[Jarek Duda (OP)]

Exactly like in the "Fluid mechanics" picture I have attached above from the Wikipedia article, indeed we can imagine gravitomagnetism by swirls and displacement of some fluid - or in other words: of the field.
There is no need for intrinsic spacetime curvature like in GRT here.

However, I wouldn't say that this "fluid" literally has a mass - it has inertia instead, which requires energy to increase e.g. kinetic energy.
There is also some "dark mass/energy", but it might be just 2.7K thermal noise for not only EM degrees of freedom, but also those corresponding to other interactions (weak/strong) and so difficult to directly observe.

[liquidspacetime]

What is thought to be virtual particles is actually the chaotic nature of the aether.

For example, the following hydrodynamical representation of the Casimir Effect is analogous to the chaotic nature of the aether.

'Water wave analogue of the Casimir effect'

NON-LINEAR WAVE MECHANICS A CAUSAL INTERPRETATION by LOUIS DE BROGLIE

“Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of [the wave-function wave], arise from the interaction of the particle with a “subquantic medium” which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty space”.”

The “subquantic medium” is the aether.

‘Fluid mechanics suggests alternative to quantum orthodoxy’
http://newsoffice.mit.edu/2014/fluid-systems-quantum-mechanics-0912

“The fluidic pilot-wave system is also chaotic. It’s impossible to measure a bouncing droplet’s position accurately enough to predict its trajectory very far into the future. But in a recent series of papers, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris applied their pilot-wave theory to show how chaotic pilot-wave dynamics leads to the quantumlike statistics observed in their experiments.”

A “fluidic pilot-wave system” is the aether.

‘When Fluid Dynamics Mimic Quantum Mechanics’
http://www.sciencedaily.com/releases/2013/07/130729111934.htm

“If you have a system that is deterministic and is what we call in the business ‘chaotic,’ or sensitive to initial conditions, sensitive to perturbations, then it can behave probabilistically,” Milewski continues. “Experiments like this weren’t available to the giants of quantum mechanics. They also didn’t know anything about chaos. Suppose these guys — who were puzzled by why the world behaves in this strange probabilistic way — actually had access to experiments like this and had the knowledge of chaos, would they have come up with an equivalent, deterministic theory of quantum mechanics, which is not the current one? That’s what I find exciting from the quantum perspective.”

What waves in a double slit experiment is the aether.

[Jarek Duda (OP)]

"Virtual particles" are artifacts of the perturbation approximation - useful tool for calculations.
I don't think anybody imagines Coulomb attraction as constant exchange of photons.
In field vacuum/liquid there can be spontaneously created pairs of vortex, anti-vortex. Such formation could start and then go back - what can be imagined as virtual particle, leads to vacuum polarization.

However, saying field or aether is only a nomenclature here - they are nearly equivalent pictures, but the aether word has currently very negative connotation - a few people will treat you seriously if you use it, especially that it suggests something without Lorentz invariance.

What problem do you see with using the standard modern: field word instead?

[liquidspacetime]

'Empty' space has mass which physically occupies three dimensional space and is physically displaced by the particles of matter which exist in it and move through it.

Check out the video starting at the 2:00 minute mark.

What is referred to as the mass of the 'empty' space of the proton is the mass of the aether which exists where the quarks do not.

'Fields', with mass, popping into and out of existence out of nothing is nonsense.

The reason why mainstream physics is so screwed up is because they are unable, or unwilling, to understand the space unoccupied by particles of matter has mass.

The 'stuff' which fills the space unoccupied by particles of matter was originally called the aether so we should just call it by its original name.

[Jarek Duda (OP)]

You are mixing stuff.
First of all - there is energy conservation. Sure you can spontaneously create pairs of particle-antiparticle, but it requires energy - which can come from thermal fluctuation (Boltzmann distribution etc.), see sine-Gordon "Rubber Band Model of the Universe" - energy of random fluctuations create lots of kink-antikink pairs:

Regarding mass of the field - all fields have inertial mass: you need to invest some energy to e.g. make it move (give kinetic energy).
From the other side, "dark energy" can have purely thermodynamical nature - be a random noise/fluctuations. Like 2.7K random noise of EM degrees of freedom, but of other degrees of freedom: corresponding to weak, strong and gravitational degrees of freedom - this kind of noise is tough to directly observe.

