Wave-particle duality at Macro scale?

[bohm2]

Can the double slit illustration in the droplet videos produced intereference patterns?

Yes as posted in a number of posts above:

The wave emitted by the droplet "interfered with its own reflections," and that the droplet's normally straight trajectory deviated when passing through the slit. The remarkable feature was that even with identical initial conditions, the deviation of a given individual walker appeared random, while the deviation of many walkers revealed an interference pattern.

http://phys.org/news78650511.html

Single-particle diffraction and interference at a macroscopic scale
http://users.isy.liu.se/en/jalar/kurser/QF/assignments/Couder2006.pdf

 

[kye]

Yes as posted in a number of posts above:


http://phys.org/news78650511.html

Single-particle diffraction and interference at a macroscopic scale
http://users.isy.liu.se/en/jalar/kurser/QF/assignments/Couder2006.pdf

Why was this missed for a hundred years ago since the lecture by De Broglie about the pilot waves. What's the community reactions to this and what problems they still have to solve or surmount. What's the QFT version of it? I think I read in sciam about black hole being described by fluid dynamics. So does this mean the vacuum is fluid or something like this? What is the ramifications.

 

[bohm2]

Why was this missed for a hundred years ago since the lecture by De Broglie about the pilot waves. What's the community reactions to this and what problems they still have to solve or surmount. What's the QFT version of it? I think I read in sciam about black hole being described by fluid dynamics. So does this mean the vacuum is fluid or something like this? What is the ramifications.

See post # 42. I think it should answer most of your questions.

 

[bohm2]

I thought this was an interesting relationship between Khrennikov's classical model and Couder experiments. Khrennikov evades non-locality by relying on a non-Kolmogorov probability contextual probabilistic model. With respect to correlations seen between trials in the two-slit experiment he argues that:

Trials in the two slit experiment are not independent. We have to test our prediction in physical experiments. At the moment, we do not know where the information about previous trails is accumulated? There are three (less or more natural) possibilities:

(1) It is accumulated in the aperture. A new particle does not go through the aperture independently with previous particles.

(2) Previous particles change a structure of the screen. The position of a new particle on the screen depends on these previous changes.

(3) The source of particles accumulates an information about previous particles.

It seems to be that (1) and (3) are the most important possibilities. What kind of experiments may test these hypothesis? To exclude the correlations in the source of particle, we need a source of single particles which could not accumulate the information on previous particles.To exclude the correlations due to (1) or (2), we have to change both shields ( the shield with apertures and the screen) after each single particle. Hence, we should get only one point on every screen. Finally we should construct the histogram of points using a large statistical ensemble of screens with a single point on each of them. We predict that there should be no interference rings on this histogram or at least the interference should be very weak. Then we may realize experiments to separate hypothesis (1)-(3). For instance, we may change only screens after every experiment with a single particle. These experiments seem to be very simple from the theoretical point of view.

p-adic probability prediction of correlations between particles in the two-slit and neutron interferometry experiments
http://arxiv.org/pdf/0906.0509v1.pdf

I'm thinking there's a better explanation using Couder-type pseudo non-locality/memory effect where the wavelike behaviour of particle trajectories can result from feedback of the remote sensing of the surrounding world by the waves they emit. I thought it was also interesting that there are experiments that show that a time delay between photon release gets rid of the intereference pattern:

In one experiment, Kim et al. controlled the exact interval between independent signal photons emitted in pairs [12]. As the time delay between photons was increased, first-order interference gradually vanished. This shows that the interval between the quanta was more important than the state of the source for the final outcome...

Interpreting Negative Probabilities in the Context of Double-Slit Interferometry
http://arxiv.org/pdf/physics/0611043v1.pdf

 

[bohm2]

Indeed the Couder's experiments are amazing - giving a hope to get below the QM. I've participated in "Emergent Quantum Mechanics" conference in Vienna two years ago - he gave the opening talk and most of speakers expressed excitation about these experiments. If someone is interested, there is second edition (free admission) in a few weeks and Coder will be there: http://srv14116.omansrv14.omanbros.com/

Gerhard Grössing et al. have posted their slide presentation of this recent conference in this group's web page:

Relational Causality and Classical Probability: Grounding Quantum Phenomenology in a Superclassical Theory
http://www.nonlinearstudies.at/files/ggEmQM13.pdf

 

[JAWChemist]

Membrane

Assuming the Couder's experiments are a literal model the quantum particle world, then a logical extrapolation suggests some sort of vibrating membrane would be transferring energy to the particle. The choice of the word membrane was deliberate.

