Wave-particle duality at Macro scale?

  • Thread starter bohm2
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  • #1
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No-one is suggesting that this is exactly the same as the wave-particle duality that exists at the quantum scale (e.g. non-locality) but I thought these papers looking at the behaviour of “walking droplets” that can be seen at the macroscale were very interesting:

By virtue of its wave particle nature, the walking drop exhibits several features previously thought to be peculiar to the microscopic realm, including single-particle diffraction, interference, tunneling, and now, quantized orbits. These studies raise a number of fascinating questions. Are the macroscopic and microscopic worlds really so different? Might the former yet yield insight into the latter? Is there really a connection between this bouncing droplet system and the microscopic world of subatomic particles? Or is it all just an odd coincidence? By virtue of its accompanying pilot wave, the walker’s dynamics are temporally nonlocal, depending on its bouncing history, its memory.

Quantum mechanics writ large
http://www-math.mit.edu/~bush/PNAS-2010-Bush.pdf

Walking Droplets-A form of Wave-particle duality at macroscopic scale?
http://www.df.uba.ar/users/dasso/fis4_2do_cuat_2010/walker.pdf

Path-memory induced quantization of classical orbits
http://www.pnas.org/content/107/41/17515.full.pdf

Full thesis:
http://bictel.ulg.ac.be/ETD-db/coll...1-010800/unrestricted/2011_Terwagne_these.pdf
 

Answers and Replies

  • #2
No-one is suggesting that this is exactly the same as the wave-particle duality that exists at the quantum scale (e.g. non-locality) but I thought these papers looking at the behaviour of “walking droplets” that can be seen at the macroscale were very interesting:



Quantum mechanics writ large
http://www-math.mit.edu/~bush/PNAS-2010-Bush.pdf

Walking Droplets-A form of Wave-particle duality at macroscopic scale?
http://www.df.uba.ar/users/dasso/fis4_2do_cuat_2010/walker.pdf

Path-memory induced quantization of classical orbits
http://www.pnas.org/content/107/41/17515.full.pdf

Full thesis:
http://bictel.ulg.ac.be/ETD-db/coll...1-010800/unrestricted/2011_Terwagne_these.pdf


My! That's got to be one of the cleverest experimental setups ever.
 
  • #3
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Certainly no surprises.

Yves Couder emailed me back this:

Hi,

Your question is excellent. We call a walker the ensemble of the droplet and its associated wave. Since the work you refer to we have shown that the wave field contains a memory of the past trajectory that is at the origin of the quantum like effects we observe. You will find attached a recent work dealing with this effect.
In the double slit experiment, while the droplet passes through one slit the associated wave passes through both so that one coud say that the walker passes through both.
Our system is similar to a pilot wave system and this is what we are working on recently. These models are usually called de Broglie - Bohm models, a term that is very misleading because the two approaches are different from one another.
Bohm gets a dynamical equation from Shrödinger equation so that it concerns the dynamics of a maximum of probability. What de Broglie had in mind was a the dynamics of an individual particle associated with a wave.
Our system appears to be closer to de Broglie.

Best regards

Yves Couder
 
  • #4
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Bohm gets a dynamical equation from Shrödinger equation so that it concerns the dynamics of a maximum of probability. What de Broglie had in mind was a the dynamics of an individual particle associated with a wave. Our system appears to be closer to de Broglie.

I think Antony Valentini is very much supportive of de Broglie's approach vs Bohm's, from my understanding and is particularly critical of imposing a Lorenz-invariant extension into the pilot wave. I'm not sure what Valentini thinks of H. Nikolic's relativistic covariant version of Bohmian mechanics? There does seem to be a divergence of opinion between him and the Goldstein/Durr/Tumulka et al. team also with respect to the ontology of the wave function/pilot wave. The latter treating it as nomological while Valentini prefering a new type of non-local "causal" agent. Regardless, this stuff is very interesting for people who favour the "realist" interpretation. An interesting passage from Valentini is the following:

It has taken some 80 years for de Broglie's theory to be rediscovered, extended and fully understood. Today we realize that de Broglie's original theory contains within it a new and much wider physics, of which ordinary quantum theory is merely a special case-a radically new physics that might perhaps be within our grasp.

