The Myth of Wave-Particle Duality

[Varon]

Ballentine mentioned in "The Statistical Interpretation of Quantum Mechanics" published in 1970 in the Review of Modern Physics the following which allegedly showed that the wave-like behavior of a particle if some kind of illusion (now after 40 years, are there no experiments that can refute his statement)??

Ballentine Wrote:

If the expression "wave-particle duality" is to be used at all, it must not be intepreted literally. In the above-mentioned scattering experiment, the scattered portion of the wave function may be equally distributed in all directions (as for an isotropic scatterer), but anyone particle will not spread itself isotropically; rather it will be scatered in some particular direction. Clearly the wave function describes not a single scattered particle but an ensemble of similarly accelerated and scattered particles. At this point the reader may wonder whether a statistical particle theory can account for interference or diffraction phenomena. But there is no difficulty. As in any scattering experiment, quantum theory predicts the statistical frequencies of the various angles through which a particle may be scattered. For a crystal or diffraction grating there is only a discrete set of possible scattering angles because momentum fransfer to and from a periodic object is quantized by a multiple of delta p = h/d, where delta p is the component of momentum tranfer parallel to the direction of the periodic displacement d. This result, which is obvious from a solution of the problem in momentum representation, was first discovered by Duane (1923), although this early paper had been much neglected until its revival by Lande (1955, 1965). There is no need to assume that an electron spreads itself, wavelike, over a large region of space in order to explain diffraction scattering. Rather it is the crystal which is spread out, and the electron interacts with the crystal as a whole through the laws of quantum mechanics. For a longer discussion of this and related problems such as the two-slit experiment, see Lande (1965). In every case a diffraction pattern consists of a statistical distribution of discrte particle events which are separately observative if one looks in fine enough details. In the words of Mott (1964, p. 409), "Students should not be taugh to doubt that electrons, protons and the like are particles ... The wave cannot be observed in any way than by observing particles."

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Can you cite just one example of an experiment that can refute what Ballentine mentioned? Implication of what he was claiming was that an electron has no probability wave as described by the Schroedinger Equation.. and this equation described not an individual system but an ensemble.
(Btw... you can read the entire paper of Ballentine published in 1970 by goggling "Ballentine Statistical Interpretation" and click the site with the pdf file)

 

[Demystifier]

For a closely related discussion see also Sec. 2 of
http://xxx.lanl.gov/abs/quant-ph/0609163 [Found.Phys.37:1563-1611,2007]

 

[Fra]

In the words of Mott (1964, p. 409), "Students should not be taugh to doubt that electrons, protons and the like are particles ... The wave cannot be observed in any way than by observing particles."

I still the use of the word "particle" gives it a flavour of far too much realism that is justified.

I am more radical that that: All we observer "directly" is simple distinguishable events. To call a "event click" a particle is a huge leap if along with the word follows the classical picture.

To take this to it's extreme (and I am all for it) we should note that all we have are registrations of distinguishable events. All other "pictures" of waves or particles are merely inferred pictures from the direct observations. So what I think we should do is to focus on the process of how the observed events are collected, stored and process in the state of the observer, and how this then "encodes" information about hte system (in terms of expectations of further registrations).

I'm not sure how many of you that are willing to call a click event, say increasing the counter state, "detection of a particle". The word "particle" is still loaded. How about just settling with counter states? and considering howto use this data set to produce an expectation of the future?

/Fredrik

 

[strangerep]

I'm not sure how many of you that are willing to call a click event, say increasing the counter state, "detection of a particle". The word "particle" is still loaded.

You might recall some threads from ealier this year that debated this topic? I found the "field" picture compelling, in view of the analysis in Mandel & Wolf, which (afaict) leads to a variant on your:

How about just settling with counter states? and considering how to use this data set to produce an expectation of the future?

 

[Dmitry67]

"Students should not be taugh to doubt that electrons, protons and the like are particles ... The wave cannot be observed in any way than by observing particles."

is based on the magic role of the measurement. So it is valid in Stochastics Mechanics or Shut Up and Calculate. In MWI particles are just an illusion, created by the decoherence.

So it is Interpretation Dependent.

 

[Schrodinator]

is based on the magic role of the measurement. So it is valid in Stochastics Mechanics or Shut Up and Calculate. In MWI particles are just an illusion, created by the decoherence.

So it is Interpretation Dependent.