Regarding baryons, we need to understand their structure and sure only a small fraction of energy of this structure corresponds to the charges (quarks).
What structure is it? We need a stable structures like a vortex - they are generally called solitons.
Here is the one I consider: http://fqxi.org/community/forum/topic/1416 , slides: http://dl.dropboxusercontent.com/u/12405967/soliton.pdf
Below is a s general picture of its speculation of baryons/nuclei structure:



So the basic structures of this model are lines having spin 1/2 configuration in cross-section (kind of Abrikosov vortex but in vacuum) and there are three types of them with growing energy density: electron, muon and taon spin loops.
This kind of magnetic 1D structures are observed in Sun's corona ( https://en.wikipedia.org/wiki/Magnetic_reconnection ), and would allow to explain holding nucleus together against Coulomb repulsion (like He4 in the picture).
Electron is such electron spin line with 180 deg rotation inside - getting hedgehog configuration - topological charge which is interpreted as electric charge (Gauss-Bonnet theorem acts as Gauss law).

Baryons would correspond to such loop around spin line (like above) - geometry says that they have to be of different types (the lowest energy is for electron-muon) and that such loop enforces some partial internal rotation - a fractional charge ("quark").
So baryon structure itself requires some (fractional) charge - proton has only this charge (can be narrow), while neutron has to compensate it with opposite charges like in the picture - has to be wide - has larger energy ... getting intuitive explanation of why proton is lighter than neutron (we still don't understand from QCD).
Next, deuteron is lighter than p + n because they can share their single charge like in the figure.

The energy of charge structure (like 511keV) is tiny comparing to other energies in these structures - mainly of the stress between spin loop and line - which can be interpreted as gluons in pertubative approximation.

[liquidspacetime]

In a double slit experiment it is the mass which fills the space unoccupied by particles of matter that waves.

[Jarek Duda (OP)]

There are at least 4 types of mass:
- energy released while annihilation with antiparticle - usually as massless photons, like on this animation of kink - antikink annihilation:
https://en.wikipedia.org/wiki/Topological_defect#Images
- inertial mass - in Newton's: F = m*a
- gravitational mass - e.g. F = m * g
(still not confirmed for electron: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.19.1049 )
- de-Broglie's clock/zittebewegung defining frequency of waves coupled with the corpuscle
direct observation: http://link.springer.com/article/10.1007%2Fs10701-008-9225-1

Which mass are you talking about?

In double slit we need a medium (field) propagating the waves like in Couder's experiments - the only type of mass required for this medium is inertial mass - relating applied energy with kinetic properties.

[liquidspacetime]

Mass is defined as that which physically occupies three dimensional space.

[Jarek Duda (OP)]

Oh, so you just have another name for your liquid/aether.
No, this definition of yours is not in agreement with anything I have met with.

Sure, if you want only to talk with yourself, you can call stuff as only you can imagine.
However, if you would also like to communicate with others, the best way way is to use a standard nomenclature, for example that the medium filling the spacetime is a field and by default is Lorentz invariant.
Best,
Jarek

[liquidspacetime]

The medium filling spacetime is the aether which has mass, is physically displaced by the particles of matter which exist in it and move through it and is what waves in a double slit experiment.

[Jarek Duda (OP)]

If like in Couder's picture we agree that QM is an effective model - describing our limited of knowledge, enhancing classical mechanics by the wave nature of particles (generated by some internal periodic process), we need to finally face the question of trajectories of particles - including electron's in atoms.