In the author’s view, the pilot wave should be interpreted as a new causal agent, more abstract than forces or ordinary fields. This causal agent is grounded in configuration space – which is not surprising in a fundamentally ‘holistic’, nonlocal theory.

Durr et al. have proposed what is, in effect, a mixture of first-order (Aristotelian) dynamics with second-order (Galilean) kinematics. We assert on the basis of the above reasoning that such a mixture is physically incongruous. An Aristotelian dynamics requires an Aristotelian kinematics.

Thus Holland is consistent when he asserts that Galilean invariance is a fundamental symmetry, for he bases the dynamics on the quantum potential. But then things become rather inelegant, and also difficult. The quantum potential itself is inelegant. The Galilean transformation of the wavefunction is mathematically peculiar, having no simple geometrical interpretation. And a Galilean-invariant theory invites attempts at a Lorentz-invariant extension, leading to enormous complications.

Beyond the Quantum
http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.2758v1.pdf

On Galilean and Lorentz invariance in pilot-wave dynamics
http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.4941v1.pdf
 
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  • #5
It's good to see thoughts are evolving since we first discussed this experiment on Physics Forums. I would be interested in having any information on recent Heinz von Foerster congress on Emergent Quantum Mechanics where Yves Couder held the http://www.univie.ac.at/hvf11/congress/EmerQuM.html".
 
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  • #6
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It's good to see thoughts are evolving since we first discussed this experiment on Physics Forums. I would be interested in having any information on recent Heinz von Foerster congress on Emergent Quantum Mechanics where Yves Couder held the opening lecture.

Actually, I was at that conference. What specifically are you interested in?
 
  • #7
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Another interesting paper on this topic. Can someone summarize what the hi-lited parts are implying?

From Abstract:
It is shown that each shock emits a radial travelling wave, leaving behind a localized mode of slowly decaying Faraday standing waves. As it moves, the walker keeps generating waves and the global structure of the wave field results from the linear superposition of the waves generated along the recent trajectory. For rectilinear trajectories, this results in a Fresnel interference pattern of the global wave field. Since the droplet moves due to its interaction with the distorted interface, this means that it is guided by a pilot wave that contains a path memory. Through this wave-mediated memory, the past as well as the environment determines the walker's present motion.

From the body/discussion part of the paper:
Early in the history of quantum mechanics, de Broglie suggested that elementary particles could be guided by their association with a pilot wave (de Broglie 1926). In an attempt to restore determinism in quantum mechanics, this idea was revisited by Bohm (1952). Our system, in which a particle (the droplet) is guided by its associated wave, appears as the first experimental implementation of the idea of a pilot wave and it does lead to quantum-like behaviours. However, in our system, while the association of the particle with the wave is a necessary condition to obtain those behaviours, it is not sufficient. Their observation also requires that the waves contain information on the droplet’s past trajectory, what was called (Fort et al. 2010) the wave-mediated path memory of the system.

When the walker is forced into a circular motion by an applied transverse force, only certain trajectories are possible, generating a wave field with a fixed structure that rotates with the droplet. This leads to a quantization of the possible orbits as shown in Fort et al. (2010). Other dramatic effects of the memory are observed whenever boundaries generate any kind of confinement of the walker. In these situations, the waves emitted in the past and reflected by the boundaries lead to a complex structure of the interference field and correspondingly to a disorder in the droplet motion (Couder & Fort 2006). The present quantitative analysis will be an essential tool for a further investigation of those situations where a forced spatial localization generates an uncertainty in the walker velocity. Finally, the possible relevance of this type of temporal non-locality to particle physics appears an interesting open problem.


Information stored in Faraday waves: the origin of a path memory
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8266690

http://www.lpm.u-nancy.fr/webperso/chatelain.c/GrpPhysStat/PDF/WorshopNancy_EFort.pdf [Broken] (very cool slide presentation!)
 
