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

[bhobba]

This thread is in response to another thread where the issue of what De-Broglie's interpretation says came up.

For reference here is a paper that details it:
http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf

It was posted that theory contains a singularity at the particle. But, as the reference points out, it is only like a singularity to a first approximation.

It was also posted that, in that interpretation, cohesion is lost when wave-function collapse occurred. I could not find anything on cohesion in the theory, but that was clarified to mean in phase.

But that leaves me scratching my head because the interpretation specifically states it remains constantly in phase with it. In fact on page 9 it is proved that must always be the case. But, since quantum objects are subject to constant observation all the time it would quickly loose any phase.

I pointed out the interpretation was similar to DBB. That was not thought to be correct because the wave-function isn't real in De-Brogloie.

I don't want to get into a fruitless semantic argument, but since they both have particles associated with waves that is the sense I mean it is similar.

Anyway if anyone wants to continue the discussion - feel free.

Thanks
Bill

 

[bhobba]

I have been going through the paper and the first thing I note is the physical wave v is connected to the wave function u by u = cv where c is a normalising factor. This of course means its exactly the same, physically, as far as QM is concerned, as the wave-function. Because of that its pretty much the same as DBB - although slightly different in that the guiding wave is related to the wave-function by a simple constant which de-Broglie introduces for his own reasons.

Thanks
Bill

 

[liquidspacetime]

First, let's decide which de Broglie theory is under discussion. I am discussing de Broglie's Double Solution theory, not his pilot-wave theory. In order to distinguish between the two I am going to refer to the physical wave of de Broglie's Double Solution theory as the physical wave which guides the particle.

Also, DBB is incorrectly named as de Broglie disagreed with it. It should be referred to as Bohmian mechanics which is what I will call it.

In Bohmian mechanics the wavefunction is considered to be physically real. de Broglie disagreed with this. In de Broglie's Double Solution theory there is the physical wave which guides the particle and the wavefunction wave which is a statistical, non-physical, mathematical construct used to determine the probabilistic results of experiments.

In order to observe the quantum object you need to physically interact with it. When you strongly interact with the particle the particle is no longer in phase with its associated physical wave.

de Broglie uses the term singularity to refer to the particle, which occupies a very small region of the associated wave.

'Interpretation of quantum mechanics by the double solution theory - Louis de BROGLIE'
http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf

“When in 1923-1924 I had my first ideas about Wave Mechanics I was looking for a truly concrete physical image, valid for all particles, of the wave and particle coexistence discovered by Albert Einstein in his "Theory of light quanta". I had no doubt whatsoever about the physical reality of waves and particles.”

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

"For me, the particle, precisely located in space at every instant, forms on the v wave a small region of high energy concentration, which may be likened in a first approximation, to a moving singularity."

"the particle is defined as a very small region of the wave"

A particle may be likened in a first approximation to a moving singularity which occupies a very small region of its associated physical wave. The physical wave propagates through the hidden medium.

It is the particle, the moving singularity, which passes through a single slit in a double slit experiment. It is the associated physical wave in the hidden subquantum medium which passes through both.

 

[bhobba]

First, let's decide which de Broglie theory is under discussion. I am discussing de Broglie's Double Solution theory, not his pilot-wave theory. In order to distinguish between the two I am going to refer to the physical wave of de Broglie's Double Solution theory as the physical wave which guides the particle.

But they are related by a simple constant.

You are really pushing it saying multiplying something by a constant turns something from unreal to real. All that does is change units.

Thanks
Bill

 

[bhobba]

It is the particle, the moving singularity, which passes through a single slit in a double slit experiment. It is the associated physical wave in the hidden subquantum medium which passes through both.

Lets be clear - he specifically states 'For me, the particle, precisely located in space at every instant, forms on the v wave a small region of
high energy concentration, which may be likened in a first approximation, to a moving singularity.'

He may use singularity later - but that's simply being lazy - he specifically states its only like a singularity, and then only to first approximation. Its important to understand exactly what he means by the term.

