This inspires the proposal that protons at hydrogen bonds and also the valence electrons of metals can be transferred to the gravitational Bohr orbits. This proposal unifies the previous picture. For electrons the reduction of binding energy would be a fraction me/mp from that for protons. This would give a precise identification for the notion of dark ion as an effective ion due to the delocalization of a proton of hydrogen bond or of valence electron. This leads to the understanding of the role of quantum gravity in the TGD inspired quantum biology.
About the notion of magnetic body (MB)
The proposed picture allows us to reconsider a long-standing question relating to the notion of MB with an onion-like layered structure. What could this sentence mean quantitatively?
- The 4-surfaces X4 with 1-D CP2 projection and 3-D M4 projection having 2-D membrane as E3 projection are good candidates for various membrane objects in TGD Universe. The E3 projection is not a 2-D minimal surface although X4 is and this possible if the 1-D CP2 projection is dynamical. The flux tubes of MB should be assignable to kind of membrane-like surface.
- The gravitational magnetic body could be a layered structure containing the Bohr orbits with Bohr radii rn ∝ n2 of particles in the gravitational field of Earth. Particles with different masses would concentrate at the same orbits. Earth could be seen as a gravitational analog of atom containing large numbers of particles at the Bohr orbits. Physical intuition suggests that Exclusion Principle applies only inside the Bohr orbits which correspond to flux tubes. The dynamics of bio-sphere would involve an an essential manner quantum gravitation.
- Flux sheets with a cylindrical rotational symmetry containing the orbits can be considered. These surfaces should be realized as preferred extremals of the action and should be minimal surfaces in H=M4× CP2. As closed surfaces they cannot define minimal surfaces of the Euclidean 3-space E3. Indeed, soap bubbles are not minimal surfaces but require a constant pressure difference between interior and exterior. The analog of pressure difference would be non-trivial and dynamic 1-D projection of 4-D surface to CP2 (see this). The liberation of metabolic energy quantum would be analogous to a transition of hydrogen atom to a lower energy state.
This picture makes it also possible to formulate a more precise view about the model of cell membrane as a generalized Josephson junction for which the generalized Josephson energy for charge Ze is the sum EJ = ZeV +Δ Ec of ordinary Josephson energy ZeV and difference Δ Ec of dark cyclotron energies for the flux tubes at the two sides of the cell membrane having in general different strengths of magnetic field.
The model requires large heff in order that Josephson frequencies can correspond to frequencies in the EEG range. This justifies the assumption that dark ions have heff=hgr . The ionization would be effective and caused by the transformation of protons of hydrogen bonds and valence electrons to dark charge carriers at the gravitational flux tubes.
The physical meaning of the criticality against the generation of nerve pulse for a critical membrane potential eVcr ≈ .05 eV has remained open.
- Since voltage gives rise to negative potential energy, it seems clear that there must be positive contribution to the energy and this could come from the reduction Δ Egr of the gravitational potential energy due to the positive resp. effective ionization of atoms of metal atoms resp. electronegative atoms with hydrogen bonds.
The reduction of the gravitational potential energy for electrons is fraction me/mp from that for protons so that protonic contribution should dominate in the reduction of gravitational potential energy if dark electrons and protons correspond to the same shell of gravitational atom. The first guess is that the energy shell and thus the distance from the Earth's surface is the same.
The parametrization of the reduction of the gravitational energy per atom and for the difference Δ Ec of cyclotron energies should in the standard picture correspond to a thermo-dynamical formulation using chemical potentials to fix the ion concentrations. The water has very special thermodynamic properties in the range between freezing and boiling points and anomalies are largest near physiological temperatures. This would be due to the presence of dark hydrogen bonds, which supports the view that the number of dark protons and electrons depends on temperature.
- In the first approximation the negative Coulombic interaction energy for the cell membrane is given by ECoul= -Qtot eV =-∑i Ni(out) Zi eV, where Ni is the number effective ions with charge Zie. The contribution of positive charges is negative since V corresponds to a negative net charge for the cell. The situation is stable for |ECoul| > |ECoul,crit|= Np Δ Egr. The system becomes critical at QtoteVcr= NpΔ Egr. The system becomes critical at QtoteVcr= NpΔ Egr. The value of the critical potential energy is given by eVcr= Np Δ Egr/Qtot and is roughly constant for a given neuron. This suggests that the ratio Np/Qtot characterizes the cell. Neurons and ordinary cells could differ in that ordinary cells are either subcritical or so overcritical that nerve pulses do not occur. Subcriticality looks the more plausible option. The emergence of the nervous system would mean the discovery of quantum criticality as a control tool of MB.
- In the generation of the nerve pulse the dark protons and electrons become ordinary ones in the reduction hgr→heff< < hgr for them and the membrane potential changes sign. In ZEO this transition could correspond to BSFR ("big" state function reduction) inducing time reversal and change of membrane potential. The second BSFR would bring back the original situation and membrane potential would return to the over-critical value.
In the TGD Universe quantum gravitation would be associated with the cell membrane, in particular neuronal membrane. Quantum gravitation has been speculatively assigned with microtubules (MTs) rather than cellular or neuronal membranes. What is the situation in TGD?
- Axonal MTss are highly critical systems, which continually change their lengths. The surface of MTs has one GDP per tubulin dimer and the ends of MT has GTPs so that there is a constant negative charge per unit length. The number of GTPs is larger at the second end so that there is an electric field along MT.
- GTP<ftrightarrow GDP process accompanies the variation of the length of the MT. The transformation of the protons assignable to the phosphate hydrogen bonds to gravitationally dark protons could be an essential element of the MT dynamics. The periods of increasing/decreasing MT length could be initiated by BSFR and would correspond to different arrows of time. The effective ionization affects the effective charge of the axonal interior and therefore of membrane potential. This suggests a strong correlation with the variation of axonal MT lengths and nerve pulse propagation.
The propagation of nerve pulse through the myelinated sections of the axons, where ion transfer with cell exterior is not possible, remains a mystery in the standard model. Without axonal MTs the nerve pulse propagation would not be possible. This could allow us to understand why various neuronal diseases involve a reduced MT stability (this).
For a summary of earlier postings see Latest progress in TGD.