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 heff/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.
In TGD classical radiation should have also large heff/h=n photonic counterparts with much larger energies E=heff×f to explain the quantal effects of ELF radiation at EEG frequency range on brain (see this). The general proposal is that heff equals to what I have called gravitational Planck constant hbargr=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 heff = hgr 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 background see the chapter Quantum Model for Bio-Superconductivity: II .