After more than 3 decades of irreproducable claims, not much hope has left, rather only wishthinking.

Without electron assistance, you would need to cross ~500keV energy barrier to get to a few fm distance so nuclear force could take over - I don't see sources of this energy in these materials.

fm distance is not required for fusion to occur, pm range is plenty enough because of quantum tunneling.

There is this ~500kB energy barrier - for reaching 3fm by two protons, probability of jumping through it with Boltzmann distribution in 1000K is ~exp(-500000/0.1). What do you think is probability of tunneling through it?

LeBob,

please specify - which experiment you think undermines Coulomb repulsion while taking two nuclei from nanometers to a few femtometers?

390MeVs is definitely not EM, but some other interactions.

Sure, at ~3fm it can have helpers ... but the difficulty is getting to 3fm through larger distances, what would directly require ~500keVs energy from Coulomb ... unless there is (single!) electron between them.

Wanting to negate Coulomb interaction, not having to exclude lots of other effects, you need to show an experiment where it fails in larger than a few femtometers distance.

Combining electron with proton into neutron again requires to invest energy which is completely inaccessible in these conditions: 782keVs.

And if you don't do it, electron is just too light and EM interacting to calmly wait - for fusion it would need to wait between two nuclei down to fm-distance.

If it cannot just wait, as it is attracted by both nuclei - it can travel there and forth between them in nearly lines - being backscattered every time.

And in theory such single back-scatterings are possible, the difficulty is getting multiple in statistically non-negligible way.

That's the only hope for LENR - electron jumping between the two nuclei down to fm distance.

This is ~100000 smaller distance than condensed matter scale - we cannot just rely on condensed matter effects here.

RoberBryant, sure - scatterings are definitely much more complicated than just Coulomb:

- there is additional magnetic dipole-charge v/r^3 and dipole-dipole 1/r^4 interaction, which become essential in such tiny distances,

- there might be also weak/strong interaction if this minimal distance gets down to fm-scale,

- there might be also other effects like virtual particle creation in Feynman diagrams - they successfully use to describe scatterings.

But these are additions to Coulomb, which might become stronger in such tiny distance - but how do you think it contradicts Coulomb????

But neutron is much further - adding weak/strong interactions, QCD, nuclear forces holding protons together in nucleus against Coulomb - which is still necessary e.g. in droplet nucleus model: https://en.wikipedia.org/wiki/…mass_formula#Coulomb_term

These additional forces start acting in ~fm distance, long range interactions are mainly EM - requiring investing huge energy e.g. ~500keV to take two protons to 3fm distance - such that nuclear forces can start acting.

Neutron is unstable because it is heavier than proton: p + e + 782keV -> n.

If you need to ignore Coulomb to explain LENR, nobody outside your hermetic group will treat this field seriously.

And we don't have to ignore it - if localizing electron between the two nuclei - this thread is focused on, please leave made up physics for other threads.

Just wow, electromagnetism is "an outdated theory" ... what more? Earth is flat and vaccines are bad? And then you wonder why people see LENR as another freak show...

If you want LENR to be treated seriously, what becomes less and less possible, you cannot just close in your world of some made up physics, but need to work within what is confirmed.

Sure there might be needed some tiny corrections in EM, but definitely not some magical allowance for ignoring Coulomb repulsion.

And generally I am not even trying to leave this single thread here - please let it be an oasis of real physics in this forum, come only if you want to discuss the topic in title - not your made up physics.

Thus we can pretty much exclude that the coulomb barrier plays any role in cold fusion.

To bring two positive charges to r distance, we need to invest kqQ/r energy (Coulomb), what for protons and r=3fm nuclear force distance is ~500keV.

Where do you want to get this enormous energy from???

Thermal energy in 1000K is just ~0.1eV.

The only realistic way to get these two nuclei together in ~1000K is putting electron between them, e.g. "p----e----p" initial static situation would electromagnetically collapse into a point. In reality this electron should/could be dynamic - discussion in this thread.

The only hope for LENR is electron assistance - that electron remains localized between the two nuclei to screen Coulomb repulsion, down to femtometer scale distance.