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This is a real cool video show this quantum-like macroscopic behaviour through the double-slit

Yves Couder . Explains Wave/Particle Duality via Silicon Droplets [Through the Wormhole]

https://www.youtube.com/watch?v=W9yWv5dqSKk
 
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Another paper on this topic that came out:
Macroscopic walkers were shown experimentally to exhibit particle and wave properties simultaneously. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to walkers, no constant inflow of energy is required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show that such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, spontaneous emission of radiation have their counterparts in classical mechanics. In the light of these findings, we hypothesize that quantum mechanics may emerge as approximation from a more profound theory on a deeper level...One can speculate that a concept of wave function may emerge as a mathematical tool to cope with lack of information about all degrees of freedom of a soft body, and the Schrodinger equation may even be deduced from the first principles. Such program is in line with the vision of A. Einstein who predicted: ”Assuming the success of efforts to accomplish a complete physical description, the statistical quantum theory would, within the framework of future physics, take an approximately analogous position to the statistical mechanics within the framework of classical mechanics. I am rather firmly convinced that the development of theoretical physics will be of this type, but the path will be lengthy and difficult.”. The present paper advocates making first steps along this path.
Wave-particle duality in classical mechanics
http://lanl.arxiv.org/pdf/1201.4509.pdf

What I just don't understand is the conflicting opinions on this topic. I thought that the PBR (Pusey-Barrett-Rudolph) theorem that was discussed ad nauseum on this forum ruled out such a possibility (see links below)? I'm lost.

Papers:
The quantum state cannot be interpreted statistically (this is the original paper)
http://lanl.arxiv.org/abs/1111.3328
Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena
http://xxx.lanl.gov/abs/1111.6304
Completeness of quantum theory implies that wave functions are physical properties
http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.6597v1.pdf

Popular:
Quantum theorem shakes foundations
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

Blogs:
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/ (best article)
http://www.scottaaronson.com/blog/?p=822
http://www.fqxi.org/community/forum/topic/999
 
  • #10
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A very interesting lecture presentation (~ 83 minutes) from Perimeter by Yves Couder:
It is usually assumed that the quantum wave-particle duality can have no counterpart in classical physics. We were driven into revisiting this question when we found that a droplet bouncing on a vibrated bath could couple to the surface wave it excites. It thus becomes a self-propelled "walker", a symbiotic object formed by the droplet and its associated wave. Through several experiments, we addressed one central question. How can a continuous and spatially extended wave have a common dynamics with a localized and discrete droplet? Surprisingly, quantum-like behaviors emerge; both a form of uncertainty and a form of quantization are observed. This is interesting because the probabilistic aspects of quantum mechanics are often said to be intrinsic and to have no possible relation with underlying unresolved dynamical phenomena. In our experiment we find probabilistic behaviors and they do have a relation with chaotic individual trajectories. These quantum like properties are related in our system to the non-locality of a walker that we called its "wave mediated path memory". The relation of this experiment with the pilot wave model proposed for quantum mechanics by de Broglie will be discussed.
A Macroscopic-scale Wave-particle Duality : the Role of a Wave Mediated Path Memory
http://pirsa.org/displayFlash.php?id=11100119
 
  • #11
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What I just don't understand is the conflicting on this . I thought that the PBR (Pusey-Barrett-Rudolph) theorem that was discussed ad nauseum on this forum ruled out such a possibility (see links below)? I'm lost.

not yet (and maybe never)...

arguing for ψ-epistemic
Epistemic view of quantum states and communication complexity of quantum channels
Alberto Montina
http://arxiv.org/pdf/1206.2961.pdf

...We show that classical simulations employing a finite amount of communication can be derived from a special class of hidden variable theories where quantum states represent statistical knowledge about the classical state and not an element of reality...
...In this paper, we will show that ψ-epistemic theories have a pivotal role also in quantum communication and can determine an upper bound for the communication complexity of a quantum channel...


Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an
epistemic restriction

Stephen D. Bartlett, Terry Rudolph, Robert W. Spekkens
http://arxiv.org/pdf/1111.5057.pdf

...The success of this model in reproducing aspects of quantum theory provides additional evidence in favour of interpretations of quantum theory where quantum states describe states of incomplete knowledge rather than states of reality...


----
arguing for ψ-ontic

Maximally epistemic interpretations of the quantum state and contextuality
M. S. Leifer, O. J. E. Maroney
http://arxiv.org/pdf/1208.5132.pdf

...This implies that the Kochen-Specker theorem is sufficient to establish both the impossibility of maximally epistemic models and the impossibility of preparation noncontextual models...
..........but
...If one could prove, without auxiliary assumptions, that the support of every distribution in an ontological model must contain a set of states that are not shared by the distribution corresponding to any other quantum state, then these results would follow. Whether this can be proved is an important open question...
 