 

[StevieTNZ]

I believe Howard Carmichael, a Professor of Physics, pointed out that in Couder article they mentioned the oil droplet wasn't a quantum system, when I asked him.

 

[bohm2]

Assuming the Couder's experiments are a literal model the quantum particle world, then a logical extrapolation suggests some sort of vibrating membrane would be transferring energy to the particle.

You might want to search papers by Donatello Dolce on some possibilities:

http://www.ph.unimelb.edu.au/~ddolce/

 

[bohm2]

This paper came out today:

In 2005, Couder, Protiere, Fort and Badouad showed that oil droplets bouncing on a vibrating tray of oil can display nonlocal interactions reminiscent of the particle-wave associations in quantum mechanics; in particular they can move, attract, repel and orbit each other. Subsequent experimental work by Couder, Fort, Protiere, Eddi, Sultan, Moukhtar, Rossi, Molacek, Bush and Sbitnev has established that bouncing drops exhibit single-slit and double-slit diffraction, tunnelling, quantised energy levels, Anderson localisation and the creation/annihilation of droplet/bubble pairs.

In this paper we explain why. We show first that the surface waves guiding the droplets are Lorentz covariant with the characteristic speed c of the surface waves; second, that pairs of bouncing droplets experience an inverse-square force of attraction or repulsion according to their relative phase, and an analogue of the magnetic force; third, that bouncing droplets are governed by an analogue of Schrodinger's equation where Planck's constant is replaced by an appropriate constant of the motion; and fourth, that orbiting droplet pairs exhibit spin-half symmetry and align antisymmetrically as in the Pauli exclusion principle. Our analysis explains the similarities between bouncing-droplet experiments and the behaviour of quantum-mechanical particles. It also enables us to highlight some differences, and to predict some surprising phenomena that can be tested in feasible experiments.

Why bouncing droplets are a pretty good model of quantum mechanics
http://arxiv.org/pdf/1401.4356.pdf

Slideshow:
Forty-two? Ground-breaking experiments in the last 10 years
http://www.cl.cam.ac.uk/~rmb4/talk20131015.pdf

 

[bohm2]

Another interesting summary/overview of these experiments:

Fluid Tests Hint at Concrete Quantum Reality
http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/

The comments section is pretty interesting, particularly the discussion by Maudlin, Groessing and Anderson.

 

[atyy]

Another interesting summary/overview of these experiments:

Fluid Tests Hint at Concrete Quantum Reality
http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/

The comments section is pretty interesting, particularly the discussion by Maudlin, Groessing and Anderson.

What a crackpot article! The fluid experiments are only a mathematically analogous, and are not quantum experiments. Also, it insinuates that the pilot-wave theory is making a "come back" - how can it "come back" when it is already a leading solution to the measurement problem, and the only universally acknowledged solution without technical flaws for at least non-relativistic quantum mechanics. Many-worlds is also a leading approach, but it is not universally acknowledged to be without technical problems, even by proponents.

 

[TrickyDicky]

What a crackpot article! The fluid experiments are only a mathematically analogous, and are not quantum experiments.

What specific claim of the article do you find crackpot?

 

[nonequilibrium]

Another interesting summary/overview of these experiments:

Fluid Tests Hint at Concrete Quantum Reality
http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/

The comments section is pretty interesting, particularly the discussion by Maudlin, Groessing and Anderson.

I rather like this article, but it totally loses me at two points:

1. "If space and time behave like a superfluid, or a fluid that experiences no dissipation at all, then path memory could conceivably give rise to the strange quantum phenomenon of entanglement [...] But in the pilot-wave version of events, an interaction between two particles in a superfluid universe sets them on paths that stay correlated forever because the interaction permanently affects the contours of the superfluid."

