What is De-Broglie's interpretation and how does it relate to DBB theory?

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De Broglie's interpretation, particularly his Double Solution theory, posits that particles are guided by a physical wave, which differs from the wavefunction that exists in a fictitious configuration space. The discussion clarifies that while both De Broglie's theory and Bohmian mechanics (DBB) involve waves associated with particles, De Broglie views the wavefunction as a non-physical construct used for probabilistic predictions. There is contention regarding the concept of singularity in De Broglie's theory, where it is described as a moving singularity that occupies a small region of the guiding wave. Ultimately, the conversation highlights the distinctions between these interpretations and their implications for understanding quantum mechanics.
  • #31
bhobba said:
You have explained previously down-conversion is parametric down-conversion from quantum optics.

Precisely what has that got to do with QM in general?

Thanks
Bill

I am correctly explaining entanglement. I am explain why Bell's theory does not apply to downconverted photons. I'm explaining why de Broglie's double solution theory is realistic and local.
 
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  • #32
bhobba said:
Thats not the uncertainty principle. What it is has been discussed plenty of times on this forum. Google is your friendSure - I will call it BM - but as for being that different - I not so sure. But it is different - so point taken.

Thanks
Bill

There is one wave in Bohmian mechanics, the statistical one. There are two waves in de Broglie's double solution theory, the statistical one and the physical one.
 
  • #33
liquidspacetime said:
His particle is located in a very small region of the associated physical wave, which has nothing to do with the fictitious wavefunction wave.

Nothing to do with it? Excuse me while my head shakes. Its a simple multiple of it.

Thanks
Bill
 
  • #34
bhobba said:
Nothing to do with it? Excuse me while my head shakes. Its a simple multiple of it.

Thanks
Bill

You are mistaking statistics with physical reality. When you say the particle occupies a very small region of it you are saying the particle occupies a very small region of the physical wave. The particle does not physically occupy a very small region of a fictitious wavefunction.
 
  • #35
liquidspacetime said:
I am correctly explaining entanglement. I am explain why Bell's theory does not apply to downconverted photons. I'm explaining why de Broglie's double solution theory is realistic and local.

Please explain exactly how it is non-local, realistic, and explains Bell for entangled electrons.

Thanks
Bill
 
  • #36
liquidspacetime said:
There is one wave in Bohmian mechanics, the statistical one.

That is incorrect.

The wave in BM is very real - its not statistical.

The only difference between De-Broglie and BM is his physical wave is the wave-function divided by a large constant to make his integrals come out nicer - see equations 34 and 35.

Thanks
Bill
 
  • #37
bhobba said:
Please explain exactly how it is non-local, realistic, and explains Bell for entangled electrons.

Thanks
Bill

I assume you mean local, realistic and explains Bell ...

http://en.wikipedia.org/wiki/Bell's_theorem

"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."

de Broglie's double solution theory is not a local hidden variable theory, therefore, Bell's theorem does not apply.

"Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables)"

In order for there to be conservation of momentum, the downconverted photons are created with opposite angular momentums.

Each of the pair can determine the position and momentum of the other based upon their own position and momentum.

de Broglie's double solution theory is a non-local (hidden from us, not from each other) variable theory.
 
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  • #38
liquidspacetime said:
There is one wave in Bohmian mechanics, the statistical one. There are two waves in de Broglie's double solution theory, the statistical one and the physical one.

There are also 2 waves in Bohmian mechanics, the physical one and the statistical one. Like the double solution theory, only the statistical wave is normalized.

In the double solution theory, the physical wave ##v## is also in configuration space, since it is just a constant multiple of ##\psi##.
 
  • #39
bhobba said:
That is incorrect.

The wave in BM is very real - its not statistical.

No according to de Broglie's double solution theory.

"During the summer of 1951, there came to my attention, much to my surprise, a paper by David Bohm which appeared subsequently in The Physical Review [3]. In this paper Bohm went back to my theory of the pilot-wave, considering the W wave as a physical reality* He made a certain number of interesting remarks on the subject, and in particular, he indicated the broad outline of a theory of measurement that seemed to answer the objections Pauli had made to my approach in 1927.3 My first reaction on reading Bohm’s work was to reiterate, in a communication to the Comptes rendus de VAcademic des Sciences [4], the objections, insurmountable in my opinion, that seemed to render impossible any attribution of physical reality to the W wave, and consequently, to render impossible the adoption of the pilot-wave theory."
 