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buyers beware....


R. Spekkens

http://arxiv.org/pdf/1209.0023v1.pdf
...Such a principle does not force us to operationalism, the view that one should only seek to make claims about the outcomes of experiments...

but he contradicts itself !

http://www.perimeterinstitute.ca/en/Events/Quantum_Foundations_Summer_School/QFSS_Abstracts/ [Broken]
...it is useful to characterize the theory entirely in terms of the observable consequences of experimental procedures, that is to say, operationally...
 
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  • #13
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buyers beware....


R. Spekkens

http://arxiv.org/pdf/1209.0023v1.pdf
...Such a principle does not force us to operationalism, the view that one should only seek to make claims about the outcomes of experiments...

but he contradicts itself !

http://www.perimeterinstitute.ca/en/Events/Quantum_Foundations_Summer_School/QFSS_Abstracts/ [Broken]
...it is useful to characterize the theory entirely in terms of the observable consequences of experimental procedures, that is to say, operationally...
Perhaps pointing out the contradiction would be helpful. I don't see it?
 
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The best I can figure you are drawing a dichotomy between operationalism verses (general) realism. That is to say that you are implying that Spekkens contradicted himseld by on the one hand saying operational descriptions where "useful", while on the other saying we are not forced into operationalism. Only the "law of excluded middle" does not apply here, i.e., the implied dichotomy is false.

Sighting a target through the provided sights of a gun is operationally "useful", but you are by no means required to do so. To provide an operational characterization is indeed useful, regardless of how limited such an operational description is in a given theoretical construct. Just consider what immediately followed what you quoted of Spekkens.

Such a principle does not force us to operationalism, the view that one should only seek to make claims about the outcomes of experiments. For instance, if one didn’t already know that the choice of gauge in classical electrodynamics made no difference to its empirical predictions, then discovery of this fact would, by the lights of the principle, lead one to renounce real status for the vector potential in favour of only the electric and magnetic field strengths. It would not, however, justify a blanket rejection of any form of microscopic reality
 
  • #15
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Perhaps pointing out the contradiction would be helpful. I don't see it?


not a dichotomy, is abrogate a method and later downplay it.
nothing to do with X versus Y...... `realism vs operationalism´ stuff
 
  • #16
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not a dichotomy, is abrogate a method and later downplay it.
nothing to do with X, versus Y...... "realism vs operationalism"
I figured I was off in my characterization of your contradiction. Which is why I asked before making a guess. However, you didn't explain what contradiction you intended with this response?

First off Spekkens never abrogated operationalism, nor its negation. To say some principle does not "force" us into operationalism is not an abrogation of operationalism. Operationalism fully retains its "usefulness" irrespective of whether we entirely restrict ourselves to it or not. neither does admitting the "usefulness" of operationalism downplay the claim that theoretical constructs are not required to be strictly operational descriptions.

I guess what I really need is a better explanation of exactly how you think he may have contradicted himself?
 
  • #17
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To say some principle does not "force" us into operationalism is not an abrogation of operationalism.


who said that ?



.
 
  • #18
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To say some principle does not "force" us into operationalism is not an abrogation of operationalism.
who said that ?

.
I'll answer the above question, but why haven't you answered my question? The same question started with and repeated.

Answer:
Spekkens, from your quote, said: "...Such a principle does not force us into operationalism,... To which you responded to me pointing out the use of the term "force" with: "is abrogate a method and later downplay it".

Question:
So answer the original question... What was the contradiction you thinks Spekkens was guilty of? With the above question you posed I don't even know what you claimed was abrogated or downplayed.
 
  • #19
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I figured I was off in my characterization of your contradiction. Which is why I asked before making a guess. However, you didn't explain what contradiction you intended with this response?

First off Spekkens never abrogated operationalism, nor its negation. To say some principle does not "forces" us into operationalism is not an abrogation of operationalism. Operationalism fully retains its "usefulness" irrespective of whether we entirely restrict ourselves to it or not. neither does admitting the "usefulness" of operationalism downplay the claim that theoretical constructs are not required to be strictly operational descriptions.

