How quantum is wave-particle duality of Couder's walking droplets?

[Duda Jarek]

There are getting popularity great Couder's experiments about classical objects having wave-particle duality: oil droplets on vertically vibrating liquid surface - constantly creating periodic waves around - interaction with these waves allows to observe 'quantum effects':interference pattern in double-slit experiment, tunneling depending on practically random hidden parameters or orbit quatization condition - that particle has to 'find a resonance' with field perturbations it creates - after one orbit, its internal phase has to return to the initial state.

It's difficult to find good intuition about these experiments from only static pictures - the first time I had occasion to see videos was on recent congress on emergent quantum mechanics where Couder had the opening lecture and most of speakers were excited about these experiments. Fortunately I've recently found youtube video of these experiments:

 

The main qualitative difference with physics is that while Couder uses external clock, particles should rather have internal one - such understanding of wave-particle duality was started by de Broglie in his doctoral thesis:

that with particle's energy: E = mc^2

comes some internal periodic process: E = hf

It is reminded in very interesting Hestenes paper, in which there is also described recent experimental confirmation of this effect (called e.g. zitterbewegung): http://fqxi.org/data/essay-contest-files/Hestenes_Electron_time_essa.pdf

Such internal periodic motion creates periodic wave-like perturbations of surrounding field - giving localized entity also wave nature ... localized constructions of the field are called soltions, so it suggests to search for particles solitons models, which often have such internal periodic motion, like breathers.

 

What do you think about these experiments? About such understanding of wave-particle duality?

Have particles both natures simultaneously, or maybe only one of them at the time?

In such case when and how it is switched? What about Afshar experiment?

Edited April 4, 2012 by Duda Jarek

[Strange]

Here is an update to this (only 6 years late).

Apparently Couder and his team did claim to recreate the results of the double-slit experiment in 2015 (I missed that). But more recent experiments have failed to reproduce it. And a simple thought experiment shows that the de Broglie pilot wave model cannot work.

Famous Experiment Dooms Alternative to Quantum Weirdness

[Duda Jarek]

Oh, muuuch more has happened - see my slides with links to materials: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

1. Interference in particle statistics of double-slit experiment (PRL 2006) - corpuscle travels one path, but its "pilot wave" travels all paths - affecting trajectory of corpuscle (measured by detectors).

2. Unpredictable tunneling (PRL 2009) due to complicated state of the field ("memory"), depending on the history - they observe exponential drop of probability to cross a barrier with its width.

3. Landau orbit quantization (PNAS 2010) - using rotation and Coriolis force as analog of magnetic field and Lorentz force (Michael Berry 1980). The intuition is that the clock has to find a resonance with the field to make it a standing wave (e.g. described by Schrödinger's equation).

4. Zeeman-like level splitting (PRL 2012) - quantized orbits split proportionally to applied rotation speed (with sign).

5. Double quantization in harmonic potential (Nature 2014) - of separately both radius (instead of standard: energy) and angular momentum. E.g. n=2 state switches between m=2 oval and m=0 lemniscate of 0 angular momentum.

6. Recreating eigenstate form statistics of a walker's trajectories (PRE 2013).

In the slides there are also hydrodynamical analogous of Casimir and Aharonov-Bohm.

[Strange]

Just now, Duda Jarek said:

Oh, muuuch more has happened

So it is clearly an interesting set of experiments but apparently is not a model of (all) quantum effects.

[Duda Jarek]

Sure, it misses a lot from real physics, like it seems impossible to model 3D this way, also clock here is external while in physics it is rather internal of particles (de Broglie's, zitterbewegung):

https://physics.stackexchange.com/questions/386715/does-electron-have-some-intrinsic-1021-hz-oscillations-de-broglies-clock

But these hydrodynamical analogues provide very valuable intuitions about the real physics ...

[Duda Jarek]

Lecture about these experiments by Yves Couder: https://www.youtube.com/watch?v=QvHREXA3cl0
By John Bush: https://www.youtube.com/watch?v=8MsMuQa80fI
Materials and great videos: http://dualwalkers.com/
More materials about hydrodynamical QM analogues: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

[joigus]

I meant to +1 Strange on the update to Couder.

I remember back when I studied quantum mechanics, at some point we tackled the really hairy aspects of the mathematics. There were several attempts to formulate QM based on real numbers, quaternions and even octonions, if I remember correctly. The argument was that using a complex-number based mapping of the amplitudes seemed to be minimally essential to describing its properties satisfactorily. If that's true (I didn't completely understand the reason because it was not explained in detail,) it would be too much to expect that waves that are well-modeled by real functions would be able to reproduce all of QM. Especially fermions. Analogically mimicking photons would be a problem too, for obvious reasons.

I'm confident that once we understand where the logical necessity of using complex numbers arises, we will understand the nature of a double solution better than De Broglie-Bohm. That's why I've voted for the 1st option.

On 10/13/2018 at 10:47 PM, Duda Jarek said:

Oh, muuuch more has happened - see my slides with links to materials: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

1. [...]

In the slides there are also hydrodynamical analogous of Casimir and Aharonov-Bohm.

+1. Thank you. But those are pre-2015. Aren't they?

