How AC voltage at critical frequencies could induce transition to microtubular superconductivity?

Blog and Facebook discussions have turned out to be extremely useful and quite often new details to the existing picture emerge from them. We have had interesting exchanges with Christoffer Heck in the comment section to the posting Are microtubules macroscopic quantum systems? and this pleasant surprise occurred also now thanks to a question by Christoffer.

Recall that Bandyopadhyay's team claims to have detected the analog of superconductivity, when microtubules are subjected to AC voltage (see this). The transition to superconductivity would occur at certain critical frequencies. For references and the TGD inspired model see the article.

The TGD proposal for bio-superconductivity - in particular that appearing in microtubules - is same as that for high Tc superconductivity. Quantum criticality,large h_eff/h=n phases of of Cooper pairs of electrons and parallel magnetic flux tube pairs carrying the members of Cooper pairs for the essential parts of the mechanism. S=0 (S=1) Cooper pairs appear when the magnetic fields at parallel flux tubes have opposite (same) direction.

Cooper pairs would be present already below the gap temperature but possible super-currents could flow in short loops formed by magnetic flux tubes in ferromagnetic system. AC voltage at critical frequency would somehow induce transition to superconductivity in long length scales by inducing a phase transition of microtubules without helical symmetry to those with helical symmetry and fusing the conduction pathways with length of 13 tubulins to much longer ones by reconnection of magnetic flux tubes parallel to the conduction pathways.

The phonon mechanism for the formation of Cooper pair in ordinary superconductivity cannot be however involved with high Tc superconductivity nor bio-superconductivity. There is upper bound of about 30 K for the critical temperature of BCS superconductors. Few days ago I learned about high Tc superconductivity around 500 K for n-alkanes (see the blog posting) so that the mechanism for high Tc is certainly different .

The question of Christoffer was following. Could microwave radiation for which photon energies are around 10^-5 eV for ordinary value of Planck constant and correspond to the gap energy of BCS superconductivity induce phase transition to BCS super-conductivity and maybe to micro-tubular superconductivity (if it exists at all)?

This inspires the question about how precisely the AC voltage at critical frequencies could induce the transition to high Tc- and bio-super-conductivity. Consider first what could happen in the transition to high Tc super-conductivity.

1. In high Tc super conductors such as copper-oxides the anti-ferromagnetism is known to be essential as also 2-D sub-lattice structures. Anti-ferromagnetism suggests that closed flux tubes form of squares with opposite directions of magnetic field at the opposite sides of square. The opposite sides of the square would carry the members of Cooper pair.
   
   
2. At quantum criticality these squares would reconnect to very long flattened squares by reconnection. The members of Cooper pairs would reside at parallel flux tubes forming the sides of the flattened square. Gap energy would consists interaction energies with the magnetic fields and the mutual interaction energy of magnetic moments.
   

   This mechanism does not work in standard QM since the energies involved are quite too low as compared to thermal energy. Large h_eff/h=n would however scale up the magnetic energies by n. Note that the notion of gap energy should be perhaps replaced with collective binding energy per Cooper pair obtained from the difference of total energies for gap phase formed at higher temperature and for superconducting phase formed at Tc by dividing with the number of Cooper pairs.
   

   Another important distinction to BCS is that Cooper pairs would be present already below gap temperature. At quantum criticality the conduction pathways would become much longer by reconnection. This would be represent an example about "topological" condensed matter physics. Now hover space-time topology would be in question.
   
   

3. The analogs of phonons could be present as transversal oscillations of magnetic flux tubes: at quantum criticality long wave length "magneto-phonons" would be present. The transverse oscillations of flux tube squares would give rise to reconnection and formation of
   
   

If the irradiation or its generalization to high Tc works the energy of photon should be around gap energy or more precisely around energy difference per Cooper pair for the phases with long flux tubes pairs and short square like flux tubes.

1. To induce superconductivity one should induce formation of Cooper pairs in BCS superconductivity. In high Tc super-conductivity it should induce a phase transition in which small square shaped flux tube reconnect to long flux tubes
   forming the conducting pathways. The system should radiate away the energy difference for these phases: the counterpart of binding energy could be defined as the radiated energy per Cooper pair.
   
   
2. One could think the analog of stimulated emission. Assume that Cooper pairs have two states: the genuine Cooper pair and the non-superconducting Cooper pair. This is the case in high Tc superconductivity but not in BCS superconductivity, where the emergence of superconductivity creates the Cooper pairs. One can of course ask whether one could speak about the analog of stimulated emission also in this case.
   
   
3. Above Tc but below gap temperature one has the analog of inverted population: all pairs are in higher energy state. The irradiation with photon beam with energy corresponding to energy difference gives rise to stimulated emission and the system goes to superconducting state with a lower energy state with a lower energy.
   
   

This mechanism could explain the finding of Bandyopadhyay's team that AC perturbation at certain critical frequencies gave rise to a ballistic state (no dependence of the resistance on the length of the wire so that the resistance must be located at its ends). The team used photons with frequency scales of MHz, GHz, and THz. The corresponding photon energy scales are about 10^-8 eV, 10^-5, 10^-2 eV for the ordinary value of Planck constant and are below thermal energies.

In TGD classical radiation should have also large h_eff/h=n photonic counterparts with much larger energies E=h_eff×f to explain the quantal effects of ELF radiation at EEG frequency range on brain (see this). The general proposal is that h_eff equals to what I have called gravitational Planck constant hbar_gr=GMm/v₀ (see this or this). This implies that dark cyclotron photons have universal energy range having no dependence on the mass of the charged particle. Bio-photons have energies in visible and UV range much above thermal energy and would result in the transition transforming dark photons with large h_eff = h_gr to ordinary photons.

One could argue that AC field does not correspond to radiation. In TGD framework this kind of electric fields can be interpreted as analogs of standing waves generated when charged particle has contacts to parallel "massless extremals" representing classical radiation with same frequency propagating in opposite directions. The net force experienced by the particle corresponds to a standing wave.

Irradiation using classical fields would be a general mechanism for inducing bio-superconductivity. Superconductivity would be generated when it is needed. The findings of Blackman and other pioneers of bio-electromagnetism about quantal effects of ELF em fields on vertebrate brain stimulated the idea about dark matter as phases with non-standard value of Planck constant. Also these finding could be interpreted as a generation of superconducting phase by this phase transition.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.