MWI is a bit far fetched for my liking and eternally unprovable. It's pure philosophical sophistry IMHO. I may not like the implications of shut up and calculate or other more wave-particle like formulations but I am not prepared yet to go completely into science fiction. If I send a message to myself in another reality, and I get it, maybe then I will change my mind.

 

[Varon]

We can settle it by experiments. Aren't there experiments that can show overwhelmingly the wave behavior of matter?

How about a single atom. The electron only exist in energy levels or Bohr orbital because of the de Broglie wavelength. After Born discovered the probability interpretation, it's a wave of probability that makes the electrons stay in certain orbital clouds. So this shows the wave side of matter, isn't it? Hence this refutes the Ballentine claim that says there is really no wave.

 

[SpectraCat]

Varon ... buddy ... this is an INTERPRETATION issue. Ballentine, just like Neumaier, or a Bohmian, or an MWI adherent, is a smart guy who has thought about this stuff long and hard, and drawn his own conclusions that are consistent with available experimental evidence as well as their own notions about how the world ought to be. Can a flaw be found? Maybe, but you should have learned by now that this stuff is like religion ... getting someone to change their mind about their favorite interpretation of QM (if they have one) is almost impossible. For every counter-example you can come up with, they will almost certainly have a refutation ready ... that refutation will unlikely be satisfying to YOU, but you will not be able to dismiss it unequivocally.

Still, having said all of that, I would like to see how Ballentine explains phenomena like Bose-Einstein condensation, or superfluidity, or even the fact that helium remains liquid down to 0 K, without considering that quantum "particles" are delocalized in some way. Once you admit that individual quantum particles can be delocalized, then whether you call that behavior "wave-like" or something else, is either a matter of semantics, or just an assertion that cannot be shown experimentally to be true or false (as with Bohmian mechanics).

 

[Fra]

We can settle it by experiments. Aren't there experiments that can show

The point of the argument is that if you look exactly how you "infer the wave picture", you see that it is done by means of detectors, or by different means sensor readings.

So in the end, you do not directly observe waves (and I argue not particles either). All you observer is counter states. These observations can then give the illusion of a particle, or a wave. The "wave" or is emergent only in the statistical view of the acquired data. In the indirect sense, then sure you can view that as an inference of a wave structure. But this inference is still ambigous, since the raw data can be processed and encoded in different ways.

All I care about, and which is interesting, is from the point of view of predictive power, which encoding and processing that is likely to be chosen by nature.

Compare with how the human brain, process, recodes and stores information. There is in fact a CHOICE to be made, what information to remember and what to discard. No observing structure can encode ALL time history data. That's not possible unless the observer mass would be constantly inflating.

/Fredrik

 

[Demystifier]

After Born discovered the probability interpretation, it's a wave of probability that makes the electrons stay in certain orbital clouds. So this shows the wave side of matter, isn't it? Hence this refutes the Ballentine claim that says there is really no wave.

Since Ballentine is not here, let me play his advocate for a moment.*

You correctly say, which Ballentine would agree with, that the wave is actually the PROBABILITY wave. But probability is a property of a statistical ensemble, not a property of an individual element. Therefore, it is semantically meaningless to say that the probability-wave makes the individual electron posses some property. When Ballentine says that there is really no wave, he means that there is no wave as an INDIVIDUAL entity.

*Disclaimer: As a good advocate, I don't necessarily agree with the position I take.

 

[Demystifier]

Aren't there experiments that can show overwhelmingly the wave behavior of matter?

Yes, but no INDIVIDUAL experiment shows the wave behavior of an INDIVIDUAL piece of matter. It's always after a repetition of many similar experiments, or after an experiment on many similar individuals (e.g. electrons), that a wave behavior appears.

 

[Varon]

Yes, but no INDIVIDUAL experiment shows the wave behavior of an INDIVIDUAL piece of matter. It's always after a repetition of many similar experiments, or after an experiment on many similar individuals (e.g. electrons), that a wave behavior appears.

But electrons stay in the atomic orbitals (different energy levels) because of the wavelength... even though it's probability wave. de Broglie first showed this. Then Schroedinger made a master wave equation.

Unless you are saying HUP alone is enough to make the electrons stay at certain energy levels? What is the standard explanation?

 

[Schrodinator]

The point of the argument is that if you look exactly how you "infer the wave picture", you see that it is done by means of detectors, or by different means sensor readings.