  • #40
atyy said:
There are also 2 waves in Bohmian mechanics, the physical one and the statistical one. Like the double solution theory, only the statistical wave is normalized.

In the double solution theory, the physical wave ##v## is also in configuration space, since it is just a constant multiple of ##\psi##.

Incorrect. The physical wave of de Broglie's double solution theory exists in three-dimensional space.

"An important point is the justification of the guidance formula and of the statistical meaning of the W wave in the case of interacting systems of particles—-a case where the W wave considered in usual Wave Mechanics is supposed to be propagated in configuration space, which is an obviously fictitious space. From the causal point of view adopted by the Double Solution it must be demonstrated that the guidance formula and the statistical interpretation of W both result from interactions between the singular regions of w-type waves evolving in three-dimensional physical space.

Schrodinger’s idea of identifying the W wave of a system in configuration space at first shocked me very greatly, because, configuration space being a pure fiction, this conception deprives the W wave of all physical reality. For me the wave of Wave Mechanics should have evolved in three-dimensional physical space. The numerous and brilliant successes that resulted from adopting Schrodinger's point of view' obliged me to recognize its value; but for a long time I remained convinced that the propagation of the W wave in configuration space was a purely imaginary way of representing wave phenomena which, in point of fact, take place in physical space. We will see in the second part of the present work (Chapter XII) how, from 1927 on, I had sought to develop this approach within the framework of the theory of the Double Solution.

Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of W, arise from the interaction of the particle with a “subquantic medium” which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty space"."
 
  • #41
liquidspacetime said:
Incorrect. The physical wave of de Broglie's double solution theory exists in three-dimensional space.

"An important point is the justification of the guidance formula and of the statistical meaning of the W wave in the case of interacting systems of particles—-a case where the W wave considered in usual Wave Mechanics is supposed to be propagated in configuration space, which is an obviously fictitious space. From the causal point of view adopted by the Double Solution it must be demonstrated that the guidance formula and the statistical interpretation of W both result from interactions between the singular regions of w-type waves evolving in three-dimensional physical space.

Schrodinger’s idea of identifying the W wave of a system in configuration space at first shocked me very greatly, because, configuration space being a pure fiction, this conception deprives the W wave of all physical reality. For me the wave of Wave Mechanics should have evolved in three-dimensional physical space. The numerous and brilliant successes that resulted from adopting Schrodinger's point of view' obliged me to recognize its value; but for a long time I remained convinced that the propagation of the W wave in configuration space was a purely imaginary way of representing wave phenomena which, in point of fact, take place in physical space. We will see in the second part of the present work (Chapter XII) how, from 1927 on, I had sought to develop this approach within the framework of the theory of the Double Solution.

Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of W, arise from the interaction of the particle with a “subquantic medium” which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty space"."

Where are you quoting from? Is it in the paper http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf we are discussing?
 
  • #42
liquidspacetime said:
No according to de Broglie's double solution theory.

What you are saying is de-Brogle didnt think it was. Thats his opinon and he is entitled to it.

But insted of quoting De-Brogle - why not explain in own words why you think so?

IMHO, since De-Broglie's wave is a simple multiple of the wave function it's the same thing. That's my view. De-Broglie explains why he thinks its different after he explains its introduction via equations 34 and 35:

'This result may be interpretated by stating that the current statistical theory considers as spread out in the entire wave, devoid of singularity, that which in reality is totally concentrated in the singularity. It is on account of the foregoing interpretation that I simultaneously considered two distinct solutions of the wave propagation equation connected by eq. (33), one, v, having physical reality, and the other, Ã, normed, and of statistical character. I therefore named this reinterpretation of wave mechanics the double solution theory. By distinction of the two waves v and Ã, the mystery of the double character, subjective and objective, of the wave in the usual theory, vanishes, and one no longer has to give a simple probability representation the strange property of creating observable phenomena. Moreover, the distinction between the v and à waves leads to a new outlook on a large number of important problems such as the interpretation of interference phenomena, measurement theory, distant correlations, definition of pure and mixed states, reduction of a probability wave packet, etc.'

