[Jarek Duda (OP)]

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 ("pilot") waves allows us to observe 'quantum effects' (most articles from Physical Review Letters):
- interference pattern in double-slit experiment (particle goes a single trajectory, but it interacts with waves it created - going through all trajectories),
- tunneling depending on practically random hidden parameters (highly complex state of the field),
- orbit quatization condition (that particle has to 'find a resonance' with the field - after single orbit, its internal phase has to return to the initial state),
- Zeeman splitting analogue for these discrete orbits (Lorentz force was simulated by Coriolis force).

It is difficult to find good intuition about these experiments from only static pictures - the first time I had occasion to see videos was recent congress on emergent quantum mechanics where Couder had the opening lecture and most of speakers were excited about these experiments. Fortunately there is a youtube video of these experiments (from Morgan Freeman "Through the wormhole" series):

Some free materials: two-slit experiment paper, Europhysicsnews general paper, the opening lecture, slides.

The main qualitative difference with microscopic 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 and they often have such internal periodic motion (so called 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 in one time?
In such case, when and how it is switched? What about Afshar experiment?

[JP]

I read briefly over some of the links you provided.  As far as I can tell, what Couder's done is to show a classical analogue to quantum phenomena where a substrate acts like a wave, and droplets on the substrate act like particles.  Because they're tiny droplets, they can be taken as discrete particles, but because their motion is controlled by the continuous wave substrate, they move in a wavelike manner.  This system can demonstrate a lot of quantum effects and is closely linked to one interpretation of the mathematics of QM that postulates that particles ride around on an undetectable wave (the de Broglie-Bohm theory).

This is a very cool demonstration and interesting to study, especially for providing a nice picture of some really abstract ideas in quantum mechanics.  However, it is at risk of being a bit overhyped, especially in that Morgan Freeman clip.  It's just a classical model that mimics quantum behavior.  It's not telling us something deep and fundamental about quantum mechanics.

[Jarek Duda (OP)]

Indeed it is providing nice picture (and intuitions) of some really abstract ideas of quantum mechanics.
For example here is Feynman quote about interference from his QM book:
« … In this chapter we shall tackle immediately the basic element of the mysterious behavior in its most strange form. We choose to examin a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which is at the heart of quantum mechanics. In reality it contains the only mystery. We cannot make the mystery go away by explaining how it works . We will just tell you how it works.… »
Which is no longer true ...

The goal is instead of just "shut up and calculate" as everybody do, finally try to understand quantum mechanics, especially the wave-particle duality. Orthodox view often says that e.g. electron is just its wavefunction - completely forgetting about the particle nature. Couder's experiments show that being simultaneously both wave and particle (which goes a concrete trajectory) does not prevent e.g. quantum interference. And so we need to to get below the Schroedinger picture - see wavefunction as emerging from hidden dynamics of an object with wave-particle duality...

What lead me a few years ago to conclusion that corpuscular nature does not prevent quantum behavior was working on Maximal Entropy Random Walk(MERW) for my last PhD. It occurs that standard way of choosing transition probabilities in stochastic models usually only approximates the basic principle thermodynamical models should be based on: the maximal uncertainty principle. Doing it finally right in MERW-like approaches lead to similar local behavior, but usually completely different global behavior: while standard approach has weak localization properties (in opposite to QM!), this time it thermalizes exactly to the quantum ground state probability density (squares of coordinates of dominant eigenvector of Hamiltonian).
For example here is evolution from point distribution on defected lattice (with removed some vertices: squares):

So properly made thermodynamics of corpuscular objects (like these bouncing droplets), turns out in agreement with thermodynamical predictions of quantum mechanics - as we should expect. This "classical" model also gives natural intuitions of many "quantum" properties, like "squares" relating amplitudes with probabilities.
Here is our PRL paper, preliminary version of thesis, presentation, simulator.

[yor_on]

This is interesting Jarek. I will need to read this I think.
=

And this one make sense.

"The main qualitative difference with microscopic 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"

If mass is connected to observers experience of 'clocks' ticking differently then I expect mass to be able to interact with itself too. It all depends on where you draw the limits for what a particle can be seen as it seems? As a 'whole uniform' object, or as something just presenting such a expression macroscopically?
=
That is, assuming a oscillation, but then again, can't you get that from HUP? Better read the papers first and see what I can assimilate:)

[Jarek Duda (OP)]

I have just found great youtube presentation about these walking droplets:

It also mentions that long term behavior averages to solutions of Schrodinger equation - it is exactly what properly made (using maximal uncertainty principle) stochastic modeling says: based on Maximal Entropy Random Walk above.

