The Myth of Wave-Particle Duality

[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?

 

[Schrodinator]

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.

Whatever dude, just indulge in whatever fantasy suits you. I can't re explain things and have you accept them, now can I. The double slit does show particle wave duality: you clearly don't accept that. What am I supposed to do then if reality isn't good enough?

It doesn't matter what view you hold, clearly you aren't paying attention or are just being deliberately ignorant. Either way I'm not going to waste my time rehashing what I already said and which experiments show what.

A single photon fired through a slit interferes with itself. You either accept that or you don't, there's nothing more I can say.

 

[Fra]

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.

I certainly don't believe that.

*My* point was completely different. In my post I never argued for particle vs wave. My point was that the mental picture of a realist wave, is as much a realist illusion as is the mental picture of particle.

/Fredrik

 

[Fra]

A single photon fired through a slit interferes with itself. You either accept that or you don't, there's nothing more I can say.

My point is that the pattern can be explain without wave ontologies. With "classical" wave we understand interference, but I think we can agree that a QM wave is different. My opinon is that just as using the "particle" concept is loaded, so is the wave concept. Mainly because it's neither "classical particles" nor "classical waves".

I think there are better abstractions that both particles and waves. Noone would deny the interference pattern.

/Fredrik

 

[Schrodinator]

My point is that the pattern can be explain without wave ontologies. With "classical" wave we understand interference, but I think we can agree that a QM wave is different. My opinon is that just as using the "particle" concept is loaded, so is the wave concept. Mainly because it's neither "classical particles" nor "classical waves".

I think there are better abstractions that both particles and waves. Noone would deny the interference pattern.

/Fredrik

Yeah well saying that wave-particle duality is incomplete as a description is pretty trite tbh. No ****.

Since we cannot measure the wave without disturbing its nature we are pretty much inferring everything inductively. The best we can say is that it appears to act like a wave or a particle according to how or if it is measured. And the Schrödinger equation is derived or works backwards from results of experiment and may or may not depict a real entity.

 

[Varon]

Ballentine paper assumes all particles have positions at all times. This means in Bell's Theorem. He indeed believed that the particles were connected with superluminal link? In Ballentine 1989 textbook which I studied, he mentioned:

Are the experiments conclusive?
If we accept the theoretical arguments that quantum mechanics is incompatible with locality, the next question is whether the experiments are adequate for ruling out locality. We have already seen that, strictly speaking, they are not, because of inefficiencies of the detectors and other instrumental problems. However, the fact that those photon pairs that are detected are correlated in the manner predicted by quantum theory is certainly strong evidence for the correctness of those predictions. Although it is possible to devise local models that would obey Bell’s inequality for ideal detectors, but which agree with quantum theory for the imperfect instruments presently available, such models seem rather contrived. This is especially true in view of the fact that the effect of the various systematic errors that experimentalists have studied is to reduce the coincidence detection rate. But quantum theory predicts a coincidence rate that is greater than is permitted by Bell’s inequality.

Question. Anything wrong by assuming entangled particles exist at all times even 100 billion light years away and since Bell's Theorem is violated, they really are connected with superluminal link? This is the consequence of Ballentine's Statistical Interpretation.

Bohr arguments was the particles attributes like position didn't exist before measurements, so there was no non-local link because the particles wasn't there at all.

 

[Demystifier]

Ballentine paper assumes all particles have positions at all times.

I don't think that the Ballentine paper assumes that. What makes you think so?

 

[zonde]

Ballentine paper assumes all particles have positions at all times. This means in Bell's Theorem. He indeed believed that the particles were connected with superluminal link? In Ballentine 1989 textbook which I studied, he mentioned:

Where do you see that he believed in superluminal link?
From one side he says:
"... the next question is whether the experiments are adequate for ruling out locality. We have already seen that, strictly speaking, they are not ..."
From other side he says:
"Although it is possible to devise local models that would obey Bell’s inequality for ideal detectors, but which agree with quantum theory for the imperfect instruments presently available, such models seem rather contrived."

Does not seem like anything conclusive. More like he tries to be open for both possibilities:
1) that conclusive experiment is performed that rules out locality
2) that non-contrived local model is devised that obeys Bell’s inequality for ideal detectors, but which agree with quantum theory for the imperfect instruments

 

[Varon]

I don't think that the Ballentine paper assumes that. What makes you think so?