Thanks
Bill

 

[liquidspacetime]

But they are related by a simple constant.

You are really pushing it saying multiplying something by a constant turns something from unreal to real. All that does is change units.

Thanks
Bill

I'm discussing physical reality. In de Broglie's double solution theory there is a physical wave which physically guides the particle. This is a completely different wave than a wavefunction wave which exists in a purely fictitious configuration space. Meaning, the wavefunction wave is a mathematical construct only, it doesn't physically exist.

"Schrödinger’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 Schrödinger'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.

So I saw clearly that the pilot-wave theory could not supply the interpretation I sought; it did not achieve the clearcut separation of the objective and subjective, which had been given up by Bohr and his disciples, but which it was necessary to maintain if I was to arrive at a concrete and causal interpretation of Wave Mechanics.
On the other hand, my original theory of the Double Solution, by distinguishing the W wave, with its probabilistic and subjective character, from the singularity-wave (« wave), which was to be a description of objective reality, might possibly supply the more classical type of interpretation I was after But I knew only too well that the theory of the double solution likewise involved numerous difficulties, especially when it came to the existence and form of singularity-waves and to their relation to the W waves, or when one had to interpret in terms of singularity-waves interference experiments of the Young-slit type, etc.
Confronted with ail these difficulties, I gave up these attempts, for their outcome struck me as far too problematical. From 1928 on I embraced Bohr's probabilistic interpretation as the basis of my personal research, my teaching and my books.
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.

I thereby succeeded in representing the motion of the interacting particles as being effected in physical space, without being obliged to have recourse to configuration space. This fictitious space and the propagation of the W wave in that space would then become merely tools for calculation convenient in making statistical predictions." - de Broglie

 

[liquidspacetime]

Lets be clear - he specifically states 'For me, the particle, precisely located in space at every instant, forms on the v wave a small region of
high energy concentration, which may be likened in a first approximation, to a moving singularity.'

He may use singularity later - but that's simply being lazy - he specifically states its only like a singularity, and then only to first approximation. Its important to understand exactly what he means by the term.

Thanks
Bill

What's important to understand is it is that singularity which travels a well defined path through a single slit in a double slit experiment. It is the associated physical wave in the hidden medium which passes through both.

 

[bhobba]

It is the particle, the moving singularity, which passes through a single slit in a double slit experiment. It is the associated physical wave in the hidden subquantum medium which passes through both.

Since his wave function is related to the DBB wave-function by a simple constant its exactly the same in DBB as well. Indeed many DBB guys don't think its real either, simply a codification of sub-quantum processes.

Thanks
Bill

 

[liquidspacetime]

Since his wave function is related to the DBB wave-function by a simple constant its exactly the same in DBB as well. Indeed many DBB guys don't think its real either, simply a codification of sub-quantum processes.

Thanks
Bill

However, the wavefunction wave exists in configuration space, which is also fictitious. You also get into problems with Bohmian mechanics being a hidden variable theory and non-local where de Broglie's Double Solution theory is not a hidden variable theory and is not non-local.

You're mistaking making mathematical changes with the underlying physical understanding of the theory.

There is a physical wave in de Broglie's Double Solution theory which doesn't exist in Bohmian mechanics.

 

[bhobba]

I'm discussing physical reality. In de Broglie's double solution theory there is a physical wave which physically guides the particle. This is a completely different wave than a wavefunction wave which exists in a purely fictitious configuration space. Meaning, the wavefunction wave is a mathematical construct only, it doesn't physically exist.

You can quote all you like.

It is however simply the wave-function multiplied by a constant - see page 3.

That is simply a change of units.

Now, please explain in your own words, not via quote or a link, but in your own words, why he does that?

Thanks
Bill

 

[bhobba]

However, the wavefunction wave exists in configuration space

Then his wave is equally fictitious since its a simple constant multiple.

But to forestall further going around in circles he, like DBB, associates it with the wave of a single particle which avoids the issue.