There are no doubts that such hypothetical trajectories of electrons should average to densities of quantum wavefunctions - and considering statistical physics on them: Boltzmann distribution among paths, it is clear that theromodynamically they should average to quantum densities (euclidean path integrals / Maximal Entropy Random Walk).
There is a nice experiment that literally makes photos of atoms: measure this electron density - by pulling out single electrons, measuring their position while leaving the atom and finally averaging over positions of thousands of electrons:
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165404


But the question is what are the short-time trajectories of electron in atom?
Standard answer is circular Bohr trajectories - which is still used especially for Rydberg atoms: https://en.wikipedia.org/wiki/Rydberg_atom
However, Bohr's model is known to be generally in disagreement with experiment - can it be repaired?

So Bohr model sees only charge of electron, while it has also extremely strong (for its mass) magnetic dipole moment - electron is also a tiny magnet.
This magnetic moment corresponds to "quantum" spin-orbit interaction, but it has also a classical consequence: Lorentz force for this tiny magnet traveling in electric field of the nucleus.
This force is perpendicular to velocity and spin direction and is proportional with v/r^3.
It is usually practically negligible, unless very large velocity and tiny distance - while free-falling, this force prevents electron falling into nucleus. Instead, the trajectory is bent and electron misses nucleus, then returns to the original distance, but on different angle.
This way zero angular momentum hydrogen can rotate - complex objects can rotate even having zero angular momentum, like in the falling cat problem: https://en.wikipedia.org/wiki/Falling_cat_problem

This free-fall atomic model is claimed to give much better agreement: https://en.wikipedia.org/wiki/Free-fall_atomic_model
Here is derivation of the classical spin-orbit correction: https://dl.dropboxusercontent.com/u/12405967/freefall.png
Single-electron simulator in Mathematica: https://dl.dropboxusercontent.com/u/12405967/freefall.nb

And somebody's simulation for up to 10 electron atoms ( youtube.com/watch?v=P2IsIkSn5bk ):

[Jarek Duda (OP)]

All the news say that the "impossible drive" has been confirmed by NASA:
http://arc.aiaa.org/doi/full/10.2514/1.B36120

The problem is 3rd Newton law - there is a sealed resonant chamber and they claim it produces thrust.

The main hypothesis in this paper is that there is no problem because this momentum is just transferred by pilot waves (?) - like those in Couder's experiments.

What do you think about it?

[alancalverd]

Nothing to do with Couder, but apparently another manifestation of radiation pressure from a radiofrequency source. Same principle as photon momentum but at a lower frequency.

[Jarek Duda (OP)]

Indeed momentum transfer as leak of EM waves was also my first thought when I have heard about it a few years ago - like while using laser for repulsion, but with much lower frequencies.

I have mixed feelings about it, but generally pilot wave could carry some tiny momentum (?) - allowing it to give some tiny thrust ... (they cite Couder-Fort and some following papers).
And in contrast to EM waves, pilot waves would penetrate through the metal walls of this resonator.

update: walking droplets from Veritasium - million views in 3 weeks ( youtube.com/watch?v=WIyTZDHuarQ ):

[Jarek Duda (OP)]

Great webpage about walking droplets from the Paris group - nice explanations, dozens of videos:
https://dualwalkers.com/
Including many videos of self-organized "crystals": https://dualwalkers.com/crystals.html , e.g.


stack: https://physics.stackexchange.com/questions/386711/couders-walking-droplets-what-are-issues-of-using-its-intuitions-to-interpret

ps.One of papers ( https://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.011001 ) shows that statistics of trajectories recreate "quantum" eigenstates.
Wanting to understand it from stochastic point of view, it is worth to look at MERW: https://en.wikipedia.org/wiki/Maximal_entropy_random_walk
It shows that standard random walk/diffusion often uses only approximation of the maximal entropy principle - doing it right, Maximal Entropy Random Walk turns out to lead to stationary probability distribution exactly like for quantum ground state - with strong localization property.
Here is example for defected lattice: nodes have self-loop (to itself: degree 5), which is removed in defects marked by squares (degree 4) - while standard random walk/diffusion nearly does not see the defects, MERW localizes exactly in quantum ground state:

[Jarek Duda (OP)]

Lecture about these experiments by Yves Couder:

By John Bush:

Materials and great videos: http://dualwalkers.com/
More materials about hydrodynamical QM analogues: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

About soliton particle models (mainly Faber's):