So in the end, you do not directly observe waves (and I argue not particles either). All you observer is counter states. These observations can then give the illusion of a particle, or a wave. The "wave" or is emergent only in the statistical view of the acquired data. In the indirect sense, then sure you can view that as an inference of a wave structure. But this inference is still ambigous, since the raw data can be processed and encoded in different ways.

All I care about, and which is interesting, is from the point of view of predictive power, which encoding and processing that is likely to be chosen by nature.

Compare with how the human brain, process, recodes and stores information. There is in fact a CHOICE to be made, what information to remember and what to discard. No observing structure can encode ALL time history data. That's not possible unless the observer mass would be constantly inflating.

/Fredrik

It should at least be possible to get people to agree that wave particle duality is an inherent feature of quantum systems, but it seems even that is not possible. I do think people who think that particle and determinist models are all that is necessary are "allowed" to believe that but I still think experiment tends to make such claims moot. Personally I find the idea of Many Worlds to be as delusional as the idea of millions of dimensions or even infinite dimensions. It sounds like some fantastic fairy tale, but some notable scientists do seem to like the determinism of this interpretation. I think they are mental but meh, everyone's allowed an opinion.

 

[Schrodinator]

Yes, but no INDIVIDUAL experiment shows the wave behavior of an INDIVIDUAL piece of matter. It's always after a repetition of many similar experiments, or after an experiment on many similar individuals (e.g. electrons), that a wave behavior appears.

Doesn't the Feynman two slit show that even with a single photon it interferes with itself to produce interference fringes and exhibits particle like behaviour only when measured. That I would say was a pretty good example of wave-particle duality in a single piece of matter. If consequent photons are allowed to hit the screen then the normal distribution we see with entire packets of photons builds up too. Likewise if we measure the entire wave packet then the particles strike the screen in a single place according to which slit they passed through (50/50 distribution is observed) as if they were bullets fired from a gun. We then know which slit the photons passed through with precision but the wavelike behaviour has now decohered.

Anyhoo its beside the point as the argument isn't about duality per se it is mostly about what happens at decoherence (or even if it takes place at all), since before we measure it the state cannot be known. Copenhagen AKA Shut up and calculate says that the wave function is not real but a figurative inductive mathematical construct which collapses to a defined state only on measurement ie quantum systems are probabilistic not classical, and MWI says the wave function is an exactly pictoral image of the wave, the superposition of which exists in all possible worlds, and measurement simply selects one state in our world ie there is no collapse and the wave function is entirely deterministic not probabilistic.

"Is the moon still there when I am not looking at it?"

"God does not play dice with the Universe."

Albert Einstein.

"My only regret is that I will not be alive to see the demise of quantum mechanics."

Erwin Schrödinger.

I always find it ironic that two such giants who did a lot to bring quantum mechanics to life and to model it, were such strong opponents of it in particular as it pertained to interpretations. As Bohr opined in response to Einstein though "Stop telling God what to do with his dice Einstein."

The great meeting of minds, the conference at Solvey saw Einsten, Schrödinger et al deposed and Pauli, Heisenberg and Bohr et al are said to have won the day. It's still just as contentious now though.

 

[Demystifier]

Doesn't the Feynman two slit show that even with a single photon it interferes with itself to produce interference fringes and exhibits particle like behaviour only when measured.

Not really. Nobody ever seen interference fringes with a SINGLE photon. With many independent photons transmitted through the slits one by one - yes, but with a single photon - no.

 

[Schrodinator]

Not really. Nobody ever seen interference fringes with a SINGLE photon. With many independent photons transmitted through the slits one by one - yes, but with a single photon - no.

No but since the photon does not behave like a particle it is inferred is it not? If multiple single photons are used then an interference fringe appears on the screen, surely we can't say that the first photon behaved like a particle and all the rest didn't. Admittedly it isn't a proof but it is logically consistent to assume the photons all interfered with themselves much more than saying the first one didn't but all the rest did.

 

[Varon]

Not really. Nobody ever seen interference fringes with a SINGLE photon. With many independent photons transmitted through the slits one by one - yes, but with a single photon - no.

But remember that in the region with destructive interferences, there are no photons or particles detected... so in the ensemble or statistical interpretation, how do all the particles conspire to be at the regions that don't belong to the destructive interferences area.

Now if you will do a one particle at a time doube slit experiment, the fact that when you do this a thousand times and the particle still doesn't get detected in the destructive interferences region, it means it can interfere. Hence by "interfere" means a wave is involved.