Thanks
Bill

 

[liquidspacetime]

You can quote all you like.

It is however simply the wave-function multiplied by a constant - see page 3.

That is simply a change of units.

Now, please explain in your own words, not via quote or a link, but in your own words, why he does that?

Thanks
Bill

You can ignore the quotes all you like. However, you will continue to not understand the whole point of de Broglie's double solution theory if you choose to do so.

In de Broglie's double solution theory there are two waves. There is the physical wave which guides the particle and the wavefunction wave of quantum mechanics.

There are two waves. That's why he named the theory the double solution theory.

He does that because there is a statistical, non-physical, mathematical wavefunction wave in his Double Solution theory.

There is also a physical wave which guides the particle.

 

[liquidspacetime]

Then his wave is equally fictitious since its a simple constant multiple.

But to forestall further going around in circles he, like DBB, associates it with the wave of a single particle which avoids the issue.

Thanks
Bill

Correct. de Broglie's wavefunction wave is as fictitious as the wavefunction wave of Bohmian mechanics as they are the same statistical, non-physical, mathematical construct.

In de Broglie's double solution theory there is also the physical wave which guides the particle.

 

[bhobba]

You can ignore the quotes all you like. However, you will continue to not understand the whole point of de Broglie's double solution theory if you choose to do so.

I am simply stating a fact.

Now, in your own words why does he do that?

I can probably go through the paper and nut it out. But you are the one promulgating this interpretation, so you should be able to explain why.

Thanks
Bill

 

[liquidspacetime]

I am simply stating a fact.

Now, in your own words why does he do that?

I can probably go through the paper and nut it out. But you are the one promulgating this interpretation, so you should be able to explain why.

Thanks
Bill

He does that because there are two waves in his Double Solution theory. That's why he called it the Double Solution theory. There is the mathematical, statistical, non-physical wavefunction wave which he uses to determine the probabilistic results of experiments. There is also the physical wave which guides the particle.

 

[bhobba]

Correct. de Broglie's wavefunction wave is as fictitious as the wavefunction wave of Bohmian mechanics as they are the same statistical, non-physical, mathematical construct.

No - they are exactly the same. The issue comes when you have entangled particles - they can't be described by a wave - simply something that resides in Hilbert space. A single particle can - a fact both DBB and De-Broglie make use of.

Added Later:
Here I mean interpreting it as a wave - that can only be done for single particles - entangled particles of course still have a wave-function - but can't be interpreted as a wave. In that case the wave part of pilot-wave is a misnomer.

Thanks
Bill

 

[bhobba]

He does that because there are two waves in his Double Solution theory.

That can't be - because its a simple multiple of it. All that does is change units.

He is undoubtedly doing it for some reason - I would simply like you to explain what it is.

Again to forestall going around in circles I consulted the paper. C is introduced because the particle is concentrated in a very small region - see equation 34 and 35 in the linked paper.

Thanks
Bill

 

[liquidspacetime]

No - they are exactly the same. The issue comes when you have entangled particles - they can't be described by a wave - simply something that resides in Hilbert space. A single particle can - a fact both DBB and De-Broglie make use of.

Thanks
Bill

Correct. In terms of determining the probabilistic results of experiments.

However, the non-physical, statistical, mathematical construct wavefunction wave which is part of the fictitious configuration space does not explain what is occurring physically in nature.

You need the PHYSICAL wave and a PHYSICAL understanding of what is occurring PHYSICALLY in nature to do that.

 

[liquidspacetime]

That can't be - because its a simple multiple of it. All that does is change units.

He is undoubtedly doing it for some reason - I would simply like you to explain what it is.

Thanks
Bill

Are you saying you are unable to understand there are two waves in de Broglie's double solution theory? One statistical and one physical?

 

[bhobba]

Are you saying you are unable to understand there are two waves in de Broglie's double solution theory? One statistical and one physical?

That's exactly what I am saying. Since its multiplying by a simple constant all it is is a change of units.