I guess what I really need is a better explanation of exactly how you think he may have contradicted himself?

you did, not me......
 
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Apparently you don't want to answer the question. Nor does the above quote make any sense.
 
  • #21
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Nor does the above quote make any sense.

A lot of sense, you attribute to me, things I have not done, but you do not become aware...
see below

Spekkens, from your quote, said: "...Such a principle does not us into operationalism,... To which you responded to me pointing out the use of the term "force" with: "is abrogate a method and later downplay it".

i answered, what ?!
the term FORCE with quotations marks ? :surprised
where !!! i answered that ?
pointing out ?!!! what ?!
no way, re-read the posts and you will see....


read your post 17 and you will see your mistake.
 
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A lot of sense, you attribute to me, things I have not done, but you do not become aware...
see below
Yeah, I accepted that. But I asked for clarification which you never provided.



i answered, what ?!
The problem is you never did answer.


the term FORCE with quotations marks ? :surprised
I put the word "force" in quotations before it was a quote of Spekkens, not you. I even requoted Spekkens and put the word "force" in red so you would know what it referred to.


where !!! i answered that ?
pointing out ?!!! what ?!
no way, re-read the posts and you will see....
How can I see when you still haven't answered my question.

read your post 17 and you will see your mistake.
Post #17 was the one where I admitted my characterization was probably wrong.
I figured I was off in my characterization of your contradiction. Which is why I asked before making a guess. However, you didn't explain what contradiction you intended with this response?
Yet you still have not answered.

Answer this one question:
What contradiction was you referring to in post #13?
Repeat:
What contradiction was you referring to in post #13?
Repeat:
What contradiction was you referring to in post #13?
 
  • #23
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Love these links you throw at us, Bohm2 :-)

But: I'm trying to understand this in a intuitive way as I lack the mathematical insight.

I have two questions regarding the link form an earlier post by Bohm2, november 2011:

Beyond the Quantum by Valentini:
http://arxiv.org/PS_cache/arxiv/pdf/...001.2758v1.pdf [Broken]

On top of page 6, Valentini writes about the fate of The Pilot Wave Theory on the 1927 Solway conference: "de Broglie seems not to have recognized that his dynamics was irreducibly non-
local. Nor was this recognized by anyone else at the conference. The action of
the wave in multidimensional configuration space is such that a local operation
on one particle can have an instantaneous effect on the motions of other (distant)
particles."

Why is the Pilot Wave Theory irreducibly non-local - which aspect of the theory predicts that entangled particles react to each other instantly, disregarding relativity? Can someone please try to explain that to me... in plain english if possible? (It's a classical description of quantum mechanics, so we can start visualising things again, right?)

AND from that same link page 7, line 4:

"Bell made it clear that the pilot wave is a ‘real objective field’ in configuration
space, and not merely a mathematical object or probability wave."

I'm having trouble understanding/picturing what is meant by "configuration space" and a "wave in multidimensional configuration space". Would it be approximately right to think of this wave in configuration space as the wave of each particle existing in it's own space-time interacting with all other particles waves in their space-times... or more dramatic: "The particle's universal wave up against the United Universal Waves of The Universe" ("United Space" for short :-)?

Hope someone can help me to understand this better - I find it very interesting.

Best, Henrik
 
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I'm having trouble understanding/picturing what is meant by "configuration space" and a "wave in multidimensional configuration space".
Not sure if this is what you are looking for or if you've already read the links in that thread but I started a thread on the topic wth many intoductory links on the topic. You might find the papers in that thread very interesting and they're pretty descriptive/more philosophical:

The reality of configuration space
https://www.physicsforums.com/showthread.php?t=554543
 
  • #25
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Just to echo Hernik, thanks for your efforts here, bohm. Once again I've got plenty of new homework waiting for me!
 