   
   Firstly, how could the droplet model ever give rise to something mimicing entanglement? After all, while superpositions, quantization, etc are all quite quantum in nature, the TRUE quantum property is entanglement, and we know a classical (local) model, like the droplets, cannot exhibit entanglement. So what are they talking about?
   
   Secondly, in the second part, are they referring to pilot-wave theory as in de Broglie-Bohm theory (as opposed to the droplet analogy)? Because I don't see how pilot-wave theory explains entanglement as a kind of memory-effect.
   
2. space

   "In its current, immature state, the pilot-wave formulation of quantum mechanics only describes simple interactions between matter and electromagnetic fields, according to David Wallace, a philosopher of physics at the University of Oxford in England, and cannot even capture the physics of an ordinary light bulb."

   
   Why would Wallace say that? Surely pilot-wave theory/de Broglie-Bohm theory can explain at least as much as the conventional formulation, since the former contains all the results of the latter... (If David Wallace is claiming that there is no pilot-wave formulation for QFT, well, that's not true.)

Can anyone shed some light on either issue?

 

[atyy]

Another interesting summary/overview of these experiments:

Fluid Tests Hint at Concrete Quantum Reality
http://www.simonsfoundation.org/quanta/20140624-fluid-tests-hint-at-concrete-quantum-reality/

The comments section is pretty interesting, particularly the discussion by Maudlin, Groessing and Anderson.

Good to see that Maudlin had similar complaints about the article that I had!

 

[bhobba]

What a crackpot article! The fluid experiments are only a mathematically analogous, and are not quantum experiments. Also, it insinuates that the pilot-wave theory is making a "come back" - how can it "come back" when it is already a leading solution to the measurement problem, and the only universally acknowledged solution without technical flaws for at least non-relativistic quantum mechanics. Many-worlds is also a leading approach, but it is not universally acknowledged to be without technical problems, even by proponents.

Good to see that Maudlin had similar complaints about the article that I had!

What was it meatloaf said - oh yea - you took the words right out of my mouth.

Could not agree more.

Thanks
Bill

 

[bhobba]

Why would Wallace say that? Surely pilot-wave theory/de Broglie-Bohm theory can explain at least as much as the conventional formulation, since the former contains all the results of the latter... (If David Wallace is claiming that there is no pilot-wave formulation for QFT, well, that's not true.)

I think he is claiming a lot of work hasn't been done on pilot wave QFT - which is true.

Not sure if key theorems have been produced showing QFT as say detailed by Wienberg in his text on the matter is equivalent to a BM version.

Demystifier can probably give more detail.

Thanks
Bill

 

[Demystifier]

Demystifier can probably give more detail.

I've said much, so I will not repeat myself.

 

[TrickyDicky]

Good to see that Maudlin had similar complaints about the article that I had!

He also said he appreciated the article.
I agree with the critic about the pilot wave part, I don't think the experiments with droplets have much to do with de Broglie-Bohm theory except superficially,

The interpretation in relational terms by the Groessing group seems promising though.

 

[bohm2]

Good to see that Maudlin had similar complaints about the article that I had!

Ross Anderson in the comments section disagrees with Maudlin and argues that

...the droplet experiments do indeed allow you to visualise a pilot wave in the configuration space of two or more particles...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 \psi; 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.

He cites his paper:
Why bouncing droplets are a pretty good model of quantum mechanics
http://arxiv.org/pdf/1401.4356v1.pdf

But I had trouble following Anderson's argument even though I've read his paper previously. If anybody can follow Anderson's points, I'd appreciate their input.

 

[Hernik]

The group behind this study has not been able to reproduce Couder's double slit interference pattern from 2006.

In a paper from 2006, Couder and Fort [1] describe a version of the famous double slit experiment performed with drops bouncing on a vibrated fluid surface, where interference in the particle statistics is found even though it is possible to determine unambiguously which slit the “walking” drop passes. It is one of the first papers in an impressive series, showing that such walking drops closely resemble de Broglie waves and can reproduce typical quantum phenomena like tunneling and quantized states [2–13]. The double slit experiment is, however, a more stringent test of quantum mechanics, because it relies upon superposition and phase coherence. In the present comment we first point out that the experimental data presented in [1] are not convincing, and secondly we argue that it is not possible in general to capture quantum mechanical results in a system, where the trajectory of the particle is well-defined.

http://arxiv.org/pdf/1405.0466.pdf

henrik

 

[bohm2]

The group behind this study has not been able to reproduce Couder's double slit interference pattern from 2006.