 

[Demystifier]

But electrons stay in the atomic orbitals (different energy levels) because of the wavelength... even though it's probability wave.

Well, it is an interpretation. A reasonable one, but still an interpretation, not a fact. Let me illustrate this by some possible alternatives.

1) How do you know that electrons stay in the atomic orbitals before you observe them? Perhaps they live somewhere else and then suddenly pop out when you try to detect them? Or perhaps they don't even exist unless you perform a measurement? The Ballentine interpretation is open to all such logically possible alternatives, no matter how unintuitive they may look. More precisely, the Ballentine interpretation is agnostic with respect to such alternatives.

2) Perhaps electrons really stay in the atomic orbitals, but a true reason for this is not the wave function. True, we can predict the experimental data very well with the assumption of waves, but maybe the wave-description is only an approximation, while the ultimate theory (which we don't know yet) is something completely different. The Ballentine interpretation is open/agnostic to such possibilities as well.

3) Perhaps there is no true logical reason why electrons stay in the atomic orbitals. Instead, they may stay there just because God wishes so. Again, the agnostic Ballentine would be agnostic to that as well.

Of course, you may say that all these possibilities look very unreasonable. And I would agree. Yet, they are all logical possibilities which cannot be excluded. The essence of Ballentine thinking is that, as long as many alternatives without existing waves are at least conceivable, we have no rights to claim that waves exist.

 

[Studiot]

I thought that 'single particle interference' (whatever that means see below) had been observed in several different experiments.

eg http://www.physorg.com/news78650511.html

I would observe that there are those who have not grasped the fundamental fact of life, which that reality is more complex than any of our models.
I use the word model because that is all the wave or particle theories are - models.

Models are such that they provide an formulation, equation or law that is obeyed in certain circumstances.
But never all circumstances.
That is why those who ask

"But what is XXX really?" will never be satisfied.

The only real answer is XXX is XXX, but in the following circumstances it behaves according to the following prescription.

As a matter of interest why are folks so uncomfortable wave-particle duality. Physics abounds with entities that possesses some characteristics of one model and some of another.

Finally is there not something a bit strange about specifying 'a single particle' and then requiring it to behave like a wave?

go well

 

[Demystifier]

... so in the ensemble or statistical interpretation, how do all the particles conspire to be at the regions that don't belong to the destructive interferences area.

The essence of the ensemble interpretation is that it is agnostic with respect to this question. How do these particles conspire? The answer of that interpretation is that we don't know! Perhaps there really are some waves which do the job, or perhaps there are angels which do that, or perhaps ... Many possibilities are conceivable, but as long as we don't know with certainty, we cannot claim that waves exist.

(Let me repeat that I do not necessarily like such a view. I am merely explaining it.)

 

[Demystifier]

To summarize:
The ensemble interpretation does not claim: "Waves do not exist".
Instead, it claims: "We cannot directly prove that waves exist, so let us not say that they do."

 

[Schrodinator]

The essence of the ensemble interpretation is that it is agnostic with respect to this question. How do these particles conspire? The answer of that interpretation is that we don't know! Perhaps there really are some waves which do the job, or perhaps there are angels which do that, or perhaps ... Many possibilities are conceivable, but as long as we don't know with certainty, we cannot claim that waves exist.

I think like MWI proponents they are grasping at straws. I wouldn't go so far as to say they were indulging in fantasy (as MWI people are) but they really are indulging in something unreal. Fiction is a comfortable safety net for people who won't accept experiment. Personally I think like Einstein they won't accept reality, and will spend the rests of their lives indulging in comfortable fantasy (nothing against Einsteins search for classical mechanics and determinism btw, just that if all evidence tells us it does not happen we should focus on why not try and be apologists for Newton et al). It's their lookout but they are wasting scientific time, these people are obviously smart, why then are they indulging in religions? God does not play dice? Well prove it then and stop just talking the talk. Solvey wasn't a loss for Einstein et al because of talk it was a loss because experiment agreed with talk.

(Let me repeat that I do not necessarily like such a view. I am merely explaining it.)

No we get that, explaining it. Scool.

To summarize:
The ensemble interpretation does not claim: "Waves do not exist".
Instead, it claims: "We cannot directly prove that waves exist, so let us not say that they do."

