Wave-particle duality at Macro scale?

[bohm2]

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/collection/available/ULgetd-09262011-010800/unrestricted/2011_Terwagne_these.pdf

 

[PatrickPowers]

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/collection/available/ULgetd-09262011-010800/unrestricted/2011_Terwagne_these.pdf

My! That's got to be one of the cleverest experimental setups ever.

 

[StevieTNZ]

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 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

 

[bohm2]

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

 

[ArjenDijksman]

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".

 

[akhmeteli]

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?

 

[bohm2]

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 traveling 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 (very cool slide presentation!)

 

[bohm2]

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

 

[bohm2]

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

 

[bohm2]

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

 

[audioloop]

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...

 

[audioloop]

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/
...it is useful to characterize the theory entirely in terms of the observable consequences of experimental procedures, that is to say, operationally...

 

[my_wan]

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/
...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?

 

[my_wan]

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

 

[audioloop]

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

 

[my_wan]

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?

 

[audioloop]

To say some principle does not "force" us into operationalism is not an abrogation of operationalism.

who said that ?



.

 

[my_wan]

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.

 

[audioloop]

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...

 

[my_wan]

Apparently you don't want to answer the question. Nor does the above quote make any sense.

 

[audioloop]

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 ?
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.

 

[my_wan]

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 ?

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?

 

[Hernik]

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

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.

Henrik

 

[bohm2]

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

 

[eloheim]

Just to echo Hernik, thanks for your efforts here, bohm. Once again I've got plenty of new homework waiting for me!

 

[bohm2]

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 traveling 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

 

[harrylin]

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!

 

[Hernik]

"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?

Henrik

 

[bohm2]

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

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.

 

[Hernik]

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?

Henrik

 

[bohm2]

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.

 

[Hernik]

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 got to behave classically + it contradicts Bohm’s idea of the Schrödinger wave being physical?

Henrik

 

[bohm2]

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 got to 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

 

[bohm2]

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

 

[pilotwave]

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?

 

[bohm2]

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?

The video is summarizing most of the stuff linked above. But what is the microscopic equivalent to the vibrating bath seen in droplet experiments? I've come across papers suggesting some form of "intrinsic periodicity" as per de Brogle's idea suggesting that inside the particle there was a periodic process that was equivalent to a clock. Donatello Dolce has published a few papers on this topic, but I haven't seen it much discussed elsewhere:

We interpret the relativistic quantum behavior of elementary particles in terms of elementary cycles. This represents a generalization of the de Broglie hypothesis of intrinsically “periodic phenomenon”, also known as “de Broglie internal clock”. Similarly to a “particle in a box” or to a “vibrating string”, the constraint of intrinsic periodicity represents a semi-classical quantization condition, with remarkable formal correspondence to ordinary relativistic quantum mechanics. In this formalism the retarded local variations of four-momentum characterizing relativistic interactions can be equivalently expressed in terms of retarded local modulations of de Broglie space-time periodicity, revealing a geometrodynamical nature of gauge interaction.

On the intrinsically cyclic nature of space-time in elementary particles
http://arxiv.org/pdf/1206.1140.pdf

 

[bohm2]

This is another paper by the Gerhard Grossing et al. group that uses some of the insights gained from the bouncing/walking droplets in the experiments of Couder's group to model certain QM phenomena:

In a new approach to explain double-slit interference "from the single particle perspective" via "systemic nonlocality", we answer the question of how a particle going through one slit can "know" about the state of the other slit. We show that this comes about by changed constraints on assumed classical sub-quantum currents, which we have recently employed to derive probability distributions and Bohm-type trajectories in standard double-slit interference on the basis of a modern, 21st century classical physics. Despite claims in the literature that this scenario is to be described by a dynamical nonlocality that could best be understood in the framework of the Heisenberg picture, we show that an explanation can be cast within the framework of the intuitively appealing Schrodinger picture as well. We refer neither to potentials nor to a "quantum force" or some other dynamics, but show that a "systemic nonlocality" may be obtained as a phenomenon that emerges from an assumed sub-quantum kinematics, which is manipulated only by changing its constraints as determined by the changes of the apparatus. Consequences are discussed with respect to the prohibition of superluminal signaling by standard relativity theory...