In page 4 of his 1970 paper. Ballentine mentioned:

"In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency |psi(r)|^2 in an ensemlbe of similarily prepared experiments."

In the paper, Bell test experiments were not mentioned. This was because Clauser and company experiment started in 1972 (2 years after the paper). I even studied the latest textbook in 1989 mentioned in the message prior to this.
Do you believe that 2 particles 100 billions light years away can be connected superluminally?
If not. Then Ballentine is thus refuted.

 

[Varon]

Where do you see that he believed in superluminal link?
From one side he says:
"... the next question is whether the experiments are adequate for ruling out locality. We have already seen that, strictly speaking, they are not ..."
From other side he says:
"Although it is possible to devise local models that would obey Bell’s inequality for ideal detectors, but which agree with quantum theory for the imperfect instruments presently available, such models seem rather contrived."

Does not seem like anything conclusive. More like he tries to be open for both possibilities:
1) that conclusive experiment is performed that rules out locality
2) that non-contrived local model is devised that obeys Bell’s inequality for ideal detectors, but which agree with quantum theory for the imperfect instruments

It's mentioned in his 1989 book Ballentine Quantum Mechanics: A Modern Development.

Now since he believes a particle has position at all times. And since Bell test experiments violated Bell's Theorem. Then the consequence is that the entangled particle A and B 100 billion light years away are connected by superluminal link.

 

[SpectraCat]

Whatever dude, just indulge in whatever fantasy suits you. I can't re explain things and have you accept them, now can I. The double slit does show particle wave duality: you clearly don't accept that. What am I supposed to do then if reality isn't good enough?

What does that have to do with electrons in atoms? You claimed that it had been experimentally demonstrated somehow that electrons in atoms behaved in certain ways when they are NOT being measured. That is what I asked you to back up with references .. not the double slit experiment. As you say, you have "explained" that ... (more below).

It doesn't matter what view you hold, clearly you aren't paying attention or are just being deliberately ignorant. Either way I'm not going to waste my time rehashing what I already said and which experiments show what.

I never asked you to repeat yourself ... are you even reading my posts?

A single photon fired through a slit interferes with itself. You either accept that or you don't, there's nothing more I can say.

The experiments show that the above statement COULD be true, but nothing says that is the only explanation. Any other explanation that involves each individual particle being detected at a single location, and predicts the probability distribution exhibited experimentally (i.e. interference fringes) when the experiment is repeated many times also COULD be true. That is all I have ever maintained ... I have never denied that wave-particle duality COULD exist, only that it has not been conclusively demonstrated that it is the ONLY possible INTERPRETATION of the experimental data.

 

[SpectraCat]

Yeah well saying that wave-particle duality is incomplete as a description is pretty trite tbh. No ****.

Since we cannot measure the wave without disturbing its nature we are pretty much inferring everything inductively. The best we can say is that it appears to act like a wave or a particle according to how or if it is measured. And the Schrödinger equation is derived or works backwards from results of experiment and may or may not depict a real entity.

How is that different from what I have been saying?

 

[zonde]

Now since he believes a particle has position at all times. And since Bell test experiments violated Bell's Theorem. Then the consequence is that the entangled particle A and B 100 billion light years away are connected by superluminal link.

I can post it one more time. From the quote you gave:
"... the next question is whether the experiments are adequate for ruling out locality. We have already seen that, strictly speaking, they are not ..."

And I can add that Bell test experiment violate Bell inequalities under fair sampling assumption.
There are no fair sampling tests performed.
So it's still the same - performed Bell tests are not conclusive in ruling out locality.

 

[Varon]

In page 4 of his 1970 paper. Ballentine mentioned:

"In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency |psi(r)|^2 in an ensemlbe of similarily prepared experiments."

In the paper, Bell test experiments were not mentioned. This was because Clauser and company experiment started in 1972 (2 years after the paper). I even studied the latest textbook in 1989 mentioned in the message prior to this.
Do you believe that 2 particles 100 billions light years away can be connected superluminally?
If not. Then Ballentine is thus refuted.

Here's more. Page 14:

Ballentine said:

"But if one assumes that the state vector completely describes an individual system, then the dispersion must somehow be a property of the individual system, but it is nonsensical to suppose that a macroscopic pointer has no definite position. None of the attempts to solve this problem using some form of reduction of the state vector are satisfactory.

