experiments. But I predict you will fail in this most simplest of requirements to support your claim.

Get the picture?

All too well-- which is why I have pointed out the holes in your logic.

Other interesting features in your post is I noticed you did not recant your preposterous claim that Bohr would not have been able to hold his correspondence principle had he known about electron and neutron diffraction, which of course he did know about. The rest of your post, as usual, was a criticism of some make-believe stance that you think I purported, but is just a cartoon caricature of what I actually said, so is pointless to refute. In particular, your "Grand Finale" missed completely the meaning of the very quote you bolded. I'd blame myself if I hadn't taken pains to spell it out so clearly, yet still you manage to see something different than what the words actually say: if a quantum theory and a classical theory made different predictions in the classical limit, one or the other would have to be replaced (for the simple reason that they couldn't both agree with experiment, obviously). Why you don't understand that I really can't guess.

 

[DevilsAvocado]

 

[Ken G]

I'm afraid that's the last refuge of someone who has not been able to present a logically correct argument. Here's the bottom line folks:
It is a fundamentally internally inconsistent argument to claim that diffraction is a strictly quantum phenomenon with no classical analog for several reasons:
1) photon diffraction was initially discovered, and described satisfactorily, purely classically, so to hold the above claim requires that one restrict it to saying that only the diffraction of particles with mass is a strictly quantum phenomenon. No one has presented or even justified that argument on this thread. Logical hole #1 in the claim.
2) the way particle diffraction is normally described as "strictly quantum" is by referencing the de Broglie wavelength, which is a strictly quantum mechanical entity but only if you correctly follow its logic: the deBroglie wavelength is a mapping from the wavelike attributes to the particlelike attributes when one needs to invoke wave/particle duality, but when does not need to invoke that (as for photon diffraction in a classical limit of a large ensemble), then the wavelength is still purely classical, and no quantum elements appear at all. In other words, de Broglie wavelength can be perfectly well viewed as a map from the classical-wave concept of wavelength to the quantum mechanical concept of particle momentum, rather than the other way around. The irony here is that only by referencing a classical stalwart, the concept of wavelength, is the argument even made that diffraction is strictly quantum in nature! Logical hole #2 in the claim.
3) If the claim is made that diffraction (of only the particles with mass, apparently) is a "strictly quantum" phenomenon, it behooves the claimant to suggest what it is about diffraction that jumps up and says "I'm a quantum." Saying "it comes from the Schroedinger equation" just doesn't cut it, because 100 years ago it "came from Maxwell's equations," and 100 years from now, it might "come from string theory" or from the "holographic field", who knows what. Logical hole #3.

In short, the claim that diffraction is a "strictly quantum phenomenon" is the only claim here that is not even wrong. Frankly, it's a failure to even understand what physics is. The actual truth of the situation is nicely described by the general logic of the correspondence principle: every time we come up with a more fundamental theory, it must agree with the previously successful but less fundamental theory in the domain of applicability of that previous theory. This implies two things:
1) the previous theory supplies constraints on the new theory
2) concepts from the previous theory may be already understood, and form a useful basis for understanding the concepts in the new theory that they are the analogs of.
That, my friends, is the point of the correspondence principle, as I have been saying all along. I will blame the faulty logic in the objections presented above on the difficulties of being heard and the ambiguities in the meaning of "the correspondence principle", as there certainly are plenty of ways to hear what I am saying differently than what I actually did say, and I think we saw almost every possible misconstrual that can be imagined in the above. Communication is always the hardest thing, but hopefully this simple summary makes it clear both what I am saying, and the flaws in the objections to what I am saying. Let that set the record straight, as concern was voiced for lurkers who might somehow be led astray by the "crackpottery" of my actually logically bulletproof position. Who knows, maybe even my detractors above will learn something if they can get themselves out of the way and actually listen to what I said.

 

[SpectraCat]

It is a fundamentally internally inconsistent argument to claim that diffraction is a strictly quantum phenomenon with no classical analog ...

Nobody ever claimed that. YOU claimed in post #113 that, "There certainly is a classical explanation for the diffraction of electrons! It is called "wave mechanics", and it applies to a classical ensemble of electrons (and yes, it came as a large surprise that it applied, but it is still a perfectly classical version)." That claim is inconsistent with mainstream physics, and you have proved unable to provide either a mathematical derivation, or a literature reference to support it. Therefore it is a personal theory of yours.

1) ... the diffraction of particles with mass is a strictly quantum phenomenon. No one has presented or even justified that argument on this thread. Logical hole #1 in the claim.

Wrong. The claim that diffraction of massive particles is an exclusively quantum phenomenon has been explained and justified many times .. you either fail or refuse to understand it, and insist on promoting your personal mis-interpretations of both QM and the correspondence principle. This is the last reminder I will give you that PF explicitly forbids such actions.