As we employ no "quantum force", therefore, we consider "systemic nonlocality" as a phenomenon that emerges from a sub-quantum kinematics, which is manipulated only by changing its constraints as determined by the changes of the apparatus. In fact, with our approach we have in a series of papers obtained essential elements of quantum theory. They derive from the assumption that a particle of energy E = ħω is actually an oscillator of angular frequency ω phase-locked with the zero-point oscillations of the surrounding environment, the latter of which containing both regular and fluctuating components and being constrained by the boundary conditions of the experimental setup via the buildup and maintenance of standing waves. The particle in this approach is an off-equilibrium steady-state maintained by the throughput of zero-point energy from its vacuum surroundings. This is in close analogy to the bouncing/walking droplets in the experiments of Couder's group, which in many respects can serve as a classical prototype guiding our intuition.

"Systemic Nonlocality" from Changing Constraints on Sub-Quantum Kinematics
http://lanl.arxiv.org/pdf/1303.2867.pdf

 

[bohm2]

Some 2013 papers that add to this interesting work in this subject:

We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.

Wavelike statistics from pilot-wave dynamics in a circular corral
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/Harris-Corrals-2013.pdf

Interaction of walking drops and the surface waves reflected from the boundaries or from other drops leads to a variety of interesting phenomena reminiscent of quantum mechanics (Bush 2010). Examples include tunnelling across a subsurface barrier (Eddi et al. 2009b), single-particle diffraction in both single- and double-slit geometries (Couder & Fort 2006), quantized orbits analogous to Landau levels in quantum mechanics (Fort et al. 2010) and orbital level splitting (Eddi et al. 2012). Harris et al. (2013) considered a drop walking in confined geometries, and demonstrated that the resulting probability distribution function is simply related to the most unstable Faraday wave mode of the cavity. Rationalizing these remarkable macroscopic quantum-like phenomena provided the motivation for this study.

Droplets bouncing on a vibrating bath
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/MB1-2013.pdf

Our results form the basis of the first rational hydrodynamic pilot-wave theory.

Droplets walking on a vibrating bath: Towards a hydrodynamic pilot-wave theory
http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/MB2-2013.pdf

Finally, we have highlighted a mixed state, in which the walking drop shifts between two distinct modes, a state that may serve as an analog of a superposed state in quantum mechanics.

Exotic states of bouncing and walking droplets
http://windw.dk/2013Bouncing.pdf

 

[Hernik]

Another paper on the droplets' quantum like behavour. I'm am not able to judge the paper professionally as I'm not a physicist, but it seems to me it's claiming that the behavour of the droplets are not only quantum like but equivalent to quantum mechanics when the differences of the systems are taken into consideration and if experiments reveal certain diffraction patterns. But I'm certainly not sure I'm right about that assumption?

Droplets moving on a fluid surface: interference pattern from two slits
http://arxiv.org/pdf/1307.6920v1.pdf

 

[Hernik]

..Also the paper mentions that droplets and ANTIdroplets can form from waves meeting each other. Something which seems to take place in experiments with oil as well as water. I'd never heard about that.

 

[eloheim]

So my brain had an idea while reading the latter part of this thread... (And forgive me if this has already been discussed/addressed via reference here.) Could there be interesting things to do with this setup (the walker-table) by augmenting the (classical) 'quantum simulations' with_actual_quantum components/extensions/etc.? Unfortunately I don't have any suggestions off the top of my head but it seems there might be interesting qutantum-classical hybrid interactions/experimental scenarios to be explored? ..Are there constraints working against such endeavors due to the 'table-walker' setup?

Also as a quick more general aside: It's obvious that the 'walker' experiments that are the subject of this thread produce a quite amazing variety of quantum-like effects, especially upon first blush for someone not ever having been exposed to such an experimental setup before, or ever even considered the_possibility_ of such a thing! Acknowledging that--I'm wondering if someone can tell me what 'quantumy' effects it CAN'T reproduce?? ..Also (last q): Are there any lorentz-invariance-related issues hanging around in all this?


Thanks again to those taking time to aggregate sources and reference materials and compose or participate in threads such as this one.(!)

 

[bohm2]

Acknowledging that--I'm wondering if someone can tell me what 'quantumy' effects it CAN'T reproduce??

As acknowledged by the some of these authors themselves in this slide presentation, those experiments are still far from QM for the following reasons:

- Macroscopic scale : no relation with Planck constant.
- The system is two-dimensional.
- The system is dissipative and sustained by external forcing.
- This forcing imposes a fixed frequency: the “energy” is fixed
- The waves live on a material medium: there is an “ether

A macroscopic-scale wave-particle duality
http://www.physics.utoronto.ca/~colloq/Talk2011_Couder/Couder.pdf

Another interesting paper recently published by the Grossing group on their model and Born's rule, they also touch on your latter point regarding lorentz-invariance-related issues, etc. :

It has been shown in a series of papers that phenomena of standard quantum mechanics like Gaussian dispersion of wave packets, superposition, double slit interference, Planck's energy relation, or the Schrodinger equation can be assessed as the emergent property of an underlying sub-structure of the vacuum combined with diffusion processes reflecting also the stochastic parts of the zero-point field, i.e. the zero point fluctuations. Thus we obtain the quantum mechanical results as an averaged behavior of sub-quantum processes. The inclusion of relativistic physics has not been considered yet, but should be possible in principle.

