Hi Longview, thanks for the reply.

The last link is definitely mathematica notebook, here are Gryzinski’s lectures: http://www.cyf.gov.pl/gryzinski/indang.html

I have also his book, but it is in Polish. Sadly he has died in 2004. I plan to test his work when I will have more time.

Regarding Couder, there are definitely essential differences comparing with the microscopic physics, like that his waves are rather short-range (pilot wave is long-range), or that he uses external clock, while particles seem to have internal one (zitterbewegung/de Broglie’s clock) – which can be now directly observed: http://link.springer.com/article/10.1007%2Fs10701-008-9225-1

However, he brings great intuitions about basic “quantum” phenomena:

- interference pattern in double-slit experiment (particle goes a single trajectory, but it interacts with waves it created - going through all trajectories): http://prl.aps.org/abstract/PRL/v97/i15/e154101 ,

- tunneling depending on practically random hidden parameters (highly complex state of the field): http://prl.aps.org/abstract/PRL/v102/i24/e240401 ,

- 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): http://www.pnas.org/content/107/41/17515 ,

- Zeeman splitting analogue for these discrete orbits (Lorentz force was simulated by Coriolis force): http://prl.aps.org/abstract/PRL/v108/i26/e264503 .

Regarding the “As you know, a number of the orbital structures do take the electron(s) through the nucleus, others place the highest probability of materialization at the nucleus.”, indeed we should be careful about blindly using the Schrodinger equation, for example because it neglects the interaction with the nucleus.

Also, while thinking about multi-electron orbitals, we usually forget about electron-electron repulsion. If we do helium right, we see that position of these electrons are strongly anti-correlated.

Anyway, returning to trajectories, if we add thermodynamics there: randomly perturb trajectories and average them over time, I believe we should get exactly the Schrodinger probability clouds.

I have got to this conclusion, and generally to the search for physics below QM, thanks to working on Maximal Entropy Random Walk (my PhD thesis: http://www.fais.uj.edu.pl/docu…71-4eba-8a5a-d974256fd065 ).

Specifically, the way we choose stochastic processes turns out not always being in agreement with the basic for statistical physics: the (Jaynes) maximal entropy principle. Doing it right - starting with maximizing entropy production: Maximal Entropy Random Walk, leads to getting exactly to the ground state probability density of Schrodinger equation.

Here is a comparison of evolution of density of both approaches on a defected lattice (all nodes but the marked ones have self-loop):

Standard random walk/diffusion would say that electrons on a defected lattice should have nearly uniform probability distribution, that semi-conductor should still conduct well - one of reasons for rejecting trajectories a few decades ago.

MERW and QM say that electrons are localized (Anderson) as the quantum ground state probability density – trapped in (entropic) wells, can be difficult to conduct.

Slides about MERW: https://dl.dropboxusercontent.com/u/12405967/MERWsem.pdf

Regarding “The real problem may not be getting an electron to the nucleus”, getting electron into proton costs **m_n - m_p - m_e ~ 782keV** – it is huge energy from chemistry point of view. I don’t believe some lattice excitations could make such process reasonably high probable.

From the other side, think about this “ p ---- e ---- p ” symmetric configuration – without any additional energy, it should just collapse and fuse into deuteron.

So maybe we shouldn’t think about two-body p+e->n collisions, but rather about three body p+e+p or nucleus+e+p processes – because electron can attract both nuclei.

How to do it? Shooting electrons at nuclei, for some parameters we have backscatting: the electron goes back to the source. So imagine two closing nuclei and electron performing a few backscatterings between them: jumping between them, screening their Coulomb repulsion, making fusion much more probable.

Gryzinski’s model suggests this is quite a reasonable scenario, and his classical scattering paper has more than 1000 citations (google “Classical Theory of Atomic Collisions”).

Anyway, in contrast to other explanations of LENR, the only "exotic" assumption of electron-assisted fusion is considering trajectories of electrons.

Other non-standard assumption is adding electron's magnetic dipole moment to Bohr-like considerations (classical spin-orbit interaction).

ps. Another argument against Widom-Larsen like models (beside the need for huge 782keV energy for p+e->n), is production of gammas (and others) when this neutron would be finally absorbed by some nucleus - not observed in LENR.

As in the "p - e - p" example, three body electron-assisted fusion should allow for direct crossing of the Coulomb barrier - without starting with going up the barrier (e.g. 782 keVs).