That's how De-Broglie interprets it. He is entitled to do that. Me - I interpret it differently - simply as a change of units more convenient for his view of the nature of the wavefunction.

Thanks
Bill
 
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  • #43
  • #44
liquidspacetime said:
When a downconverted photon pair are created, in order for there to be conservation of momentum, the pair are created with opposite polarizations.

Each of the pair can determine the position and momentum of the other based upon their own position and momentum.

They are not superluminally or physically connected.

They are entangled as they can determine each other's state.

See the 2:00 minute mark in the following.



It is referred to as an exposed variable theory.

I could be mistaken but I don't think it will to get QM predictions. Here is Maudlin's and Grossing's response on the analogy between Couder's stuff and QM:
What the oil-drop experiments provide is a tangible partial analog of the pilot-wave picture, but restricted to single-particle phenomena (that is, this sort of experiment cannot reproduce the sort of phenomena that depend on entanglement). That is because only in the case of a single particle does the wave function have the same mathematical form (a scalar function over space) as do the waves in the oil. Once two particles are involved, the fact that the wave function is defined over the configuration space of the system rather than over physical space becomes crucial, and the (partial) analogy to the oil-drops fails...
Gerhard Groessing agreeing with Maudlin writes:
I agree with Tim Maudlin that it is unclear yet how the Couder experiments can be related to quantum mechanical nonlocality. Having published about 20 papers in recent years on a “subquantum” approach to QM making use of an analogy to Couder’s bouncing droplets, our group recently visited Yves Couder and Emmanuel Fort in Paris, and we agreed that this issue of nonlocality is an open one w.r.t. (in fact, any) fluid mechanics approaches.
Ross Anderson does offer your argument citing the paper you mentioned:
...the droplet experiments do indeed allow you to visualise a pilot wave in the configuration space of two or more particles. In our paper quoted in the above article, Why bouncing droplets are a pretty good model of quantum mechanics, we show that the standing wave created by the droplets bouncing on the vibrating bath is modulated with an analogue of the quantum mechanical wavefunction; where there are two droplets it’s a function of the position and momentum of both of them. In fact you can see \psi with your naked eye in the pictures of the diffraction experiments. Even although this is only a two-dimensional analogue of quantum mechanics, it could be really helpful as a teaching aid, as it can get across the idea of configuration space and the wavefunction in an intuitive and physically realistic way.
But I don't see how Bell's theorem can be avoided. If a local and realistic model was the real deal, it would be a major discovery.
http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/
 
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  • #45
bhobba said:
What you are saying is de-Brogle didbt think it was. Thats his opinon and he is entitled to it.

But insted of quoting De-Brogle - why not explain in own words why you think so?

IMHO, since De-Broglie's wave is a simple multiple of the wave function it's the same thing. That's my view. De-Broglie explains why he thinks its different after he explains its introduction via equations 34 and 35:

'This result may be interpretated by stating that the current statistical theory considers as spread out in the entire wave, devoid of singularity, that which in reality is totally concentrated in the singularity. It is on account of the foregoing interpretation that I simultaneously considered two distinct solutions of the wave propagation equation connected by eq. (33), one, v, having physical reality, and the other, Ã, normed, and of statistical character. I therefore named this reinterpretation of wave mechanics the double solution theory. By distinction of the two waves v and Ã, the mystery of the double character, subjective and objective, of the wave in the usual theory, vanishes, and one no longer has to give a simple probability representation the strange property of creating observable phenomena. Moreover, the distinction between the v and à waves leads to a new outlook on a large number of important problems such as the interpretation of interference phenomena, measurement theory, distant correlations, definition of pure and mixed states, reduction of a probability wave packet, etc.'

That's how De-Broglie interprets it. He is entitled to do that. Me - I interpret it differently - simply as a change of units more convenient for his view of the nature of the wavefunction.