[Jarek Duda (OP)]

There are lots of new paper on this subject, like about trajectories averaging to quantum trajectories like in the video above: http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/Harris-Corrals-2013.pdf
or some general papers: http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/MB1-2013.pdf , http://windw.dk/2013Bouncing.pdf
Here are some additional materials, videos: http://walkingdroplet.com/

If someone disagree that behavior of these droplets is analogous to quantum mechanical, look at de Broglie-Bohm interpretation: http://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory#Derivations
We just make Madelung transformation of Schrodinger equation: take psi=R exp(iS) and write equations for this action (S) and density rho=R^2. For density we get standard continuity equation, while for S we get Hamilton-Jacobi equation - exactly like for classical mechanics, but modified by h^2 correction because of interaction with these "pilot" waves of quantum phase.

If someone is worried if we can use such pictures of sub-quantum behavior because of Bell inequalities, here is a nice lecture and paper that these inequalities are violated e.g. in classical Ising model:
http://www.perimeterinstitute.ca/videos/can-sub-quantum-theories-based-background-field-escape-bell-s-no-go-theorem
http://arxiv.org/vc/arxiv/papers/1211/1211.1411v1.pdf
so the belief that these inequalities should be fulfilled by local deterministic models is not true.

[distimpson]

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 in one time?
In such case, when and how it is switched? What about Afshar experiment?

I just started reading all the material, so far it is great, anything that helps to demystify quantum mechanics is a noble effort imo. Thank you for posting this material, it's posts like this that have made the Naked Science Forum my favorite place on the internet.

[Jarek Duda (OP)]

Yes, nowadays there are lots of materials showing that we can get below QM, understand what's going on there. They are trying to protect their "quantum shaman" status by Bell inequalities, but it doesn't longer hold as classical systems also violate these inequalities.

It is time to finally search for real models of particles - concrete localized constructs of the field behind Feynaman diagrams - solitons.
And it is really natural to construct charges there - as topological charges.
For example imagine vector field with Higgs potential V(v)=(1-|v|^2)^2.
To be in the potential minimum, the field has to break symmetry in every point, choosing some |v|=1 direction ... however, if the field has a hedgehog configuration (e.g. v(x)=x), the field has to get out of the Higgs potential minimum to v=0 ... giving this particle rest energy - mass, which can be released while particle-antiparticle annihilation, exactly like in this animation: http://en.wikipedia.org/wiki/Topological_defect#Images
Now looking at such 2D topological charge-anticharge pair in different distances:

we see that the closer they are, the smaller stress of the field (energy) - it means that they attract (analogously the same charges repel).
And so it is very simple to get Maxwell's equations describing dynamics of such topological charges: http://iopscience.iop.org/1742-6596/361/1/012022/  http://arxiv.org/abs/hep-th/9910221
After simple expansion we get 3 different ways for charge configuration (leptons), and stable configurations resembling other known particles: http://www.fqxi.org/data/essay-contest-files/Duda_elfld_1.pdf

[Jarek Duda (OP)]

Recording of prof. Couder's presentation from EmQM13:
http://www.emqm13.org/abstracts/presentation-videos/video-yves-couder/

Also many others there, e.g. of prof. Faber about soliton particle models:
http://www.emqm13.org/abstracts/

[liquidspacetime]

Dark matter' is now understood to fill what would otherwise be considered to be empty space.

'Cosmologists at Penn Weigh Cosmic Filaments and Voids'
http://www.upenn.edu/pennnews/news/cosmologists-penn-weigh-cosmic-filaments-and-voids

"Dark matter ... permeates all the way to the center of the voids."

'No Empty Space in the Universe --Dark Matter Discovered to Fill Intergalactic Space'
http://www.dailygalaxy.com/my_weblog/2012/02/no-empty-space-in-the-universe-dark-matter-discovered-to-fill-intergalactic-space-.html

"A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter."

Dark matter which fills the space unoccupied by particles of matter is otherwise known as the aether.

Wave-particle duality is a moving particle and it's associated wave in the aether.

"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

In the following two articles the aether is what waves in a double slit experiment. In the first article the aether has mass.

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

"This medium, called also the aether, has mass and is populated by the particles of matter which exist in it and move through it" ...

... and displace it.

'EPR program: a local interpretation of QM'
http://arxiv.org/abs/1412.5612

"Wave particle duality is described as the compound system of point particle plus accompanying wave (in the æther)."

In the following articles Louis de Broglie describes wave-particle duality as a moving particle and it's associated wave in a hidden subquantic medium.

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

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

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

The hidden medium of de Broglie wave mechanics is the aether.

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

A particle may be likened in a first approximation to a moving singularity which has an associated aether displacement wave.