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

Bohr, the grand.. or Godfather of QM declared: In the absence of measurement to determine its position, the electron has no position.

Ballentine declared: But a particle has positions at all times. Blasphemy!

 

[Demystifier]

In page 4 of his 1970 paper. Ballentine mentioned:
"In contrast, the Statistical Interpretation considers a particle to always be at some position in space, each position being realized with relative frequency |psi(r)|^2 in an ensemlbe of similarily prepared experiments."

OK, thanks for the quotation.

Do you believe that 2 particles 100 billions light years away can be connected superluminally?

Yes I do. Do you?

 

[Varon]

I can post it one more time. From the quote you gave:
"... the next question is whether the experiments are adequate for ruling out locality. We have already seen that, strictly speaking, they are not ..."

And I can add that Bell test experiment violate Bell inequalities under fair sampling assumption.
There are no fair sampling tests performed.
So it's still the same - performed Bell tests are not conclusive in ruling out locality.

I didn't share the other half. Here it is (from his 1989 book):

Another concern is that most of the experiments were not carried out under
one of the conditions specified by the locality postulate: that the settings of the two instruments be adjusted, and the two measurements carried out, in spacelike separated regions of space–time, so that it would be impossible for any light speed signal to “inform” one instrument about the setting of the other. It is under such conditions that the assumptions used to derive Bell’s theorem are most compelling. To answer this objection Aspect, Dalibard, and Roger (1982) have carried out an experiment in which the instruments in Fig. 20.2 are rapidly switched between two polarizer orientations: a and a on the right, and b and b on the left. The switchings on the two sides are performed
by two independent oscillators running at incommensurate frequenices, and presumably with independent phase drifts. The lifetime of the intermediate energy level in the cascade (5 × 10−9 sec) and the switching time between polarizers (10 × 10−9 sec) were both smaller than the time for a light signal to pass from one instrument to the other (40 × 10−9 sec). The polarization correlations were found to be the same as in experiments with static settings of the analyzers, and to agree with quantum theory.

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

Analysis:

Since Ballentine believes in Bell's Theorem being violated. And he believes a particle has position at all times. Then consequence is the particles are somehow connected non-locality... what else but superluminally...

 

[Demystifier]

Since Ballentine believes in Bell's Theorem being violated. And he believes a particle has position at all times. Then consequence is the particles are somehow connected non-locality... what else but superluminally...

Yes, that's a correct line of reasoning. Do you see a problem with it?

 

[Varon]

OK, thanks for the quotation.


Yes I do. Do you?

Hmm... You are a Bohmian. Here positions are preferred. Bohm made two additional assumptions. That there is quantum potential and omnicient wave function for each particle.

How come Bohm didn't think of Ballentine position that quantum potential and omnicient wave function are not necessary. Ballentine Statistical Interpretation is NOT being agnostic (one can get this impression if one didn't read his paper and book). He gave the mechanism even of one particle behavior in the double slit. Which is that the particle is scattered with angle and trajectory (see details in posts above).

Maybe Bohm has to put the 2 additional assumptions because he wants the wave behavior to exist in one particle? But if he didn't assume this. It will become a Ballentine Interpretation?

 

[Varon]

Yes, that's a correct line of reasoning. Do you see a problem with it?

It violates Einstein Special Relativity...

But... since no information is transfered. The spirit of SR is not really violated... Hmm... But Lorentz invariance is violated.. and it is not compatible with quantum field theory.. or interacting particles.. hence Ballentine interpretation is very nearly falsified.

I hope other non-Bohmian can comment on this. Demystifier is a Bohmian and may be biased on certain aspect.

Hmm... Can't we even differentiate whether observation creates the properties like position of particles against them always existing at all times... and whether the superluminal link is direct from particle to particle or the non-local link is in the measurement outcomes? My God. Let's design experiments to distinguish them. I think we can. We have to try hard enough. Anyone can think of any Nobel calibre experiment to distinguish them?

 

[SpectraCat]

Ballentine paper assumes all particles have positions at all times. This means in Bell's Theorem. He indeed believed that the particles were connected with superluminal link? In Ballentine 1989 textbook which I studied, he mentioned:
Question. Anything wrong by assuming entangled particles exist at all times even 100 billion light years away and since Bell's Theorem is violated, they really are connected with superluminal link? This is the consequence of Ballentine's Statistical Interpretation.