Thanks
Bill

There not the same wave. If you think they are you will never correctly understand physical reality.

Pilot-wave hydrodynamics
John W.M. Bush
http://dspace.mit.edu/openaccess-disseminate/1721.1/89790

"I would be inclined to back, by virtue of its inclusivity, the logical extension of the Many-Worlds Interpretation (Everett 1957), the Many-Many-Worlds Interpretation, according to which each Quantum Interpretation is realized in some edition of the Multimultiverse, and there is even one world in which there is only one world, a world in which quantum statistics are underlaid by chaotic pilot-wave dynamics, there is no philosophical schism between large and small, and beables be."

NON-LINEAR WAVE MECHANICS
A CAUSAL INTERPRETATION
by
LOUIS DE BROGLIE

"Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of W, arise from the interaction of the particle with a “subquantic medium” which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty space"."
 
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  • #46
bohm2 said:
I could be mistaken but I don't think it will to get QM predictions. Here is Maudlin's and Grossing response on the analogy between Couder's stuff and QM:

Gerhard Groessing agreeing with Maudlin writes:

Ross Anderson does offer your argument citing the paper you mentioned:

But I don't see how Bell's theorem can be avoided. If a local and realistic model was the real deal, it would be a major discovery.
http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/

A local and realistic model is/was a major discovery. It's de Broglie's double solution theory.

http://en.wikipedia.org/wiki/Bell's_theorem

"Bell's theorem rules out local hidden variables as a viable explanation of quantum mechanics (though it still leaves the door open for non-local hidden variables)."

In order for there to be conservation of momentum, the downconverted photon pair are created with opposite angular momentums.

Each of the pair can determine the position and momentum of the other based upon their own position and momentum.

de Broglie's double solution theory is a non-local hidden (to us, not to each of the pair) variable theory.
 
  • #47
atyy said:
Where are you quoting from? Is it in the paper http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf we are discussing?

Hi Atty.

He is jumping all over the place.

I am trying to pin it down to specifics which is why I am discussing the paper.

The relevant bit is in equations 34 and 35 in that paper where a very small constant factor is introduced to multiply the normalised wave-function because De-Broglie thinks of the particle as some kind of deformation or something in the wave function. When you do that and calculate some physical quantities it makes sense to introduce it.

However De-Broglie goes further and interprets his small function as 'real' and the usual one not. That's purely his interpretation - and I personally don't agree with it. Since multiplying by a constant simply means a change of units it doesn't change the reality of anything - you are simply working in more convenient units.

Thanks
Bill
 
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  • #48
liquidspacetime said:
NON-LINEAR WAVE MECHANICS
A CAUSAL INTERPRETATION
by
LOUIS DE BROGLIE

Do you have a link? In the double solution theory that de Broglie describes in http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf the phsyical ##v## wave is in configuation space, because it is a constant multiple of the wave function. If you are correct, then de Broglie had more than one double solution theory. In the paper http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf there is a subquantum medium, but it is not the physical ##v## wave.
 
  • #49
liquidspacetime said:
A local and realistic model is/was a major discovery.

He did not discover that because Bell shows its impossible.

Thanks
Bill
 
  • #50
bhobba said:
Hi Atty.

He is jumping all over the place.

I am trying to pin it down to specifics which is why I am discussing the paper.

The relevant bit is in equations 34 and 35 in that paper where a very small constant factor is introduced to multiply the normalised wave-function because De-Broglie thinks of the particle as some kind of deformation or something in the wave function. When you do that and calculate some physical quantities it makes sense to introduce it.

However De-Broglie goes further and interprets his small function as 'real' and the usual one not. That's purely his interpretation - and I personally don't agree with it. Since multiplying by a constant simply means a change of units it doesn't change the reality of anything - you are simply working in more convenient units.

Thanks
Bill

de Broglie does not think, "of the particle as some kind of deformation or something in the wave function". de Broglie thinks of the particle as some kind of deformation of the physical wave.

de Broglie insists the wave function is fictitious and as such the particle is not some kind of deformation of it.
 
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  • #51
atyy said:
Do you have a link? In the double solution theory that de Broglie describes in http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf the phsyical ##v## wave is in configuation space, because it is a constant multiple of the wave function. .