We can though prove that matter exhibits duality, saying waves don't exist is then just sophistry. It smacks of Luddite behaviour or post modernist denial of science. Have no problem with claiming that, but show me the damned money.

Talk is cheap.

 

[Schrodinator]

Well, it is an interpretation. A reasonable one, but still an interpretation, not a fact. Let me illustrate this by some possible alternatives.

1) How do you know that electrons stay in the atomic orbitals before you observe them? Perhaps they live somewhere else and then suddenly pop out when you try to detect them? Or perhaps they don't even exist unless you perform a measurement? The Ballentine interpretation is open to all such logically possible alternatives, no matter how unintuitive they may look. More precisely, the Ballentine interpretation is agnostic with respect to such alternatives.

Because experiment tells us so. It tells us they exist in a probabilistic wave like manner, so we have to make our theories agree with reality. That is what science is.

2) Perhaps electrons really stay in the atomic orbitals, but a true reason for this is not the wave function. True, we can predict the experimental data very well with the assumption of waves, but maybe the wave-description is only an approximation, while the ultimate theory (which we don't know yet) is something completely different. The Ballentine interpretation is open/agnostic to such possibilities as well.

Again experiment. The closest approximation is the better one. Philosophising over the truthiness of something is worthy but it is not science.

3) Perhaps there is no true logical reason why electrons stay in the atomic orbitals. Instead, they may stay there just because God wishes so. Again, the agnostic Ballentine would be agnostic to that as well.

Or perhaps Heisneburg was right and more importantly Wolfgang Pauli, being as their observations and arguments agree with experiment, why would we think otherwise? Who needs God? Agnosticism is fine if the proofs are not found in empricisms, but they are.

Of course, you may say that all these possibilities look very unreasonable. And I would agree. Yet, they are all logical possibilities which cannot be excluded. The essence of Ballentine thinking is that, as long as many alternatives without existing waves are at least conceivable, we have no rights to claim that waves exist.

They can by experiment be shown to exist though.

Ballentine was obviously a crackpot. Just because you are very smart does not mean you can't be wrong, I think Ballentine was just wrong. The philosophy is sound if there are no black swans, but the conclusions are just false based on the evidence we have they are non sequiturs.

 

[SpectraCat]

Well, it is an interpretation. A reasonable one, but still an interpretation, not a fact. Let me illustrate this by some possible alternatives.

1) How do you know that electrons stay in the atomic orbitals before you observe them? Perhaps they live somewhere else and then suddenly pop out when you try to detect them? Or perhaps they don't even exist unless you perform a measurement? The Ballentine interpretation is open to all such logically possible alternatives, no matter how unintuitive they may look. More precisely, the Ballentine interpretation is agnostic with respect to such alternatives.

Because experiment tells us so.

Please explain, with cited references and in as much detail as possible, precisely which experiments tell us that Demystifier's proposal is not reflective of what electrons are "doing" when they are not being measured.

2) Perhaps electrons really stay in the atomic orbitals, but a true reason for this is not the wave function. True, we can predict the experimental data very well with the assumption of waves, but maybe the wave-description is only an approximation, while the ultimate theory (which we don't know yet) is something completely different. The Ballentine interpretation is open/agnostic to such possibilities as well.

Again experiment.

Again, please explain and give citations.

Of course, you may say that all these possibilities look very unreasonable. And I would agree. Yet, they are all logical possibilities which cannot be excluded. The essence of Ballentine thinking is that, as long as many alternatives without existing waves are at least conceivable, we have no rights to claim that waves exist.

They can by experiment be shown to exist though.

Same question ... which specific experiments on individual particles demonstrate that they have wave-like character? And please don't just say "the double-slit" .. that does not show anything of the sort .. individual particles are never observed to be at more than a single location at a time.

Ballentine was obviously a crackpot. Just because you are very smart does not mean you can't be wrong, I think Ballentine was just wrong. The philosophy is sound if there are no black swans, but the conclusions are just false.

 

[Schrodinator]

Please explain, with cited references and in as much detail as possible, precisely which experiments tell us that Demystifier's proposal is not reflective of what electrons are "doing" when they are not being measured.
Again, please explain and give citations.Same question ... which specific experiments on individual particles demonstrate that they have wave-like character? And please don't just say "the double-slit" .. that does not show anything of the sort .. individual particles are never observed to be at more than a single location at a time.

Already done this, clearly you don't accept the logic or the experiments so its a waste of time repeating myself.