[Strange]

There should have been a “neither of the above” (or “it’s complicated”) option in the poll

36 minutes ago, joigus said:

I remember back when I studied quantum mechanics, at some point we tackled the really hairy aspects of the mathematics. There were several attempts to formulate QM based on real numbers, quaternions and even octonions, if I remember correctly. The argument was that using a complex-number based mapping of the amplitudes seemed to be minimally essential to describing its properties satisfactorily. If that's true (I didn't completely understand the reason because it was not explained in detail,) it would be too much to expect that waves that are well-modeled by real functions would be able to reproduce all of QM.

You might be interested in this article: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

 

[Duda Jarek]

1 hour ago, joigus said:

But those are pre-2015. Aren't they?

Most are pre-2015, more recent is e.g. anti-ferromagnet: https://math.mit.edu/~dunkel/Papers/2018SaEtAl_PRF.pdf

But generally there more than 100 papers since 2016: https://scholar.google.com/scholar?as_ylo=2016&hl=en&as_sdt=0,5&sciodt=0,5&cites=13323743438210565407&scipsc=

A week ago there was John Bush lecture and talked about some experiments, it should be available soon.

1 hour ago, Strange said:

There should have been a “neither of the above” (or “it’s complicated”) option in the poll

Please elaborate - particle can have objectively both wave and corpuscular natures, or only one at a time ... what is the third option?

For using both natures at a time, there is e.g. this Afshar experiment: https://en.wikipedia.org/wiki/Afshar_experiment

dBB uses both natures at a time, here is its probably most known experimental confirmation: http://science.sciencemag.org/content/332/6034/1170.full

More recent paper observing both natures at a time: https://www.nature.com/articles/ncomms7407

What arguments against are there?

[joigus]

1 hour ago, Strange said:

There should have been a “neither of the above” (or “it’s complicated”) option in the poll

You might be interested in this article: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

 

Yes! The "it's complicated" one would have been my choice.

Thank you for the article. I haven't been able to read it yet, though. Octonions are very promising. John Baez has a lot of stuff on octonions too. They relate topologically to the the spinors. They kind of split into spinors through a mapping that renders the algebra non-associative, as octonions are non-assoc.

19 minutes ago, Duda Jarek said:

Most are pre-2015, more recent is e.g. anti-ferromagnet: https://math.mit.edu/~dunkel/Papers/2018SaEtAl_PRF.pdf

[...]

But generally there more than 100 papers since 2016: https://scholar.google.com/scholar?as_ylo=2016&hl=en&as_sdt=0,5&sciodt=0,5&cites=13323743438210565407&scipsc=

A week ago there was John Bush lecture and talked about some experiments, it should be available soon.

Please elaborate - particle can have objectively both wave and corpuscular natures, or only one at a time ... what is the third option?

For using both natures at a time, there is e.g. this Afshar experiment: https://en.wikipedia.org/wiki/Afshar_experiment

dBB uses both natures at a time, here is its probably most known experimental confirmation: http://science.sciencemag.org/content/332/6034/1170.full

More recent paper observing both natures at a time: https://www.nature.com/articles/ncomms7407

What arguments against are there?

Thank you for the references. This topic is very interesting.

[Strange]

1 hour ago, Duda Jarek said:

Please elaborate - particle can have objectively both wave and corpuscular natures, or only one at a time ... what is the third option?

That these properties that we assign to quanta are ones we take from analogies with macroscopic objects, but they are not what quanta "are". So we can say that there is a wavelength associated with a photon, but that doesn't mean that it is a wave. We can say that a photon can only interact indivisibly at a single location, but that doesn't mean it is a particle.

They are never particles or waves. Those are just analogies. It's complicated.

[Duda Jarek]

The complementary principle says we can observe only one of these natures at a time - is restriction for measurement like Heisenberg.

So particles have at least one of these two natures at a time, the question is if objectively they cannot have both, like observed in experiments I have linked.

Or like for the walking droplets with both natures at a time: http://dualwalkers.com/statistical.html

 

[dimreepr]

30 minutes ago, Duda Jarek said:

The complementary principle says we can observe only one of these natures at a time - is restriction for measurement like Heisenberg.

So particles have at least one of these two natures at a time, the question is if objectively they cannot have both, like observed in experiments I have linked.

Or like for the walking droplets with both natures at a time: http://dualwalkers.com/statistical.html

 

An anology is a way to relate one language too another (to explain why a wolf howl's, in human) it's not an explanation in and of itself (unless you speak wolf)... 😉

[joigus]

4 minutes ago, dimreepr said:

An anology is a way to relate one language too another (to explain why a wolf howl's, in human) it's not an explanation in and of itself (unless you speak wolf)... 😉

I agree in a short-winded kind of way.

[dimreepr]

Just now, joigus said:

I agree in a short-winded kind of way.

LOL

 

[Duda Jarek]

This is analogy to Madelung substitution: psi = sqrt(rho) exp(iS/hbar) to Schrodinger, getting continuity equation for density rho and Hamilton-Jacobi for actions S with additional "quantum potential" corresponding to interaction with pilot wave: https://en.wikipedia.org/wiki/Pilot_wave_theory#Mathematical_formulation_for_a_single_particle