  • #26
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This is another interesting paper that recently came out by Y. Couder et al. They discuss the 2 different models proposed by Bohm versus de Broglie's theory of the Double Solution with reference to the diffraction of bouncing droplets:
As a result the wave field is the linear superposition of the successive Faraday waves emitted by past bounces. Its complex interference structure thus contains a memory of the recent trajectory. Furthermore, since the travelling waves move faster than the drop, the wave field also contains information about the obstacles that lie ahead. Hence, two non-local effects exist in the wave-field driving the motion of the droplet: the past bounces influence directly the present (direct propulsion) and the trajectory is perturbed by scattered waves from distant obstacles in a kind of echo-location effect. This interplay between the droplet motion and its associated wave field makes it a macroscopic implementation of a pilot-wave dynamics.
Probabilities and trajectories in a classical wave-particle duality
http://iopscience.iop.org/1742-6596/361/1/012001/pdf/1742-6596_361_1_012001.pdf
 
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  • #27
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This is another interesting paper that recently came out by Y. Couder et al. They discuss the 2 different models proposed by Bohm versus de Broglie's theory of the Double Solution with reference to the diffraction of bouncing droplets:

Probabilities and trajectories in a classical wave-particle duality
http://iopscience.iop.org/1742-6596/361/1/012001/pdf/1742-6596_361_1_012001.pdf
I had overlooked this thread - very interesting, thanks! :smile:
 
  • #28
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"Probabilities and trajectories in a classical wave-particle duality
http://iopscience.iop.org/1742-6596/...1_1_012001.pdf"

That was great fun to read, bohm2. Adding the memory of the pilot wave to the explanation of how pilot waves function is the first time in more than 80 years that someone expands de Broglie's dual pilot wave theory, isn't it?

I have a question though: In a passage on the middle of page 4, Couder is describing the result of his diffraction experiment with walkers: "This means that the probability distribution of the deviations of a droplet is given by the
diffraction of a plane wave . This result is similar to what would be obtained with electrons
or photons except that the distribution would then be given by the square of the wave amplitude."

"Similar ... except" What does he mean - is it similar or is it different? Can it be both? So that the result given by a plane wave in two dimensions is directly comparable to a distribution given by the square of the amplitude of a wave in three dimensions - is that the way it should be understood?

Best, Henrik
 
  • #29
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Just to add to the links in case anybody is as fascinated by these experiments as I am I thought I would also post the experiment simulating the Zeeman effect by this same group of physicists:
Physicists in France have used pairs of bouncing droplets on a fluid surface to simulate the Zeeman effect – a phenomenon that played an important role in the early development of quantum mechanics. The ability to simulate purely quantum effects using such a classical system could provide insight into how the mathematics of quantum mechanics should be interpreted.
Level splitting at macroscopic scale
http://stilton.tnw.utwente.nl/people/eddi/Papers/Submitted/Zeeman.pdf [Broken]

Bouncing droplets simulate Zeeman effect
http://physicsworld.com/cws/article/news/2012/jul/09/bouncing-droplets-simulate-zeeman-effect
"Similar ... except" What does he mean - is it similar or is it different? Can it be both? So that the result given by a plane wave in two dimensions is directly comparable to a distribution given by the square of the amplitude of a wave in three dimensions - is that the way it should be understood?
If I'm understanding this (I might not be), I think Jarek in the second link offers a suggestion on that question:
The counterargument is the Bell inequality - the consequence of the squares relating amplitudes and probabilities ... but the same squares appear while we make statistical physics properly (Maximal Entropy Random Walk) - in statistical ensemble of trajectories, amplitudes are probabilities on the end of ensembles of half-trajectories toward past or future and to get probability of getting something in constant time cut, we need to get it from both past and future: multiply both amplitudes.
 
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  • #30
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The counterargument is the Bell inequality - the consequence of the squares relating amplitudes and probabilities ... but the same squares appear while we make statistical physics properly (Maximal Entropy Random Walk) - in statistical ensemble of trajectories, amplitudes are probabilities on the end of ensembles of half-trajectories toward past or future and to get probability of getting something in constant time cut, we need to get it from both past and future: multiply both amplitudes.


Well. I certainly cannot say I understand Jareks words to any depth :-). But it leaves me with the impression/hunch that the plane wave in two dimensions IS directly comparable to the three dimensional wave IF the latter represents a probability distribution and not a physical wave - is that a reasonable interpretation of Jareks comment? Jarek?

