The hierarchy of Planck constants heff=n× h has now rather strong theoretical basis and reduces to number theory (see this). Quantum criticality would be essential for the phenomenon and could explain the critical doping fraction for cathode by D nuclei. Quantum criticality could help to explain the difficulties to replicate the effect.
1. Simple modification of WL does not work
The first model is a modification of WL and relies on dark variant of weak interactions. In this case LENR would be appropriate term.
- Concerning the rate of the weak process e+p→ n+ν the situation changes if heff is large enough and rather large values are indeed predicted. heff could be large also for weak gauge bosons in the situation considered. Below their Compton length weak bosons are effectively massless and this scale would scale up by factor n=heff/h to almost atomic scale. This would make weak interactions as strong as electromagnetic interactions and long ranged below the Compton length and the transformation of proton to neutron would be a fast process. After that a nuclear reaction sequence initiated by neutron would take place as in WL. There is no need to assume that neutrons are ultraslow but electron mass remains the problem. Note that also proton mass could be higher than normal perhaps due to Coulomb interactions.
- As such this model does not solve the problem related to the too small electron mass. Nor does it solve the problem posed by gamma ray production.
2. Dark nucleosynthesis
Also second TGD inspired model involves the heff hierarchy. Now LENR is not an appropriate term: the most interesting things would occur at the level of dark nuclear physics, which is now a key part of TGD inspired quantum biology.
- One piece of inspiration comes from the exclusion ones (EZs) of Pollack (see this) (see this and this), which are negatively charged regions (see this, this, and this).
Also the work of the group of Prof. Holmlid (see this and this) not yet included in the book of Krivit was of great help. TGD proposal (see this and this) is that protons causing the ionization go to magnetic flux tubes having interpretation in terms of space-time topology in TGD Universe. At flux tubes they have heff=n× h and form dark variants of nuclear strings, which are basic structures also for ordinary nuclei but would have almost atomic size scale now.
- The sequences of dark protons at flux tubes would give rise to dark counterparts of ordinary nuclei proposed to be also nuclear strings but with dark nuclear binding energy, whose scale is measured using as natural unit MeV/n, n=heff/h, rather than MeV. The most plausible interpretation is that the field body/magnetic body of the nucleus has heff= n× h and is scaled up in size. n=211 is favoured by the fact that from Holmlid's experiments the distance between dark protons should be about electron Compton length.
Besides protons also deuterons and even heavier nuclei can end up to the magnetic flux tubes. They would however preserve their size and only the distances between them would be scaled to about electron Compton length on basis of the data provided by Holmlid's experiments (see this and this).
The reduced binding energy scale could solve the problems caused by the absence of gamma rays: instead of gamma rays one would have much less energetic photons, say X rays assignable to n=211 ≈ mp/me. For infrared radiation the energy of photons would be about 1 eV and nuclear energy scale would be reduced by a factor about 10-6-10-7: one cannot exclude this option either. In fact, several options can be imagined since entire spectrum of heff is predicted. This prediction is a testable.
Large heff would also induce quantum coherence is a scale between electron Compton length and atomic size scale.
- The simplest possibility is that the protons are just added to the growing nuclear string. In each addition one has (A,Z)→ (A+1,Z+1) . This is exactly what happens in the mechanism proposed by Widom and Larsen for the simplest reaction sequences already explaining reasonably well the spectrum of end products.
In WL the addition of a proton is a four-step process. First e+p→ n+ν occurs at the surface of the cathode. This requires large electron mass renormalization and fine tuning of the electron mass to be very nearly equal but higher than n-p mass difference.
There is no need for these questionable assumptions of WL in TGD. Even the assumption that weak bosons correspond to large heff phase might not be needed but cannot be excluded with further data. The implication would be that the dark proton sequences decay rather rapidly to beta stable nuclei if dark variant of p→ n is possible.
- EZs and accompanying flux tubes could be created also in electrolyte: perhaps in the region near cathode, where bubbles are formed. For the flux tubes leading from the system to external world most of the fusion products as well as the liberated nuclear energy would be lost. This could partially explain the poor replicability for the claims about energy production. Some flux tubes could however end at the surface of catalyst under some conditions. Flux tubes could have ends at the catalyst surface. Even in this case the particles emitted in the transformation to ordinary nuclei could be such that they leak out of the system and Holmlid's findings indeed support this possibility.
If there are negatively charged surfaces present, the flux tubes can end to them since the positively charged dark nuclei at flux tubes and therefore the flux tubes themselves would be attracted by these surfaces. The most obvious candidate is catalyst surface, to which electronic charge waves were assigned by WL. One can wonder whether already Tesla observed in his experiments the leakage of dark matter to various surfaces of the laboratory building. In the collision with the catalyst surface dark nuclei would transform to ordinary nuclei releasing all the ordinary nuclear binding energy. This could create the reported craters at the surface of the target and cause ehating. One cannot of course exclude that nuclear reactions take place between the reaction products and target nuclei. It is quite possible that most dark nuclei leave the system.
It was in fact Larsen, who realized that there are electronic charge waves propagating along the surface of some catalysts, and for good catalysts such as Gold, they are especially strong. This would suggests that electronic charge waves play a key role in the process. The proposal of WL is that due to the positive electromagnetic interaction energy the dark protons of dark nuclei could have rest mass higher than that of neutron (just as in the ordinary nuclei) and the reaction e+p→ n+ν would become possible.
- Spontaneous beta decays of protons could take place inside dark nuclei just as they occur inside ordinary nuclei. If the weak interactions are as strong as electromagnetic interactions, dark nuclei could rapidly transform to beta stable nuclei containing neutrons: this is also a testable prediction. Also dark strong interactions would proceed rather fast and the dark nuclei at magnetic flux tubes could be stable in the final state. If dark stability means same as the ordinary stability then also the isotope shifted nuclei would be stable. There is evidence that this is the case.
One can of course wonder whether even "transmutation" is an appropriate term now. Dark nucleosynthesis, which could in fact be the mechanism of also ordinary nucleosynthesis outside stellar interiors explain how elements heavier than iron are produced, might be more appropriate term.
See the chapter Cold fusion again of "Hyper-finite Factors and Dark Matter Hierarchy" or the article Cold fusion, low energy nuclear reactions, or dark nuclear synthesis?
For a summary of earlier postings see Latest progress in TGD.