Believe whatever you like it's not my problem. Logically the double slit shows wave particle duality, you do not accept it does, I will not waste my time repeating why it does. That will help nothing, your opinion as already said by someone else will not be changed by logic or real world experiment. You are entitled to your opinion, by all means indulge in it.

 

[A. Neumaier]

Not really. Nobody ever seen interference fringes with a SINGLE photon. With many independent photons transmitted through the slits one by one - yes, but with a single photon - no.

One doesn't see fringes but one _never_ observes a response in the places where destrucive interference takes place. This is a definitive prediction of QM for each single particle, and proves the wave nature of every single quantum object that can pass a double slit.

 

[A. Neumaier]

Finally is there not something a bit strange about specifying 'a single particle' and then requiring it to behave like a wave?

It may be a bit strange but it is standard practice.
Even when a quantum system is _prepared_ as a particle it need not stay one if it delocalizes, just as a drop of water remains water but need no longer be a drop after it is absorbed where it falls on the ground.

 

[Studiot]

It may be a bit strange but it is standard practice.

Perhaps I should have put a wry smiley after my remark.

 

[SpectraCat]

Already done this, clearly you don't accept the logic or the experiments so its a waste of time repeating myself.

You did nothing of the sort .. not a single one of your posts in this thread has addressed electronic states in atoms, which was the subject of the first two items I asked for experimental proof about.

Believe whatever you like it's not my problem. Logically the double slit shows wave particle duality, you do not accept it does, I will not waste my time repeating why it does. That will help nothing, your opinion as already said by someone else will not be changed by logic or real world experiment. You are entitled to your opinion, by all means indulge in it.

You are also assuming an awful lot about my point of view on the matter, based simply on my request for you to provide the experimental evidence for your claims.

Read my posts .. I am an instrumentalist. I believe in what can be demonstrated by experiment. I am willing to accept that any interpretative theory that is consistent with all available experimental evidence is POTENTIALLY valid. I use the standard formulation of QM (Schrodinger equation, Dirac notation, state space etc.) because it can be used to explain the results, and has never been shown to be incorrect. However, the same can be said of Bohmian mechanics .. at least so far. I am less familiar with the statistical interpretation, but from what I have seen, it also appears to be consistent with all available experimental evidence.

What we know is that the experimentally observed trajectories of quantum particles behave in a manner that is consistent with them having a complex phase associated with their mathematical description. When this was discovered, in was immediately put into the context of waves, which also happen to have complex phases associated with their mathematical descriptions. Thus the language of waves and wavefunctions and interference became inextricably linked with the field of quantum mechanics in its early development.

So, in the double slit experiment, what we see is behavior that is consistent with the particles having behaved as wave-like entities (i.e. entities with complex phases associated with their mathematical descriptions) at a previous time when we were not observing them, but we never actually catch them in the act of being anything other than a particle. What Demystifier was trying to explain is that there is nothing in Ballentine's statistical interpretation that is inconsistent with these experimental results. From the point of view of the statistical interpretation, a single particle in a given experiment behaves as it does because it is a member of an ensemble that gives the observed probability distribution, which happens to be the one predicted by standard quantum mechanics. It is very hard to knock a hole in this argument .. I know because I have tried, at some length.

 

[Varon]

One doesn't see fringes but one _never_ observes a response in the places where destrucive interference takes place. This is a definitive prediction of QM for each single particle, and proves the wave nature of every single quantum object that can pass a double slit.

I also thought about this region of destructive interferences which has no particles.. so we assume it has wave behavior.. but Ballentine explained it can be caused by other ways:

"At this point the reader may wonder whether a statistical particle theory can account for interference or diffraction phenomena. But there is no difficulty. As in any scattering experiment, quantum theory predicts the statistical frequencies of the various angles through which a particle may be scattered. For a crystal or diffraction grating there is only a discrete set of possible scattering angles because momentum fransfer to and from a periodic object is quantized by a multiple of delta p = h/d, where delta p is the component of momentum tranfer parallel to the direction of the periodic displacement d. This result, which is obvious from a solution of the problem in momentum representation, was first discovered by Duane (1923), although this early paper had been much neglected until its revival by Lande (1955, 1965). There is no need to assume that an electron spreads itself, wavelike, over a large region of space in order to explain diffraction scattering. Rather it is the crystal which is spread out, and the electron interacts with the crystal as a whole through the laws of quantum mechanics."