Born's Rule as Signature of a Super-Classical Current Algebra
http://arxiv.org/pdf/1308.5924.pdf

 

[audioloop]

“All our experiences tell us we shouldn't have two dramatically different conceptions of reality — there must be one huge overarching theory,” says Abhay Ashtekar, a physicist at Pennsylvania State University in University Park.

 

[bohm2]

“All our experiences tell us we shouldn't have two dramatically different conceptions of reality — there must be one huge overarching theory,” says Abhay Ashtekar, a physicist at Pennsylvania State University in University Park.

Yes, it seems that unification has been the norm in the sciences but I think that one must also recognize that this is still at most a hope that might not be realized, either because nature really is not unified/monistic, or because human cognitive capacities are not capable of discovering that unity. Either alternative is a possibility, I think.

 

[audioloop]

.

I think that one must also recognize that this is still at most a hope that might not be realized

dont despair, is the zeigeist of this epoch.

because human cognitive capacities are not capable of discovering that unity.

are you agnostic ?.

 

[Hernik]

.dont despair, is the zeigeist of this epoch..

There is hope I think. It is not quantum mechanics. But something which is not purely a wave goes through two holes at one time in a classical system. That takes some of the mystery out of quantum mechanics for me. QM might not be unexplainable after all.

And to me it is exiting to follow the attempts to see how far this droplett-analogy to QM can be stretched. How much of the weirdness from QM it might show parallels to in this limited 2-dimensional system. Entanglement of course is the big one.

- Henrik

 

[audioloop]

There is hope I think. It is not quantum mechanics. But something which is not purely a wave goes through two holes at one time in a classical system. That takes some of the mystery out of quantum mechanics for me. QM might not be unexplainable after all.

And to me it is exiting to follow the attempts to see how far this droplett-analogy to QM can be stretched. How much of the weirdness from QM it might show parallels to in this limited 2-dimensional system. Entanglement of course is the big one.

- Henrik

there are similar results from epistemic models.


.

 

[bohm2]

there are similar results from epistemic models.

But it seems to me, that given some arguably reasonable assumptions, ψ-epistemic models can be ruled out as per PBR theorem? So, if one accepts realism, we are stuck with trying to conceptualize entanglement/non-locality in ontic terms which leads to difficulties as noted by van Fraassen:

To speak of instantaneous travel from X to Y is a mixed or incoherent metaphor, for the entity in question is implied to be simultaneously at X and at Y – in which case there is no need for travel, for it is at its destination already...one should say instead that the entity has two (or more) coexisting parts, that it is spatially extended.

The reality of relations: the case from quantum physics
http://philsci-archive.pitt.edu/9959/1/Relations290813.pdf

It is interesting that quite a few authors are suggesting that our familiar space-time is something that might 'emerge' from some more fundamental stuff that is non-spatio-temporal. On the other hand, if one accepts some form of ontic dualism as some Bohmians (e.g. Bohm, Valentini) do, other problems arise:

However, one can with good reason object that simply adding a quantum force when passing from classical to quantum mechanics is an ad hoc move: that force cannot be traced back to properties of the particles, as the gravitational force can be traced back to mass and the electromagnetic force to charge. Moreover, that force cannot be treated in terms of a field defined on physical space, for it does not permit to assign values to points of space-time. If the wave-function, which is supposed to stand for the quantum force on this view, represents a field, it can only be a field on configuration space, that is, the very high dimensional mathematical space each point of which corresponds to a possible configuration of the particles in physical space. However, it is entirely mysterious how a field on configuration space could influence the motion of particles in physical space.

The reality of relations: the case from quantum physics
http://philsci-archive.pitt.edu/9959/1/Relations290813.pdf

 

[Hernik]

there are similar results from epistemic models..

Yes. I should have been more precise: QM might not be unexplainable in classical terms after all. Lots of explanations already.

 

[bohm2]

are you agnostic ?

No, I just think that like all other organisms we have cognitive limitations. There might be stuff we may never be able to fully understand/conceptualize.