I'm not sure why they couldn't reproduce their results? I'm also not sure if the MIT team did that particular double-slit experiment with the oil drops. The interesting part, for me, was that Couder team's trajectories are not compatible with Bohmian trajectories since they cross the axis of symmetry of the 2 slits. Bohmian trajectories do not.

 

[atyy]

I'm not sure why they couldn't reproduce their results? I'm also not sure if the MIT team did that particular double-slit experiment with the oil drops. The interesting part, for me, was that Couder team's trajectories are not compatible with Bohmian trajectories since they cross the axis of symmetry of the 2 slits. Bohmian trajectories do not.

But there are many possible forms of Bohmian dynamics (discussed eg. in http://arxiv.org/abs/0706.2522). Do the trajectories not cross in all versions of Bohmian dynamics?

 

[TrickyDicky]

They(Couder et al.) are using the analogy with the original version of the pilot wave theory, the one put forth by de Broglie in 1924-27, that has important differences with Bohm's 1952 theory.

 

[bohm2]

But there are many possible forms of Bohmian dynamics (discussed eg. in http://arxiv.org/abs/0706.2522). Do the trajectories not cross in all versions of Bohmian dynamics?

Yes, Bohmian trajectories do not cross in all versions or else they would not be consistent with QM:

Now recall the physics of the Bohmian evolution, which as we stressed in the introduction prevents trajectories from crossing each other...A trajectory crossing during a numerical simulation means that the simulated time-evolution is not Bohmian anymore, and thus not quantum mechanical, and therefore physically false.

Quantum Dynamics with Bohmian Trajectories
http://arxiv.org/pdf/quant-ph/0701190.pdf
http://cnls.lanl.gov/qt/QT_talks/dirk_talk2.pdf

So this is a difference between Couder's macroscopic quantum-like analogues and Bohmian. Having said that, you might want to look read over post # 33, there's some links discussing this issue. Groessing's stuff is pretty interesting.

 

[nonequilibrium]

With regards to the crossing: I thought the point was rather that in the pilot-wave set-up we are looking at a time-independent solution (as far as the wavefunction is concerned), from which one can easily derive the non-crossing of the particle trajectories. However in the Couder experiments the wavefunction is always localized around the particle and clearly time-dependent. Or are you saying this is a red herring?

 

[bohm2]

Another paper by the Bush team at MIT using the "pilot-wave-like" oil droplet model exploring for the first time possible connections/analogues to relativistic mechanics:

It has recently been demonstrated that droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic realm. The walker, consisting of a droplet plus its guiding wavefield, is a spatially extended object. We here examine the dependence of the walker mass and momentum on its velocity. Doing so indicates that, when the walker’s time scale of acceleration is long relative to the wave decay time, its dynamics may be described in terms of the mechanics of a particle with a speed-dependent mass and a nonlinear drag force that drives it towards a fixed speed. Drawing an analogy with relativistic mechanics, we define a hydrodynamic boost factor for the walkers...Some have further proposed that the interaction of moving particles with this vacuum field could give rise to a speed-dependent inertial mass, a feature of relativistic mechanics. We here explore the relevance of this perspective to the dynamics of walking droplets by inferring their wave-induced added mass.

The wave-induced added mass of walking droplets
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2014/08/Boost-JFM.pdf

 

[liquidspacetime]

de Broglie realizing the medium which waves is chaotic back in the 50's shows how far ahead of his time he was.

'Pilot-Wave Hydrodynamics
John W.M. Bush'
math.mit.edu/~bush/wordpress/wp-content/uploads/2014/09/Bush-ARFM-2015.pdf

"Finally, as concerns my alignment vis-a-vis quantum interpretations, I remain steadfastly agnostic; however, if forced to choose, 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 [wave-function wave], 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"."

John Bell understood.