2) the way particle diffraction is normally described as "strictly quantum" is by referencing the de Broglie wavelength, which is a strictly quantum mechanical entity but only if you correctly follow its logic: the deBroglie wavelength is a mapping from the wavelike attributes to the particlelike attributes when one needs to invoke wave/particle duality, but when does not need to invoke that (as for photon diffraction in a classical limit of a large ensemble), then the wavelength is still purely classical, and no quantum elements appear at all. In other words, de Broglie wavelength can be perfectly well viewed as a map from the classical-wave concept of wavelength to the quantum mechanical concept of particle momentum, rather than the other way around. The irony here is that only by referencing a classical stalwart, the concept of wavelength, is the argument even made that diffraction is strictly quantum in nature! Logical hole #2 in the claim.

That is a complete mis-interpretation of everything I have posted in regard to this question. No one has ever contested that there is an ANALOGY between wave-like behavior at the quantum and classical levels. This discussion is not about philosophical similarities between concepts, it is about physics. The PHYSICAL definition of the correspondence principle is completely irrelevant to the quantum-classical ANALOGY you are drawing. For example, QM tells us that individual water molecules can be made to diffract under the correct circumstances ... your version of the correspondence principle would apparently allow us to then derive classical descriptions of water waves by taking the classical limit of the quantum phenomenon. That is of course, complete nonsense. The point is that your specious arguments about classical descriptions of wave phenomena in plasmas (or whatever classical description of "continuous charge flux" you have been trying to define) being connected to electron diffraction involve the same MIS-application of the correspondence principle as my example above.

3) If the claim is made that diffraction (of only the particles with mass, apparently) is a "strictly quantum" phenomenon, it behooves the claimant to suggest what it is about diffraction that jumps up and says "I'm a quantum." Saying "it comes from the Schroedinger equation" just doesn't cut it, because 100 years ago it "came from Maxwell's equations," and 100 years from now, it might "come from string theory" or from the "holographic field", who knows what. Logical hole #3.

That is another false statement to add to the pile. Schrodinger's equation (and QM in general) was developed explicitly to explain such physical phenomena as diffraction of massive particles, specifically because there was no classical explanation for them. The thing that says "I'm a quantum" is the very fact that classically, there is no way for particles to diffract, because they have no wave character, and classically diffraction is a phenomenon restricted to waves. It is staggering that you refuse to acknowledge that, while still purporting to be expert enough in the area of physics to advise others about "the true meaning and value of the correspondence principle", or whatever it is that you have been going on about.

In short, the claim that diffraction is a "strictly quantum phenomenon" is the only claim here that is not even wrong. Frankly, it's a failure to even understand what physics is. The actual truth of the situation is nicely described by the general logic of the correspondence principle: every time we come up with a more fundamental theory, it must agree with the previously successful but less fundamental theory in the domain of applicability of that previous theory. This implies two things:
1) the previous theory supplies constraints on the new theory
2) concepts from the previous theory may be already understood, and form a useful basis for understanding the concepts in the new theory that they are the analogs of.
That, my friends, is the point of the correspondence principle, as I have been saying all along.

No .. that is a vague philosophical statement .. it is not the point of the PHYSICAL definition of the correspondence principle used in the context of quantum theory. Concepts that are ANALOGOUS between quantum and classical physics may or may not have a direct physical relationship (often they do not). Do the harmonic modes of a vibrating string have any direct relation to the states of a 1-D infinite square well? Of course they don't, and although the ANALOGY is useful pedagogically, it is completely unrelated to the correspondence principle. Bohr's correspondence principle is much more strictly defined. You would benefit from reading what the Stanford Encyclopedia of Philosophy has to say on the subject. In any case, the Bohr correspondence principle most assuredly does NOT say, (as you claimed in post #121) "any quantum theory gives birth to a classical theory in the limit of large occupation numbers". The issues with that statement have been pointed out to you by myself and by DevilsAvocado, but you have dismissed them without apparently understanding them. Also, you have failed to appreciate the distinction between occupation numbers and quantum numbers, although that has been explained to you more than once. It may be possible to draw a meaningful mathematical relationship between the the concepts of quantum numbers and "occupation numbers for sectors of phase space", but I have not seen it done. This is another facet of your personal theory for which you have failed to provide either a mathematical derivation, or a literature reference.

In any case, the bottom line is this: While there is no doubt that ANALOGIES can be drawn between different diffraction phenomena arising from quantum or classical theories, mainstream physics tells us that in the limit of large quantum numbers, the wave-like character of massive particles must disappear. Since diffraction phenomena are uniquely associated with wave-like character, the statement that "electron diffraction cannot be accounted for by a classical theory", is completely consistent with mainstream physics, and in fact is the logical conclusion drawn from the proper application of the Bohr correspondence principle. If you continue to claim otherwise without any literature references to support that claim, then you are just continuing to promote your own personal theory, in clear violation of PF guidelines.