But mainstream forbids such localization - requiring to spread probability cloud of this electron to ~5 orders of magnitude larger wavefunction.

The main counter-argument for such localization is Bell-theorem: seen as forbidding local realism, making controversial considerations of some hidden state behind the wavefunction.

But isn't Lagrangian formalism e.g. in EM, GR, Standard Model local realistic? Assumption of existence of some field is realism, it uses only values/derivatives, there is finite propagation e.g. in Feynman diagram - locality.

So should e.g. Standard Model particle physicists care about Bell theorem - basically saying that their work makes no sense?

Quantum mechanics is Feynman path ensemble (in time), Ising model is its Wick-rotated analogue: Boltzmann sequence ensemble (in space) - it is not the same (the latter has no interference), but they share many common features, like localization property (e.g. in rho~sin^2 in [0,1] instead of rho=1 of standard diffusion), Born rule, Bell violation.

And it also points the problem of Bell theorem - which assumes asymmetric locality (emphasizing past -> future direction), while Ising model has symmetric (P) locality, physics is fundamentally CPT symmetric - so maybe we should also solve its equations in symmetric way like through the least action principle, or path/diagrams ensembles, like in this nice animation:

So in Ising model (as in MERW: https://en.wikipedia.org/wiki/Maximal_Entropy_Random_Walk ), for E_uv energy of interaction between u and v neighboring spins or something more general, define M_uv = exp(-beta E_uv) as transition matrix and find its dominant eigenvalue/vector: M psi = lambda psi for maximal |lambda|. Now it is easy to find (e.g. derived here) that probability distribution of one and two neighboring values inside such sequence are:

The former resembles QM Born rule, the latter TSVF – the two ending psi come from propagators from both infinities as M^p ~ lambda^p psi psi^T for unique dominant eigenvalue thanks to Frobenius-Perron theorem. We nicely see this Born rule coming from symmetry here: spatial in Ising, time in QM.

Having Ising-like models as spatial realization of Boltzmann path integrals getting Born rule from symmetry, maybe we could construct Bell violation example with it?

Here is MERW construction (page 9 here) for violation of Mermin’s Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1 inequality for 3 binary variables ABC, intuitively “tossing 3 coins, at least 2 are equal” (e.g. here is QM violation) :

From Ising perspective, we need 1D lattice of 3 spins with constraints – allowing neighbors only accordingly to blue edges in above diagram, or some other e.g. just forbidding |000> and |111>.

Measurement of AB spins is defect in this lattice as above – fixing only the measured values. Assuming uniform probability distribution among all possible sequences, the red boxes have correspondingly 1/10, 4/10, 4/10, 1/10 probabilities – leading to Pr(A=B) + Pr(A=C) + Pr(B=C) = 0.6 violation.

Also in Bohr-Sommerfeld, which l=0 degeneration is basic model of Gryzinski, he has spin-orbit, Stark effect corrections.

Ten digits sounds like hyperfine correction: using also magnetic dipole moment of nucleus.

I haven't seen this kind of terms, numerical calculation was much more difficult in his times, but magnetic dipole of nucleus can be added there.

And generally this is not my field of research - I can help in recreating his work, but don't feel competent to do it alone.

ps. Talking about 10 digit energy accuracy - hyperfine level, the basic question to understand is why He3 and He4 behave so different - due to tiny difference of magnetic dipole moment of nucleus? Gryzinski comments it from perspective of his model in https://www.dropbox.com/s/r31tg6fu254jtwu/helium.pdf

This is analogous to Bohr model, which gets energy levels right. Gryzinski focuses on more sophisticated problems (e.g. scattering, screening coefficients, diamagnetic constant, multielectron atoms, molecular bonds, solid state physics, Stark effect ...) in his peer-reviewed papers, but here is some separate one

If you want to convince mainstream to LENR, introducing some crazy new unrelated physics is the last way - only further reducing credibility.

In contrast, Gryzinski just repairs Bohr model - by using Bohr-Sommerfeld degenerated to l=0 (well known e.g. for hydrogen), also adding missing classical analogue of well known spin-orbit interaction - only using mainstream physics, and confirming predictions of his model with experiment in dozens of peer-reviewed papers over a few decades:

While mainstream physicists hold together, those outside usually go own ways - incompatible with others ... if you want to convince mainstream to LENR, Gryzinski is the only way - just repairing Bohr, no magical new concepts, shown agreement with experiments (also quantitative).

