To get a deeper understanding of the central here Coulomb force, turns out long-range interactions for (quantized) topological charges are experimentally recreated in liquid crystals, e.g.:
I have prepared simple calculation of such Coulomb (materials, sources: https://github.com/JarekDuda/l…crystals-particle-models/ ) - for two topological charges in various distances, calculate total energy of such configuration by integrating energy density, getting Coulomb effective potential - attraction/repulsion of charges from energy minimization:
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Higgs potential e.g. (|n|2 - 1)^2, quite popular in physics, here just means nontrivial vacuum - e.g. "director field" in liquid crystals, leading to electromagnetism as Goldstone bosons ... potential allows to deform to finite energy to prevent infinite energy singularities.
The 1/r2 (Coulomb) force is proportional to field curvature around topological charges e.g. hedgehog configuration - hence we interpret curvature as electric field, in Gauss law getting charge quantization as topological.
Biaxial nematic has SO(3) vacuum in 3D space ... which naturally extends to SO(4) in 4D spacetime - adding 4th axis which tiny perturbations are governed by second set of Maxwell equations - popular GEM approximation of general relativity ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism )
Indeed electron being perfect point makes no sense - e.g. would have infinite energy of electric field, wouldn't have running coupling effect (as experiment and Faber have).
And so what I and Faber emphasize is regularization - deformation of this field to prevent infinite energy, what can be easily realized using Higgs-like potential: preferring e.g. unitary vectors, but also allowing to deform them to prevent infinity, discontinuity.
Electric charge can be calculated through Gauss law by integrating electric field over closed surface - what has also topological analogue if interpreting spatial curvature of field as electric field.
This way he get Coulomb potential if calculating energy of pairs of charges in various distances ... with slight deformation for very small distances - as in running coupling effect.
I use topological charge as (2,3D) winding number for field restricted to a closed surface - it gives function from the surface to sphere, which has to cover this sphere an integer number of times.
For 3D topological charge we analogously get point-like charges in 3D, Gauss law with built in charge quantization: integrating field curvature over a closed surface, we get topological charge - hence we should interpret field curvature as electric field (Faber's approach). Using Lorentz invariant model, this way there also appears magnetic e.g. Lorentz interaction.
We need magnetic dipole moment for leptons - what for biaxial nematic-like models comes from the hairy ball theorem.
"If "deep orbits" are highly relativistic, indeed de Broglie's clock slows down proportionally to gamma = sqrt(1-v^2)"
Indeed the ~10^21 Hz electron clock is slowed down for high speeds, what they also use in the experimental confirmation: ~80MeV electrons slowing down the clock so that distance between "ticks" agree with crystal structure - getting resonance: https://link.springer.com/article/10.1007/s10701-008-9225-1
Such clock/intrinsic periodic process create coupled waves, also in hydrodynamical analogs leading to quantum-like effects e.g. interference, tunneling, orbit quantization - gathered hydrodynamical analogs: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf
For electron assistance in fusion, it would need to travel between the two nuclei - for which some resonance (like in https://www.nature.com/articles/ncomms4219 ) might indeed be useful, in which time dilation could be indeed essential.
ps. Liquid crystals provide promising hydrodynamical analogs of particles - they have (topological) charge quantization, for which there are experimentally realized long-range interactions e.g. Coulomb-like: https://www.nature.com/articles/s41598-017-16200-z
Here is mathematical framework to build electromagnetism for such charges: by interpreting curvature as electric field, Gauss law counts topological charge (which is quantized): https://arxiv.org/pdf/2108.07896
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:
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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.