Best, Henrik
 
  • #31
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I'm guessing English isn't his first language but it reads better in the link of his article he cites:
There are also essential differences, mainly similar to Nelson’s interpretation, motivation is resemblance to quantum mechanics and that instead of standard evolution there is used so called Bernstein process: situation in both past and future (simultaneously) is used to find the current probability density...Abstract ensembles of four-dimensional scenarios also bring natural intuition about Born rule: the squares relating amplitudes and probabilities while focusing on constant-time cut of such ensemble. In given moment, there meets past and future half-paths of abstract scenarios we consider-we will see that the lowest energy eigenvector of Hamiltonian (amplitude) is the probability density on the end of separate one of these past or future ensembles of half paths. Now the probability of being in given point in that moment is probability of reaching it from the past ensemble, multiplied by the same value for the ensemble of future scenarios we consider-is the square of amplitude.
From Maximal Entropy Random Walk to quantum thermodynamics
http://arxiv.org/pdf/1111.2253v3.pdf

I also found this comment by Jarek discussing deBroglie model analogue of the external vibration frequency induced by Couder group interesting:
Much less problematic view was started by de Broglie in his doctoral paper: that with particle’s energy (E = mc2), there should come some internal periodic process (E = ~hω) and so periodically created waves around - adding wave nature to this particle, so that it has simultaneously both of them. Such internal clock is also expected by Dirac equation as Zitterbewegung (trembling motion). Recently it was observed by Gouanere as increased absorbtion of 81MeV electrons, while this "clock" synchronizes with regular structure of the barrier. Similar interpretation of wave-particle duality (using external clock instead), was recently used by group of Couder to simulate quantum phenomena with macroscopic classical objects: droplets on vibrating liquid surface.The fact that they are coupled with waves they create, allowed to observe interference in statistical pattern of double slit experiment, analogue of tunneling: that behavior depends in complicated way on the history stored in the field and finally quantization of orbits- that to find a resonance with the field, while making an orbit, the clock needs to make an integer number of periods.
 
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  • #32
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A very interesting lecture presentation (~ 83 minutes) from Perimeter by Yves Couder:

A Macroscopic-scale Wave-particle Duality : the Role of a Wave Mediated Path Memory
http://pirsa.org/displayFlash.php?id=11100119

I re-viewed the link.

From 70.10

...Couder is talking about deBroglie’s idea of two waves in quantum mechanics : A standing wave surrounding the particle, and a wave representing probabilities, namely the Schrödinger wave. Couder then compares this idea to the experiments with walkers passing through a slit the size of the wavelength of the standing wave generated by the droplet:

“So in fact if you reconsider our experiment: In a way it suggests a sort of implementation of de Brogle’s idea. Because if you look at one trajectory of our wave/particle association, when you look at the passage of.. at this thing passing through the slit. You have a real particle associated with a standing wave that moves through the slit and doesn’t look at all like it is a plane wave.
But if you look at the statistics, then you will see, that the statistics look, as if you had had a plane wave crossing the slit, so in a way (...) this would be the schrödinger wave.”

So I think I can answer my “similar...except”-question: The distribution of the directions of the droplets in Couder’s experiment with walkers going through slits is similar to the Schrödinger equation in the way that it is simply a probability distribution (due to the wavefronts merging after the slit after the droplet has achieved a random direction during the passing of the slit)- reflecting what Bohr convinced Schrödinger about during his famous visit in Copenhagen.

So IF Couder’s group’s experiments are valid analogies to what goes on at the quantum scale, the experiments not only support de Broglie’s ideas of two types of waves (real standing waves AND a probability-wave) at play in quantum mechanics, but also justify the Copenhagen people’s idea of a genuine randomness at play after a measurement, as well as give enormous credit to Einstein’s view that if it is part of this world it’s gotta behave classically + it contradicts Bohm’s idea of the Schrödinger wave being physical?