Let say alpha particle overcomed Coulomb repulsion between two protons - this is gigantic force (MeV-scale), doing it with magnetic: Lorentz force is not realistic, would require gigantic velocities and magnetic fields ... in contrast, alpha particle has zero spin and nearly no magnetic field - what is well confirmed e.g. in energy spectrum of helium.

Topological reasons can be used e.g. for charge/spin quantization, but atomic scale is much too large.

Regarding connection between EM and mass, again physics disagrees: there are massive particles without EM (pi0, neutrino), or EM without mass: photon.

One (top)/two(bottom) electron trajectories for molecular bonds from his book, top-left is the one which could allow for fusion: with electron traveling between two nuclei, screening their Coulomb repulsion. In the paper above he writes that Pd lattice helps stabilizing such trajectories:

Electron is a particle traveling in 3D, governed mainly by EM interactions (beside gravity and weak/strong very close to nuclei).

EM interaction here is mainly ~1/r^2 Coulomb force (charge-charge).

There is also ~v/r^3 electron magnetic dipole - nuclear charge, called spin-orbit interaction, included in Gryzinski's model as the most important correction to Bohr.

Magnetic dipole of nucleus is ~3 orders of magnitude smaller (if nonzero) - such hyperfine corrections can be usually neglected.

There are also ~1/r^4 (electron magnetic) dipole-dipole interactions for larger atoms, e.g. preferring opposite spins on a single orbital.

That's basically all, there is no way to torus-like trajectories, which would require some gigantic magnetic fields - not seen for these particles, well tested e.g. in Penning trap.

Regarding emitting energy by e-p pair, if it already reached the lowest possible energy (ground) state, it has no way to emit any more.

If there would be no strong force, the heaviest nucleus would have charge 1 - all larger would fall apart.

For electron capture EM is not sufficient - there are needed other interactions, which have ~fm range.

This thread was motivated by Gryzinski, you can find discussion on previous pages.

Free-fall repairs problems of Bohr model, in papers he also claimed good agreement with many types of experiments, especially scattering, screening coefficients, Stark effect - see slide 9 of https://www.dropbox.com/s/38xidhztpe9zxsr/freefall2.pdf ... there is much more in his papers and book.

From low energy fusion perspective, he was enthusiast of, I think the most important is that including this classical spin-orbit interaction, you can get nearly backscattering trajectories: which can "jump" localized between two nuclei, screening their Coulomb repulsion for fusion - bottom example below:

Incorrectness of Bohr model (assuming local realism against Bell violation) starts with wrong angular momentum: we know that ground state hydrogen has L=0 orbital angular momentum, while in Bohr it is huge.

Another basic counter-argument is e.g. electron capture - that sometimes nucleus can capture electron from orbital, what requires it getting to a distance of nuclear forces (fm-scale), while it Bohr it is ~5 orders of magnitude larger.

I don't think assuming trajectories on torus will repair any of above problems (?)

I don't know if this is the "second radius force" you are referring to, but crucial neglected interaction he has included is classical analogue of spin-orbit interaction: mainly between traveling magnetic dipole of electron and charge of nucleus.

Explanation: nucleus traveling in field of electron's magnetic dipole gets Lorentz force, which through 3rd Newton law also acts on electron. Thanks to Lorentz invariance, it still works if changing the reference frame such that nucleus rests and electron travels. Derivation:

You are using some your very nonstandard physics, but generally I see you also want to operate on orbits of electrons - assume they have trajectories behind quantum wavefunction.

The problem is that this is assuming "local realism" - a mainstream physicist will tell you is incorrect e.g. due to Bell inequalities: satisfied by local realistic theory, but violated by QM and nature.

Anyway, in both cases we need to understand why physics can violate Bell if wanting to convince to possibility of low temperature fusion.

My point is that we should use "4D local realism" instead: using paths as the basic object, e.g. for Feynman/Boltzmann path ensemble.

Example of Bell violation construction for such uniform path ensemble is above.