Bohr arguments was the particles attributes like position didn't exist before measurements, so there was no non-local link because the particles wasn't there at all.

That's actually a really good point. I think the Aspect experiments pose a real problem for the statistical interpretation .. at least in the form proposed by Ballentine. I also read his comments on those experiments in his book, and I found his handling of the issue quite weak and speculative .. he certainly didn't show how his theory could explain Apsect's results .. he just seemed to hope an appropriate loophole would be found later on. To me it seems like the statistical interpretation may actually be an LHV theory, and as such, should be inconsistent with QM according to Bell's theorem.

[EDIT: What I should have said above is that the statistical interpretation requires EITHER local hidden variables, OR it requires superluminal hidden variables. I guess this is what Demystifier said when he described Bohmian mechanics as a specific realization of the statistical interpretation, because BM requires the quantum potential (or equivalent) which takes care of the superluminal stuff.]

 

[Demystifier]

Bohm made two additional assumptions. That there is quantum potential and omnicient wave function for each particle.

That's not quite correct. The Bohmian approach needs only ONE of these two assumptions, because they are equivalent. And not for each particle separately, but for all particles at once.

Maybe Bohm has to put the 2 additional assumptions because he wants the wave behavior to exist in one particle? But if he didn't assume this. It will become a Ballentine Interpretation?

Well, I like to view the Bohmian interpretation as a concrete realization of the more general Ballentine interpretation.

 

[zonde]

Since Ballentine believes in Bell's Theorem being violated.

I see no justification for that statement.

 

[Demystifier]

It violates Einstein Special Relativity...

But... since no information is transfered. The spirit of SR is not really violated... Hmm... But Lorentz invariance is violated.. and it is not compatible with quantum field theory.. or interacting particles.. hence Ballentine interpretation is very nearly falsified.

I hope other non-Bohmian can comment on this. Demystifier is a Bohmian and may be biased on certain aspect.

It's true that I am biased (is there anybody who isn't?), but I must react to this. There are variants of the Bohmian interpretation which are nonlocal, but Lorentz invariant and compatible with quantum field theory and even interacting particles. See
http://xxx.lanl.gov/abs/1002.3226 [Int. J. Quantum Inf. 9 (2011) 367-377]
http://xxx.lanl.gov/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]
http://xxx.lanl.gov/abs/1007.4946

 

[Demystifier]

I see no justification for that statement.

He probably ment Bell's inequality ...

 

[Varon]

I see no justification for that statement.

He said it in page 610 of his textbook. Ballentine wrote:

"If quantum mechanics implies nonlocality, i.e. influences that are not restricted by the speed of light between distant regions, can we make use of them to send messages at superluminal speeds? No! Several people have shown that quantum correlations cannot be used to transmit messages at superluminal speeds. This is so because the locality principle used in the derivation of Bell’s inequality is stronger than the weaker locality principle that prevents superluminal transmission of information, and quantum mechanics satisfies
the latter (Ballentine and Jarrett, 1987)."

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

So Ballentine considers the possibility of nonlocality as he was aware of Aspect experiment and others. And since he believes position exists at all times. The particles are connected superluminally. Familiar with the EPR debates? It's related to this.

Anyway. After realizing that "Bohmian interpretation as a concrete realization of the more general Ballentine interpretation" and consider I prefer Copenhagen due to its more elegant "Observation creates reality" or Many Worlds where I get to be President of United States in one of the branches, then I leave it for the Bohmian to develope the theory further.

 

[SpectraCat]

That's actually a really good point. I think the Aspect experiments pose a real problem for the statistical interpretation .. at least in the form proposed by Ballentine. I also read his comments on those experiments in his book, and I found his handling of the issue quite weak and speculative .. he certainly didn't show how his theory could explain Apsect's results .. he just seemed to hope an appropriate loophole would be found later on. To me it seems like the statistical interpretation may actually be an LHV theory, and as such, should be inconsistent with QM according to Bell's theorem.

I think that what I should have said above is that the statistical interpretation requires EITHER local hidden variables, OR it requires superluminal hidden variables. I guess this is what Demystifier meant when he described Bohmian mechanics as a specific realization of the statistical interpretation, because BM requires the quantum potential (or equivalent) which takes care of the superluminal stuff. Is that correct?