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

The particle occupies a very small region of the associated aether wave.

Q. Why is the particle always detected traveling through a single slit in a double slit experiment?
A. The particle always travels through a single slit. It is the associated wave in the aether which passes through both.

The wave of wave-particle duality is a wave in the aether.

In a double slit experiment the particle travels a well defined path which takes it through one slit. The associated wave in the aether passes through both. As the wave exits the slits it creates wave interference. As the particle exits a single slit the direction it travels is altered by the wave interference. This is the wave guiding the particle. Detecting the particle strongly exiting a single slit destroys the cohesion between the particle and its associated wave in the aether, the particle continues on the trajectory it was traveling and does not form an interference pattern.

[Jarek Duda (OP)]

Sure the field theories (like electromagnetism) can be imagined as a fluid without viscosity - however, we need to remember about their Lorentz invariance, what is rather not fulfilled for standard fluid (or old "aether") as it seems to emphasize some frame of reference: in which the entities forming the liquid (like molecules) are in rest.

If there are no such "molecules" forming this "superfluid liquid", it is Lorentz invariant - and can be seen/modeled as a field (like EM) - and its vortices are technically solitons: local configurations of the field maintaining their shapes.
If they are of topological origin, like fluxon/Abrikosov vortex in superconductor: the phase has to perform a complete rotation while going along a loop around, they are called topological solitons - and topological charge is a perfect candidate for electric charge:
- it is quantized (Gauss-Bonnet theorem is analogue of the Gauss law calculating topological charge, which in integer),
- soltion models get rid of the problem of infinite energy of electric field of point charge (it is regularized thanks to potential - the center of vortex is smoothen),
- we get Coulomb interaction like in the picture in reply #7 above: increasing the distance between + and - charge increases the stress of the field: resulting in their attraction to reduce the total stress/energy,
- solitons in Lorentz-invariant theories undergo SRT effects, like Lorentz contraction - here are photos of mechanical realization (pendula on a rod connected by spring) of sine-Gordon model: the left is at rest, the right is moving

animations: https://en.wikipedia.org/wiki/Sine-Gordon_equation
slides: https://dl.dropboxusercontent.com/u/12405967/soliton.pdf

[liquidspacetime]

"The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo." - Robert B. Laughlin, Nobel Laureate in Physics, endowed chair in physics, Stanford University

[Jarek Duda (OP)]

So why don't just use the modern word: field instead?

It already denotes some medium filling the Universe, like E and B vectors defined in every point of the spacetime, with perturbations propagating with constant speed (of light).
The only difference is that for fields we highlight the Lorentz invariance: that there is no distinguished reference frame, in contrast to fluid made of molecules: emphasizing the reference frame in which molecules have zero average velocity.

[liquidspacetime]

Einstein's first 'paper'. A letter to his uncle.
http://www.worldscibooks.com/etextbook/4454/4454_chap1.pdf

"The velocity of a wave is proportional to the square root of the elastic forces which cause [its] propagation, and inversely proportional to the mass of the aether moved by these forces."

Einstein is referring to the state of displacement of the aether.

The velocity of a wave is proportional to the square root of the elastic forces which cause its propagation, and inversely proportional to the mass of the aether displaced by these forces.

'Ether and the Theory of Relativity by Albert Einstein'
http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html

"Think of waves on the surface of water. Here we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time; or else-with the help of small floats, for instance - we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics - if, in fact nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium."

if, in fact nothing else whatever were observable than the shape of the space occupied by the aether as it varies in time, we should have no ground for the assumption that aether consists of movable particles. But all the same we could characterise it as a medium having mass which is displaced by the particles of matter which exist in it and move through it.

"the state of the [ether] is at every place determined by connections with the matter and the state of the ether in neighbouring places"

The state of the aether at every place determined by its connections with the matter and the state of the aether in neighboring places is the state of displacement of the aether.

[Jarek Duda (OP)]

For me you are still describing a field, and you finally need some fields (e.g. of velocity) to work with the models you consider.
If you want to be treated seriously in the science community, just replace aether with field, also always highlight the Lorentz invariance ... and look at localized configurations of fields: solitons, starting with the sine-Gordon.

[liquidspacetime]

The space unoccupied by particles of matter has mass and is displaced by the particles of matter which exist in it and move through it.

It is the mass which fills 'empty' space that waves in a double slit experiment.

I think we should call the mass which fills the space unoccupied by particles of matter by its correct name, the aether.