Best, Henrik
 
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So IF Couder’s group’s experiments are valid analogies to what goes on at the quantum scale, the experiments not only support de Broglie’s ideas of two types of waves (real standing waves AND a probability-wave) at play in quantum mechanics, but also justify the Copenhagen people’s idea of a genuine randomness at play after a measurement, as well as give enormous credit to Einstein’s view that if it is part of this world it’s gotta behave classically + it contradicts Bohm’s idea of the Schrödinger wave being physical?
I have trouble reconciling these differences. On the one hand, I assumed that the PBR no-go theorem (with some assumptions) requires that the Schodinger wave be ontic. Furthermore, statistical trajectories conforming to the Bohmian trajectories have been observed experimentally. With respect to the trajectories of single particles in Couder's experiments versus Bohmian, note that the Bohmian trajectories obey the "no crossing rule" which are consistent with experiments unlike Couder's. As Couder writes:
Another difference is that the Bohmian trajectories do not cross the symmetry axis of the system. Those passing on the left (right) of the slits are always deviated to the left (right). This can be seen as a characteristic difference between the Bohmian trajectory that concerns a probability density and the individual trajectory of a single particle.
Grossing et al. have modeled a Couder-type system that does actually respect the "no crossing" rule:
To account for this context, we introduce a "path excitation field", which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a "particle" can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as well as the corresponding trajectories and the probability density current. The trajectories are shown to obey a "no crossing" rule with respect to the central line, i.e., between the two slits and orthogonal to their connecting line. This agrees with the Bohmian interpretation, but appears here without the necessity of invoking the quantum potential.
They go on to argue for an advantage of their model over Bohmian:
To fully appreciate this surprising characteristic, we remind the reader of the severe criticism of Bohmian trajectories as put forward by Scully and others.The critics claimed that Bohmian trajectories would have to be described as "surreal" ones because of their apparent violation of momentum conservation. In fact, due to the "no crossing" rule for Bohmian trajectories in Young's double slit experiment, for example, the particles coming from, say, the right slit (and expected at the left part of the screen if momentum conservation should hold on the corresponding macro-level) actually arrive at the right part of the screen (and vice versa for the other slit). In Bohmian theory, this "no crossing" rule is due to the action of the non-classical quantum potential, such that, once the existence of a quantum potential is accepted, no contradiction arises and the trajectories may be considered "real" instead of "surreal". Here we can note that in our sub-quantum approach an explanation of the "no crossing" rule is even more straightforward and actually a consequence of a detailed microscopic momentum conservation. As can be seen in Fig. 1, the (Bohmian) trajectories are repelled from the central symmetry line. However, in our case this is only implicitly due to a "quantum potential", but actually due to the identification of the latter with a kinetic (rather than a potential) energy: As has already been stressed in [15], it is the "heat of the compressed vacuum" that accumulates along said symmetry line (i.e., as reservoir of "outward" oriented kinetic energy) and therefore repels the trajectories. Fig. 1 is in full concordance with the Bohmian interpretation (see, for example, [24] for comparison). However, as mentioned, in our case also a "micro-causal" explanation is provided, which brings the whole process into perfect agreement with momentum conservation on a more "microscopic" level.
An explanation of interference effects in the double slit experiment: Classical trajectories plus ballistic diffusion caused by zero-point fluctuations
http://arxiv.org/pdf/1106.5994v3.pdf

A more philosophical paper and slides by Grossing discussing these ideas can be found here:

The Quantum as an Emergent System
http://www.nonlinearstudies.at/files/ggEmerQuM.pdf
http://iopscience.iop.org/1742-6596/361/1/012008/pdf/1742-6596_361_1_012008.pdf
 
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From the Gerhard Grossing et al. paper in the previous link above the authors mentioned a fortcoming paper to explain entanglement/wholeness/non-locality using analogies/insights from the Couder classical "walking" bouncer experiments:
We shall show in a forthcoming paper how this feature of "wholeness" implies the existence of nonlocal correlations. Due to the nonlocal nature of the involved diffusion wave fields, and based on our proposed model, it should be possible to prove a corresponding identity with entangled states in quantum mechanics.
This paper was just posted today:
This, at least, is what we want to propose here, i.e., that there are further insights to be gained from the experiments of Couder's group, which could analogously be transferred into the modeling of quantum behavior. Concretely, we do believe that also an understanding of nonlocality and entanglement can profitt from the study of said experiments. In fact, one indispensable prerequisite for these experiments to work, one basic commonality of all of them, is that the bath is vibrating itself...
A Classical Framework for Nonlocality and Entanglement
http://lanl.arxiv.org/pdf/1210.4406.pdf
 
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There are some new results from the walking droplets that demonstrate how wave-like statistics arise from an underlying pilot-wave dynamics through deterministic chaos.



What do you think?
 
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