"While the founding fathers agonized over the question 'particle' or 'wave', de Broglie in 1925 proposed the obvious answer 'particle' and 'wave'. Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored." - John Bell

 

[nonequilibrium]

I like the quote(s), but the pilot-wave obeys the Schrödinger equation, which can hardly be called chaotic? Or is the claim that the Schrödinger equation is merely an effective description of a more chaotic, underlying medium?

 

[liquidspacetime]

I like the quote(s), but the pilot-wave obeys the Schrödinger equation, which can hardly be called chaotic? Or is the claim that the Schrödinger equation is merely an effective description of a more chaotic, underlying medium?

In the de Broglie book referenced in my previous post there are a bunch of references to Schrödinger. I don't have time to go through them all. Maybe the following quote will help you conceptualize what de Broglie is referring to.

"The Wave Mechanics of systems of particles as we have just set forth, following Schrodinger, is an essentially non-relativistic theory because it assumes that the interactions can be represented at every instant by functions of the actual separation distances of the particles, whereas in a relativistic theory of interactions, these interactions are propagated at a finite velocity, which introduces retardation of one sort or another. A relativistic Wave Mechanics of the systems cannot be developed along the lines we have indicated, and only recently has there been any attempt to construct such a Mechanics within the framework of Quantum Field Theory (works by Tomonaga, Schwinger, Feynman, etc.). Let us simply emphasize the fact that the theory set forth above is valid only for the Newtonian approximation.
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."

In the following article the aether has mass and is what waves in a double slit experiment. It discusses the Schrödinger equation. Not sure if this answers your question.

'From the Newton's laws to motions of the fluid and superfluid vacuum: vortex tubes, rings, and others'
http://arxiv.org/abs/1403.3900

 

[liquidspacetime]

Another paper by the Bush team at MIT using the "pilot-wave-like" oil droplet model exploring for the first time possible connections/analogues to relativistic mechanics:

The wave-induced added mass of walking droplets
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2014/08/Boost-JFM.pdf

'Fluidic Electrodynamics: On parallels between electromagnetic and fluidic inertia'
http://arxiv.org/abs/1202.4611

"It is shown that the force exerted on a particle by an ideal fluid produces two effects: i) resistance to acceleration and, ii) an increase of mass with velocity. ... The interaction between the particle and the entrained space flow gives rise to the observed properties of inertia and the relativistic increase of mass. ... Accordingly, in this framework the non resistance of a particle in uniform motion through an ideal fluid (D’Alembert’s paradox) corresponds to Newton’s first law. The law of inertia suggests that the physical vacuum can be modeled as an ideal fluid, agreeing with the space-time ideal fluid approach from general relativity."

 

[bohm2]

A more critical paper came out yesterday hi-liting some of the differences between QM, Bohmian mechanics and bouncing droplet analogues:

While Bohmian quantum mechanics exhibits nonlocal features , the evolution of the droplet and the surface waves is rooted in hydrodynamics which is manifestly a local theory, unless incompressibility is assumed.

In the de Broglie-Bohm interpretation, the specific trajectory of the quantum particle does not backact onto the evolution of the wavefunction, whereas the droplet creates new surface waves at the position where it bounces. Those surface waves do evolve, to a very good approximation, according to a linear theory, but a direct mapping to the Schrodinger equation is not obvious...More importantly, however, the probability of finding a droplet in the minima never reaches zero as it does for a particle in the quantum case.

Here we note a striking contrast between the trajectories in the bouncing droplet system and those resulting from Bohmian mechanics. One of the tenants of Bohmian trajectories is that the trajectories are forbidden to cross each other, and in the double-slit experiment the trajectories from each slit will not cross the center line, but it is obvious that the trajectories in Fig. 5(d) have no such reluctance to do so.

With increasing which path information the probability density becomes more dependent on a single slit. Consequently the observed interference pattern becomes less pronounced as it is the wave function arising from both slits that gives rise to the pattern. We can make an analogy in the bouncing droplet system with the memory parameter being analogous to the which path information...The visibility will increase with increasing memory but never reach one, in contrast to quantum particles with a which path information of zero.

In view of this, it is not obvious to what extent the present classical analogy of quantum wave-particle duality can be maintained in more complex situations involving, e.g., more than one droplet.

