@Jarek are you still interested in Zitterbewegung? ran into two papers while searching on the fluid dynamics interpretation of QM...

@vzn, I am mostly interested in particle models: why e.g. charge of electron doesn't disperse (reason for quantization), why its electric field doesn't have infinite energy (it would have for point charge) ... but sure also how this localized field configuration (soliton) enforces Zitterbewegung/de Broglie's clock: some periodic evolution of this field configuration.

Regarding understanding how the clock of particle is realized, we disagree here with Manfried Faber who is the author of the basic model of electron as topological soliton ( iopscience.iop.org/article/10.1088/1742-6596/361/1/012022/meta )

His model is too simple for "static clock" - that e.g. single electron in Universe would perform Zitterbewegung

So he wants to see it as "dynamical clock" - normal modes of structure of electron (like of bridge) - which get energy in interaction ...

These modes of structure can be also seen in mass renormalization - their energy has to be added to naked mass of particle

But I think there is also some "static clock" - which cannot be "extinguished" ... some argument is Mach-Zehnder which doesn't loose interference with growing optical length ...

@JarekDuda yes, think the dynamics of an electron associated with an atom vs an electron "free in space" must be much different and agree it probably has a "clock" even in the latter case. was pursuing some other-related searches and somewhat surprisingly ran into these two papers, seen em? Salesi 2009 arxiv.org/abs/0906.4147 relates it to Madelung fluid and Hestenes 1990 link.springer.com/article/10.1007%2FBF01889466 says it generalizes across QM

I know more recent Hestenes paper where he Gouanere experiment confirming the clock: fqxi.org/data/essay-contest-files/…

They shoot high energy electrons into crystal and got increased absorption when electron's clock is synchronized with crystal structure - distance between ticks correspond to distance between layers

However, such clock could be interpreted as dynamical: synchronizing lattice with internal vibration (normal modes) of electron ...

I agree that clock seems required to explain Bohr-Sommerfeld quantization, like in Couder's pnas.org/content/107/41/17515.full

However, it is also in pure diffusion of properly made diffusion ( en.wikipedia.org/wiki/Maximal_Entropy_Random_Walk ) - excited states turn out metastable before collapsing to ground state - slide 13 here: dropbox.com/s/prwvp0tfbv3yy8l/MERWsem_UJ.pdf

But there is interference in MERW/diffusion - we definitely need a clock here - again like in Couder: clock creates "pilot" waves which travel all trajectories and can affect trajectory of the particle

In Couder clock is external, for particle it is internal - it would be great to understand its mechanism

And robustness of e.g. Mach-Zehnder interference suggests it is a static clock - does not weaken ...

Exactly like in recently hot "time crystals" en.wikipedia.org/wiki/Time_crystal

I think topological solitons can enforce internal periodic process - there is often some delambercian=0 wave equation, and topology of field structure enforces nonzero laplacian inside, what needs nonzero t'' ... structure of soliton should be able to enforce internal periodic process - the clock ... but quantitatively it turns really tough :/

Anyway, my soliton particle "essay": fqxi.org/community/forum/topic/1416 slides: dropbox.com/s/aj6tu93n04rcgra/soliton.pdf

@JarekDuda what is the frequency of the clock? it seems likely its a variation on de broglies "matter waves" and frequency is as in his eqn. and also tied with electron "spin". yes agreed the pilot waves are likely also tied to the clock. it seems likely to correspond to the "bouncing frequency" in couders experiments.

de Broglie: mc^2 = hbar * omega

was thinking more lambda = h / p en.wikipedia.org/wiki/Matter_wave

and it undergoes time dilation - high energy electrons used in Gouanare experiments have increased period ... and we have the same for simplest solitons: breathers in sine-Gordon model, like in slide 8 here: dropbox.com/s/aj6tu93n04rcgra/soliton.pdf (I have also Mathematca simulation)

sure, multiplying by velocity you get wavelength - which in Gouanare agrees with lattice constant

@JarekDuda nice! reminds me, need to go hunting again for (3d) soliton computational simulations, am nearly shocked nobody is trying it. would like to see open science/ open source prj. did you see this? cited zitterbewegung/ catillon ref from you vzn1.wordpress.com/2017/09/08/…

these are 3D simulations with really nasty nonlinearties ... for which we don't know the details - there is large freedom to choose kinetic term, and for potential it is even worse ... it requires a large experienced research group, for a single person it is just hopeless :/

@JarekDuda understand your point but think youre really overthinking it. the key is to use local eqns and a 3d grid. like a 3d cellular automaton. its almost easy, an experiment just waiting to happen. look at emergent phenomena and then try to come up with cell-spanning eqns/ generalizations after the phenomena are observed. think a lot of key particle behavior will be reproducible such as attraction/ repulsion, electron-nucleus orbiting/ orbitals, spin harmonics etc.

also have some (similar) real life fluid dynamics experiments in mind. are you in contact with anyone in the Couder group or other experimental groups? a stunning fact is that the original Couder experiments/ phenomena were found (accidentally) by undergraduates! o_O

re "time crystals" yeah wondering if they are "new phenomena" that might not be explicable within current QM framework and maybe a fluid picture/ pov could be more apropos.

@vzn, sure there will be needed discretization ... but you need to choose a field recreating our particle menagerie ...

the first point is repairing Maxwell's equations - which are great but have one crucial inaccuracy: allow for any real charge, while physics allows only quantized charge

So we need to repair Gauss law to allow for only integer charges - topological charge is natural and the only way to do it I am aware of (?)

and it has Gauss-Bonnet theorem: exactly as Gauss, but using curvature instead of electric field ...

so Faber starts with field of unitary vectors and define its curvature as EM field - recreating Maxwell's equation with this crucial correction of quantized charge

but he gets only single charge ... while we have three leptons - so I use field of 3 emphasized orthogonal direction - reper field, ellipsoid field ... stress-energy field with enforced eigenstructure

... but I don't know how to choose details of potential, and kinetic terms of this complex tensor field ...

the first step is to recreate electron - where we can assume some symmetry ... cylindrical not spherical as there is spin/magneitc dipole

I've tried to attack it a few times but gave up ... make next summer break I will find time and determination to go further ...

Whow, a lot has happened with my question, and there is Peter Shor's response: physics.stackexchange.com/questions/369590/…

Peter Shor has written that we have to "uncompute" auxiliary qubits to |0> state ... have anybody heard about something like this? I have doubts if it can be done as it finally has to be a permutation ...?