Its the same one.

I think the issue is he is not working through the math, simply getting quotes from all over the place to support a view he has formed form just reading the text and not UNDERSTANDING the math.

Thanks
Bill
 
  • #52
bhobba said:
He did not discover that because Bell shows its impossible.

Thanks
Bill

Bell shows it is impossible for local hidden variables which de Broglie's double solution theory is not.
 
  • #53
atyy said:
Do you have a link? In the double solution theory that de Broglie describes in http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf the phsyical ##v## wave is in configuation space, because it is a constant multiple of the wave function. If you are correct, then de Broglie had more than one double solution theory. In the paper http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf there is a subquantum medium, but it is not the physical ##v## wave.

de Broglie insists configuration space is fictitious so the physical wave can not be in "it".
 
  • #54
bhobba said:
Its the same one.

I think the issue is he is not working through the math, simply getting quotes from all over the place to support a view he has formed form just reading the text and not UNDERSTANDING the math.

Thanks
Bill

You are not UNDERSTANDING the whole point of de Broglie's DOUBLE Solution theory is that there are two waves. That's the DOUBLE in DOUBLE Solution.
 
  • #55
liquidspacetime said:
There not the same wave. If you think they are you will never correctly understand physical reality.

Well since philosophers can never agree on what physical reality is that's hardly surprising.

Me - I say it's what our models tell us - but that's just me.

Thanks
Bill
 
  • #56
bhobba said:
Well since philosophers can never agree on what physical reality is that's hardly surprising.

Me - I say it's what our models tell us - but that's just me.

Thanks
Bill

And de Broglie's DOUBLE Solution model tells us there are two waves. That's what the DOUBLE in DOUBLE Solution means. You can disagree with that model if you choose to but your insistence there is only one wave in de Broglie's DOUBLE Solution theory is nonsense.

de Broglie continually descibes, in his model, one of the waves as the W wave and the other wave as the u wave.
 
  • #57
liquidspacetime said:
de Broglie insists configuration space is fictitious so the physical wave can not be in "it".

I believe you misunderstand de Broglie http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf. There is potentially a wave in physical space, which is the subquantum medium. However this is not ##v##, which is what de Broglie calls a physical wave but is in configuration space. There is also a statistical wave ##\psi## which is also in configuration space. The double solution refers to ##v## and ##\psi## and does not refer to the subquantum medium.
 
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  • #58
liquidspacetime said:
You are not UNDERSTANDING the whole point of de Broglie's DOUBLE Solution theory is that there are two waves. That's the DOUBLE in DOUBLE Solution.

After going through it I understand it only too well.

De-Broglie is making an interpretive assumption I do not agree with.

As for such a wave-function, if the theory is correct, depending on some sub-quantum realm then I would say that's quite likely.

Thanks
Bill
 
  • #59
atyy said:
I believe you misunderstand de Broglie http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf. There is potentially a wave in physical space, which is the subquantum medium. However this is not ##v##, which is what de Broglie calls a physical wave but is in configuration space. There is also a statistical wave ##\psi## which is also in configuration space. The double solution refers to ##v## and ##\psi## and does not refer to the subquantum medium.

Interpretation of quantum mechanics
by the double solution theory
Louis de BROGLIE

"any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium"

"If a hidden sub-quantum medium is assumed, knowledge of its nature would seem desirable. It certainly is of quite complex character. It could not serve as a universal reference medium, as this would be contrary to relativity theory"

NON-LINEAR WAVE MECHANICS
A CAUSAL INTERPRETATION
by
LOUIS DE BROGLIE

Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of W, arise from the interaction of the particle with a “subquantic medium” which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty space".

"which escapes our observation", as in hidden.
 
  • #60
bhobba said:
After going through it I understand it only too well.

De-Broglie is making an interpretive assumption I do not agree with.

As for such a wave-function, if the theory is correct, depending on some sub-quantum realm then I would say that's quite likely.

Thanks
Bill

That's fine. No one is saying you have to agree with it. However, when you say de Broglie thinks the particle is a deformation of the wave-function then you don't understand it.
 

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