Is Ballentine right? Pls. elaborate. If he is wrong in the argument above or latest experiment has disproof it (after 1970).. then it refutes Ballentine.

 

[Varon]

To summarize:
The ensemble interpretation does not claim: "Waves do not exist".
Instead, it claims: "We cannot directly prove that waves exist, so let us not say that they do."

Are there many variants of the Ensemble (or statistical interpretation) or is the one by Ballentine the only one?

Ballentine stated flat out there is no wave behavior (see the original message). But if probability indeed behave as wave. Then his interpretation or more likely framework is not helpful. It's like we are discovering what made the DNA ticks. And someone says a human is an ensemble of DNAs and no proof the DNA is double helix (or wave-like). And so perhaps we can treat Ballentine Interpretation more like Ballentine Framework for Pragmatists (that is.. for Instrumentalists to focus on without trying to worry what lies in each particle). So for us who scrutinize the correct Interpretations to get insight on unification with General Relativity and Quantum Gravity (that is... these possibly arising from a Third Theory totally different from both of them). Let's avoid Ballentine as it's not helpful (especially if he had to flatly declared there were no waves (see original message for the quotes)).

 

[Varon]

You did nothing of the sort .. not a single one of your posts in this thread has addressed electronic states in atoms, which was the subject of the first two items I asked for experimental proof about.



You are also assuming an awful lot about my point of view on the matter, based simply on my request for you to provide the experimental evidence for your claims.

Read my posts .. I am an instrumentalist. I believe in what can be demonstrated by experiment. I am willing to accept that any interpretative theory that is consistent with all available experimental evidence is POTENTIALLY valid. I use the standard formulation of QM (Schrodinger equation, Dirac notation, state space etc.) because it can be used to explain the results, and has never been shown to be incorrect. However, the same can be said of Bohmian mechanics .. at least so far. I am less familiar with the statistical interpretation, but from what I have seen, it also appears to be consistent with all available experimental evidence.

What we know is that the experimentally observed trajectories of quantum particles behave in a manner that is consistent with them having a complex phase associated with their mathematical description. When this was discovered, in was immediately put into the context of waves, which also happen to have complex phases associated with their mathematical descriptions. Thus the language of waves and wavefunctions and interference became inextricably linked with the field of quantum mechanics in its early development.

So, in the double slit experiment, what we see is behavior that is consistent with the particles having behaved as wave-like entities (i.e. entities with complex phases associated with their mathematical descriptions) at a previous time when we were not observing them, but we never actually catch them in the act of being anything other than a particle. What Demystifier was trying to explain is that there is nothing in Ballentine's statistical interpretation that is inconsistent with these experimental results. From the point of view of the statistical interpretation, a single particle in a given experiment behaves as it does because it is a member of an ensemble that gives the observed probability distribution, which happens to be the one predicted by standard quantum mechanics. It is very hard to knock a hole in this argument .. I know because I have tried, at some length.

No. Ballentine even tried to model what happened in one single particle. So if his explanation was wrong in this single particle behavior. Then he is just wrong. He specifically said that:

"... but anyone particle will not spread itself isotropically; rather it will be scatered in some particular direction. Clearly the wave function describes not a single scattered particle but an ensemble of similarly accelerated and scattered particles. At this point the reader may wonder whether a statistical particle theory can account for interference or diffraction phenomena. But there is no difficulty. As in any scattering experiment, quantum theory predicts the statistical frequencies of the various angles through which a particle may be scattered. For a crystal or diffraction grating there is only a discrete set of possible scattering angles because momentum fransfer to and from a periodic object is quantized by a multiple of delta p = h/d, where delta p is the component of momentum tranfer parallel to the direction of the periodic displacement d. This result, which is obvious from a solution of the problem in momentum representation, was first discovered by Duane (1923), although this early paper had been much neglected until its revival by Lande (1955, 1965). There is no need to assume that an electron spreads itself, wavelike, over a large region of space in order to explain diffraction scattering. Rather it is the crystal which is spread out, and the electron interacts with the crystal as a whole through the laws of quantum mechanics."

What do you think? Do you believe it 100%?