[Jarek Duda (OP)]

If you are referring to dark mass/energy, this is an additional property.
And the soliton view has a way to explain it itself:
there is 2.7K background EM radiation which can be observed.
However, there are also degrees of freedom corresponding to other interactions (weak, strong, gravitational) - while they are tough to directly observe, they should thermalize close to these 2.7K, carrying lots of "dark" non-particle energy.

[liquidspacetime]

Dark energy and gravity are both manifestations of the mass which fills the space unoccupied by particles of matter.

A different concept than the 'Big Bang' is the notion of a 'Big Ongoing'.

'Was the universe born spinning?'
http://physicsworld.com/cws/article/news/46688

"The universe was born spinning and continues to do so around a preferred axis"

Our Universe spins around a preferred axis because it is a larger version of a galactic polar jet.

'Mysterious Cosmic 'Dark Flow' Tracked Deeper into Universe'
http://www.nasa.gov/centers/goddard/news/releases/2010/10-023.html

"The clusters appear to be moving along a line extending from our solar system toward Centaurus/Hydra, but the direction of this motion is less certain. Evidence indicates that the clusters are headed outward along this path, away from Earth, but the team cannot yet rule out the opposite flow. "We detect motion along this axis, but right now our data cannot state as strongly as we'd like whether the clusters are coming or going," Kashlinsky said."

The clusters are headed along this path because our Universe is a larger version of a polar jet.

It's not the Big Bang; it's the Big Ongoing.

'Dark matter' is now understood to fill what would otherwise be considered to be empty space.

'Cosmologists at Penn Weigh Cosmic Filaments and Voids'
http://www.upenn.edu/pennnews/news/cosmologists-penn-weigh-cosmic-filaments-and-voids

"Dark matter ... permeates all the way to the center of the voids."

'No Empty Space in the Universe --Dark Matter Discovered to Fill Intergalactic Space'
http://www.dailygalaxy.com/my_weblog/2012/02/no-empty-space-in-the-universe-dark-matter-discovered-to-fill-intergalactic-space-.html

"A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter."

Dark matter which fills the space unoccupied by particles of matter is otherwise known as the aether.

Dark energy is aether continuously emitted into the Universal jet.

Our Universe is a larger version of the following artist's image of a galactic polar jet.


​
​Matter is moving outward and away from us in three dimensional space.

'The Milky Way's dark matter halo appears to be lopsided'
http://arxiv.org/abs/0903.3802

"the emerging picture of the dark matter halo of the Milky Way is dominantly lopsided in nature."

The Milky Way's halo is not a clump of dark matter traveling along with the Milky Way. The Milky Way's halo is lopsided due to the matter in the Milky Way moving through and displacing the aether, analogous to a submarine moving through and displacing the water.

The Milky Way's halo is the state of displacement of the aether.

The Milky Way moves through and curves spacetime.

The Milky Way's halo is curved spacetime.

The state of displacement of the aether is curved spacetime.

The state of displacement of the aether is gravity.

[Jarek Duda (OP)]

Regarding GRT, so its most precise test is Gravity Probe B, which in fact tests gravitoelectromagnetic(GEM) corrections (frame-dragging, Lense-Thirring effect):
https://en.wikipedia.org/wiki/Gravitoelectromagnetism



This kind of equations were introduced by Oliver Heaviside in 1893 to make Newton's theory Lorentz-invariant: by adding analogue of magnetic field and the second set of Maxwell's equations.

Currently it seen as a low order approximation of GRT, but in fact we can only guess what are the higher order corrections, if they agree with Einstein's aesthetic evaluation:
- which is non-renormalizable,
- seems to be impossible to combine with QM,
- requires embedding in higher dimensions (e.g. a surface with constant positive internal curvature should enclose to a sphere - what is inside it?) - being infinitely flat inside something and completely not interacting with this surrounding (any interaction would lead to energy imbalance),
- allows for wormholes, which e.g. could be non-orientable (glued like in Klein bottle), making that traveling through it you would switch your past and future:
http://www.thescienceforum.com/physics/26224-thermodynamical-thought-experiment-time-reversing-loop.html



In contrast, GEM itself doesn't require intrinsic curvature of spacetime, which is just 4D - just the field(/liquid/aether) defines local light cones.
Can we be sure that GRT is its proper extrapolation - cannot everything be much simpler?

[liquidspacetime]

In the following video what is referred to as frame-dragging is actually the state of displacement of the aether.

'NASA's Gravity Probe B Confirms Two Einstein Space-Time Theories'
http://www.nasa.gov/mission_page...

""Imagine the Earth as if it were immersed in honey. As the planet rotates, the honey around it would swirl, and it's the same with space and time," said Francis Everitt, GP-B principal investigator at Stanford University."

Honey has mass and so does the aether. The swirl is the state of displacement of the aether.