 

[Ken G]

Nobody ever claimed that. YOU claimed in post #113 that, "There certainly is a classical explanation for the diffraction of electrons! It is called "wave mechanics", and it applies to a classical ensemble of electrons (and yes, it came as a large surprise that it applied, but it is still a perfectly classical version)." That claim is inconsistent with mainstream physics, and you have proved unable to provide either a mathematical derivation, or a literature reference to support it. Therefore it is a personal theory of yours.

Then you didn't look at those papers I cited? There's a whole field of study called "scalar diffraction theory", it's all perfectly classical. Oh and yes, it has been applied to neutrons and electron diffraction, it's just that many times the quantum mechanics is all you need, and is more generally applicable. That's what I mean by the "accident of history"-- had neutron and electron diffraction been known about in 1880, instead of the 1930s, it would have been more important.

The claim that diffraction of massive particles is an exclusively quantum phenomenon has been explained and justified many times .. you either fail or refuse to understand it, and insist on promoting your personal mis-interpretations of both QM and the correspondence principle.

Actually, you have never once gave a single reason why you think only the diffraction of massless particles is classically describable, but that the diffraction of neutrons has no classical analog. Would you like to take that opportunity right now? Because I have no idea why you think that.

No one has ever contested that there is an ANALOGY between wave-like behavior at the quantum and classical levels.

Excellent, then you actually agree with my central thesis all along (would you like to count the number of times I used the word "analog" in this thread?). I'm glad to discover this, I can then disregard all your objections to it because you apparently agree with it.

The PHYSICAL definition of the correspondence principle is completely irrelevant to the quantum-classical ANALOGY you are drawing.

Many things get called the correspondence principle. I've been painstakingly clear about the meaning I've taken. I'm glad to find that if you just take my meaning, you agree with me.

In any case, the bottom line is this: While there is no doubt that ANALOGIES can be drawn between different diffraction phenomena arising from quantum or classical theories, mainstream physics tells us that in the limit of large quantum numbers, the wave-like character of massive particles must disappear. Since diffraction phenomena are uniquely associated with wave-like character, the statement that "electron diffraction cannot be accounted for by a classical theory", is completely consistent with mainstream physics, and in fact is the logical conclusion drawn from the proper application of the Bohr correspondence principle. If you continue to claim otherwise without any literature references to support that claim, then you are just continuing to promote your own personal theory, in clear violation of PF guidelines.

Let's apply your exact argument to photons. You're saying that if each photon has a lot of energy, then they won't diffract. No kidding! The correspondence principle applied to bright radiation fields is a theory that describes the diffraction of classical concepts like the Poynting flux. Which, by the way, has nothing at all to do with the energy per photon, as I"ve told you about a hundred times.

 

[unusualname]

I just want to withdraw a statement I made above that Ken G has a good understanding of QM. I read a few discussions that were on an elementary level which misled me.

 

[Goldstone1]

Then you didn't look at those papers I cited? There's a whole field of study called "scalar diffraction theory", it's all perfectly classical. Oh and yes, it has been applied to neutrons and electron diffraction, it's just that many times the quantum mechanics is all you need, and is more generally applicable. That's what I mean by the "accident of history"-- had neutron and electron diffraction been known about in 1880, instead of the 1930s, it would have been more important.

Actually, you have never once gave a single reason why you think only the diffraction of massless particles is classically describable, but that the diffraction of neutrons has no classical analog. Would you like to take that opportunity right now? Because I have no idea why you think that.

Excellent, then you actually agree with my central thesis all along (would you like to count the number of times I used the word "analog" in this thread?). I'm glad to discover this, I can then disregard all your objections to it because you apparently agree with it.
Many things get called the correspondence principle. I've been painstakingly clear about the meaning I've taken. I'm glad to find that if you just take my meaning, you agree with me.

Let's apply your exact argument to photons. You're saying that if each photon has a lot of energy, then they won't diffract. No kidding! The correspondence principle applied to bright radiation fields is a theory that describes the diffraction of classical concepts like the Poynting flux. Which, by the way, has nothing at all to do with the energy per photon, as I"ve told you about a hundred times.

Strange, but I feel inclined to show you this equation derived as the energy of a shift between two planes of negative and positive solutions:

$$\Delta E \Psi= \sum_{i}^{\theta} M_{0i} \phi (\Lambda^{-1} x) \psi_i$$

based on a non-negligable, solutions for $$\phi'$$, the shifted function.

you said

''had neutron and electron diffraction been known about in 1880, instead of the 1930s, it would have been more important.''

The equation also predicts accordingly the energy resolutions in $$\phi$$ to allow a geometry of $$180^o$$. Meaning the diffraction of light of a mirror, is predicted by this equation.