I sorted why he does it - see equation 34 and 35 - its because his particle is concentrated in a small region.

Thanks
Bill

 

[bohm2]

You also get into problems with Bohmian mechanics being a hidden variable theory and non-local where de Broglie's Double Solution theory is not a hidden variable theory and is not non-local.

So the model is both local and realistic, correct? Can you explain how such a model can avoid non-locality to explain the perfect correlations that are observed in the usual EPR-Bell scenario (when a=b)?

 

[bhobba]

You are missing a key point about statistical and physical.

In both DBB and De-Broglie statistical arises from lack of knowledge of initial conditions.

Thanks
Bill

 

[liquidspacetime]

That's exactly what I am saying. Since its multiplying by a simple constant all it is is a change of units.

I sorted why he does it - see equation 34 and 35 - its because his particle is concentrated in a small region.

Thanks
Bill

I don't know what to tell you. The whole point of de Broglie's double solution theory is that there are two waves. Throughout the following, de Broglie refers to the statistical W wave and the physical u wave.

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

"However, as the work of other scientists led to further progress in Wave Mechanics, it became daily more evident that the W wave with its continuous amplitude could be used only in statistical predictions. ... and that is what led me, around 1925—1927, to believe that all problems of Wave Mechanics required a set of two coupled solutions of the wave equation: one the wave, definite in phase, but, because of the continuous character of its amplitude, having only a statistical and subjective meaning; the other, the u wave of the same phase as the W wave but with an amplitude having very large values around a point in space and which, precisely on account of its spatial singularity (a singularity, moreover, which may not be one in the strict mathematical sense of the term) can be used to describe the particle objectively."

"namely, that the equation of the propagation of the u wave is, basically, non-linear and, consequently, different from that admitted for the W wave, even though the two equations may be considered identical almost everywhere."

 

[bhobba]

So the model is both local and realistic, correct?

You beat me to it.

Evading Bells theorem would be a neat trick.

Thanks
Bill

 

[liquidspacetime]

So the model is both local and realistic, correct? Can you explain how such a model can avoid non-locality to explain the perfect correlations that are observed in the usual EPR-Bell scenario (when a=b)?

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.

 

[liquidspacetime]

You are missing a key point about statistical and physical.

In both DBB and De-Broglie statistical arises from lack of knowledge of initial conditions.

Thanks
Bill

Exactly, which is the uncertainty principle. You can't know exactly where the particle exists within its associated wave without detecting it.

Do you think you could at least try and make this a conversation by referring to the non-de Broglie double solution theory as Bohmian mechanics as de Broglie disagreed with what you call DBB?

 

[bhobba]

I don't know what to tell you. The whole point of de Broglie's double solution theory is that there are two waves.

You can quote all you like. Facts are facts. His physical wave is a simply multiple of the wave function. That is simply a change of units.

The reason he does it is explained in the paper.

Since his particle is located in a very small region dividing the wave-function by a large number makes the integrals come out better.

Thanks
Bill

 

[bhobba]

When a downconverted photon pair are created, in order for there to be conservation of momentum, the pair are created with opposite polarizations.

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

 

[liquidspacetime]

You can quote all you like. Facts are facts. His physical wave is a simply multiple of the wave function. That is simply a change of units.

The reason he does it is explained in the paper.

Since his particle is located in a very small region dividing the wave-function by a large number makes the integrals come out better.

Thanks
Bill

His particle is located in a very small region of the associated physical wave, which has nothing to do with the fictitious wavefunction wave.

 

[bhobba]

Exactly, which is the uncertainty principle. You can't know exactly where the particle exists within its associated wave without detecting it.

Thats not the uncertainty principle. What it is has been discussed plenty of times on this forum. Google is your friend

Do you think you could at least try and make this a conversation by referring to the non-de Broglie double solution theory as Bohmian mechanics as de Broglie disagreed with what you call DBB?

Sure - I will call it BM - but as for being that different - I not so sure. But it is different - so point taken.

Thanks
Bill