 

[SpectraCat]

No. Ballentine even tried to model what happened in one single particle. So if his explanation was wrong in this single particle behavior. Then he is just wrong. He specifically said that:

"... but anyone particle will not spread itself isotropically; rather it will be scatered in some particular direction. Clearly the wave function describes not a single scattered particle but an ensemble of similarly accelerated and scattered particles. At this point the reader may wonder whether a statistical particle theory can account for interference or diffraction phenomena. But there is no difficulty. As in any scattering experiment, quantum theory predicts the statistical frequencies of the various angles through which a particle may be scattered. For a crystal or diffraction grating there is only a discrete set of possible scattering angles because momentum fransfer to and from a periodic object is quantized by a multiple of delta p = h/d, where delta p is the component of momentum tranfer parallel to the direction of the periodic displacement d. This result, which is obvious from a solution of the problem in momentum representation, was first discovered by Duane (1923), although this early paper had been much neglected until its revival by Lande (1955, 1965). There is no need to assume that an electron spreads itself, wavelike, over a large region of space in order to explain diffraction scattering. Rather it is the crystal which is spread out, and the electron interacts with the crystal as a whole through the laws of quantum mechanics."

How is that any different from what I said?

What do you think? Do you believe it 100%?

I believe it as much as I believe any interpretation .. i.e. to the extent that it agrees with experiment. Since the statistical interpretation generally makes fewer assumptions about "the way things are" than other interpretations, so far I generally find it more palatable than other interpretations. Still, I would not go as far as Ballentine in saying that there is no such thing as wave-particle duality .. rather I would say that wave-particle duality is one of a number of ways of explaining experimentally observed phenomena, and so far there is no experimental evidence that anyone of them is actually the correct one.

 

[SpectraCat]

Are there many variants of the Ensemble (or statistical interpretation) or is the one by Ballentine the only one?

Ballentine stated flat out there is no wave behavior (see the original message). But if probability indeed behave as wave. Then his interpretation or more likely framework is not helpful. It's like we are discovering what made the DNA ticks. And someone says a human is an ensemble of DNAs and no proof the DNA is double helix (or wave-like). And so perhaps we can treat Ballentine Interpretation more like Ballentine Framework for Pragmatists (that is.. for Instrumentalists to focus on without trying to worry what lies in each particle). So for us who scrutinize the correct Interpretations to get insight on unification with General Relativity and Quantum Gravity (that is... these possibly arising from a Third Theory totally different from both of them). Let's avoid Ballentine as it's not helpful (especially if he had to flatly declared there were no waves (see original message for the quotes)).

Nowhere in that quote does he say "there are no waves" or anything else that can be interpreted to mean that. What he says is that the experimental observations can be explained statistically without attaching a wave-like nature to individual particles. He then asserts that attaching wave-like attributes to individual particles is not helpful to those trying to learn about quantum mechanics.

 

[Varon]

I realized that Ballentine's interpretation is a direct challenge to Bohr even in single particle.

Bohr declared that in the absence of measurement to determine its position, the electron has no position.

Ballentine declared even both position and momentum can exist!

Here's the relevant quotes from his 1970 paper:

Page 8.

"This statement is often supported by one or both of the following arguments:

(i) A measurement of q causes an unpredictable and uncontrollable disturbance of p, and vice versa. [This was first proposed by Heisenberg (1927) and is widely repeated in textbooks].

(ii) The position and momentum of a particle do not even exist with simultaneously and pefectly well defined (though perhaps unknown) values (Bohm, 1951, p.100)"
<snip>
"Argument (ii) is easily seen to be unjustified"
<snip>
"Using de Broglie's relation between momentum and wavelength, p = h / wavelength, it is then asserted that a particle cannot have definite values of both position and momentum at any instant. But this conclusion rests on the almost literal identication of the particle with the wave packet (or what amounts to the same thing, the assumption that the wave function provides an exhaustive description of the properties of the particle)."
<snip>
"A consistent application of the Statistical Interpretation yields the correct conclusion that the division of the wavepacket yields the relative probabilities for transmission and reflection of particles. But there is no justification for assertion (ii)"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Come on guys. Is there not even a single experiment that can distinguish or prove whether HUP work because of mere disturbance on existing particle or because there is no positon even in principle? Einstein, Schroedinger thought of this for their whole lifetime. How come Ballentine can formulate a whole QM using the same principles that these two great men couldn't?

Also in Bohmian Mechanics.. additional assumptions like quantum potential and omnicient wave function have to be proposed. How come Ballentine can get away with this (without proposing the two extra assumptions) in his interpretation where a particle has trajectory at all times just like Bohmian?