On the analogy of quantum wave-particle duality with bouncing droplets
http://arxiv.org/pdf/1410.1373.pdf

 

[liquidspacetime]

A more critical paper came out yesterday hi-liting some of the differences between QM, Bohmian mechanics and bouncing droplet analogues:

On the analogy of quantum wave-particle duality with bouncing droplets
http://arxiv.org/pdf/1410.1373.pdf

Which is completely missing the point. Walking droplets have nothing to do with Bohmian mechanics. de Broglie-Bohm theory is incorrectly named as de Broglie disagreed with it.

"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." - de Broglie

In de Broglie's wave mechanics and double solution theory there are two waves. There is the physical wave which guides the particle and the associated wavefunction wave which is a mathematical construct only which does not physically exist.

Walking droplets have to do with de Broglie's wave mechanics and double solution theory, not Bohmian mechanics (or the incorrectly named de Broglie-Bohm theory)

See the 2:36 mark in the following video. It says, "This physical picture is remarkably similar to an early model of quantum dynamics proposed by Louis de Broglie...". Nothing to do with Bohmian mechanics.

'The pilot-wave dynamics of walking droplets'


Your own response from Yves says the same thing.

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 could 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

Physicists can discuss flying unicorns if they want to refute walking droplets as being analogous to quantum reality. Flying unicorns are as physically real as the wavefunction wave of Bohmian mechanics.

 

[bohm2]

Which is completely missing the point. Walking droplets have nothing to do with Bohmian mechanics. de Broglie-Bohm theory is incorrectly named as de Broglie disagreed with it.

Yes, I know. But if trajectories cross, then you won't get QM predictions.

Now recall the physics of the Bohmian evolution, which as we stressed in the introduction prevents trajectories from crossing each other...A trajectory crossing during a numerical simulation means that the simulated time-evolution is not Bohmian anymore, and thus not quantum mechanical, and therefore physically false.

See post 94.

 

[liquidspacetime]

Yes, I know. But if trajectories cross, then you won't get QM predictions.

See post 94.

What part of this has nothing to do with Bohmian mechanics are you unable to understand?

Watch the following video starting at the 2:40 mark. The trajectories cross the middle plane.

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


'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

"Figure 5. The simulation of the motion of a hundred walkers impinging on a slit. Note that, as in the experiment, some trajectories cross the symmetry axis of the apparatus."

'Implications of Lorentz covariance for the guidance equation in two-slit quantum interference'
http://arxiv.org/pdf/quant-ph/0302076.pdf

"The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry."

'Fluid mechanics suggests alternative to quantum orthodoxy'
http://phys.org/news/2014-09-fluid-mechanics-alternative-quantum-orthodoxy.html

"Last year, Bush and one of his students—Jan Molacek, now at the Max Planck Institute for Dynamics and Self-Organization—did for their system what the quantum pioneers couldn't do for theirs: They derived an equation relating the dynamics of the pilot waves to the particles' trajectories."

Walking droplets have to do with de Broglie wave mechanics and double solution theory. de Broglie's wave mechanics and double solution theory has nothing to do with Bohmian mechanics.

You keep on insisting on referring to Bohmian mechanics, which has nothing to do with walking droplets, in order to refute walking droplets. Why is that?

Bohmian mechanics is fundamentally flawed. Bohmian mechanics does not correctly represent physical reality. Bohmian mechanics has nothing to do with physical reality. Bohmian mechanics has nothing to do with walking droplets.

Do you understand de Broglie's wave mechanics and double solution theory is a completely separate theory than Bohmian mechanics?

In Bohmian mechanics the particles can not cross the axis of symmetry. Who cares? We are discussing walking droplets and de Broglie's wave mechanics and double solution theory.

 

[bohm2]

You keep on insisting on referring to Bohmian mechanics, which has nothing to do with walking droplets, in order to refute walking droplets. Why is that?.

I'm not trying to refute anything. I'm interested in understanding how close of a quantum analogue, the walking droplet model is. I was under the impression (maybe wrongly) that if trajectories cross-over, then that model isn't a good quantum analogue.

Bohmian mechanics is fundamentally flawed. Bohmian mechanics does not correctly represent physical reality. Bohmian mechanics has nothing to do with physical reality.

Why is Bohmian mechanics fundamentally flawed?