Twistor lift for 2-D objects

TGD involves also 2-D objects - partonic 2-surfaces and string world sheets in an essential manner and strong form of holography (SH) states that these objects carry the information about quantum states. This does not mean that the dynamics would reduce to that for string like objects since it is essential that these objects are sub-manifolds of space-time surface. String world sheets carry induced spinor fields and it seems that these are crucial for understanding elementary particles. There are several questions to be answered.

1. Are fermionic fields localized to 2-surfaces? The generalization superconformal symmetry fixing both the bosonic and fermion parts of the action requires that also the interior of space-time carries induced spinor field. Their interpretation is not quite clear: could they perhaps give rise to a supersymmetry? The condition of super-symmetry fixes the analog of massless Dirac action uniquely for both string world sheets and interior of space-time surface. The situation is not clear for the partonic 2-surfaces, which are in special role physically in zero energy ontology (ZEO). There is an infinite number of conserved super currents associated with the modes of the modified Dirac operator defining fermionic super generators. This leads to quantum classical correspondence stating that the eigenvalues of Cartan generators for the fermionic representations of Noether charges are equal to corresponding classical Noether charges defined by the space-time dynamics.
   
   
2. A long-standing question has been whether stringlike objects and partonic 2-surfaces are fundamental dynamical objects or whether they emerge only at the level of effective action. M⁸-H duality states that space-time surfaces M⁸ picture are associative in the sense that either tangent or normal space of space-time surface at any vpoint is associative and therefore quaternionic.
   

   Number theoretic vision suggests that also 2-D objects are fundamental. In number theoretic vision also commutative sub-manifolds of space-time surfaces having induced quaternionic structure reducing to commutative (complex) structure are very natural. Either the tangent space or normal space of 2-surface can be commutative and this gives rise to string world sheets and partonic 2-surfaces as duals of each other just as space-time surfaces have regions for which either tangent spaces or normal spaces are associative (these correspond to regions of space-time with Minkowskian resp. Euclidian signatures of the induced metric). The reduction of the theory to mere string theory is not possible since partonic two surfaces have commutative normal space (partonic 2-surfaces) as part of the tangent space of space-time surface.
   
   

3. What action one should assign with the 2-D objects. The action should be assigned to string world sheets and partonic 2-surfaces representing vertices but the assignent of action with partonic 2-surfaces at the ends of CD does not look natural since they are in the role of initial values. The first guess for the action is as area action. Fermionic action would be fixed uniquely in terms of modified gamma matrices reducing to induced gamma matrices.
   

   Also space-time surfaces in the simplest scenario are minimal surfaces except for a discrete set of singular points at which there is energy transfer between Kähler action and volume term. Something similar is expected also in 2-D case: there must also second part in the action and transfer of Noether changes between the two parts in this set of points.
   

   These points have an identification as point-like particles carrying fermion number and located at partonic 2-surfaces at boundaries of causal diamond (CD) or defining topological vertices so that a classical space-time correlates for twistor diagrams emerge.
   

   Since particles in twistor approaches are associated with the ends of string boundaries at the ends of light-like orbits of partonic 2-surfaces at boundaries of causal diamond (CD), the exceptional points for both space-time surface and string world sheet would correspond to the intersections of string world sheets and partonic 2-surfaces defining also counterparts of vertices.
   
   

Twistor lift provides a first principle approach to the action assignable to the 2-D surfaces.

1. The simplest possibility is that one has also now a Kähler action but now for 4-D space-time surface in the product of twistor spaces of M⁴ and CP₂ dimensional reduced to Cartesian product of twistor sphere S² and 2-D surface representing string world sheet. The assigment of action to partonic 2-surface at the boundary of CD or 2-D generalization of vertex does not look feasible. 4-D Kähler action would be dimensionally reduced to 2-D form and area term.
   
   
2. Field equations contain two terms coming from the variation with respect to the induced metric and Kähler form respectively. The terms coming from the variation with respect to metric vanishes for minimal surfaces since energy momentum tensor is proportional to the induced metric. The term coming from the variation with respect to induced Kähler form need not vanish for minimal surfaces unless there are additional conditions.
   

   The term is of the same form as in 4-D case, which case this term vanishes for holomorphic solutions and also for all known extremals, and there are excellent reasons that this is true also in 2-D case. It therefore seems that minimal surfaces are in question except for discrete set of points as in 4-D case: this conforms with universality forced by quantum criticality stating that Kähler coupling constant disappears from dynamics except in this discrete set of points.
   

   In accordance with SH, this set of points at which minimal surface property fails would define also the correponding points for space-time surface itself. This singularity could mean breakdown of holomorphy, perhaps analogs of poles for analytic functions are in question. One cannot of course exclude the possibility that the boundaries of string world sheets defining orbits of fundamental fermions are analogous to cuts for holomorphic functions.
   
   

3. 2-D minimal surfaces in space-time are also minimal surfaces in imbedding space since the induction from space-time to 2-surface can be also thought of as an induction from imbedding space. SH suggest that space-time as 4-D surface is determined by fixing the 2-D minimal surfaces and finding space-time surface containing them. This space-time surface need not always exist, and one of the key ideas about cognition is that in p-adic case the possibility of p-adic pseudo-constants allows the existence of p-adic space-time surfaces always but that in real case this is not always the case: what is imaginable is not necessarily realizable.
   

   At the level of M⁸ the condition that the coefficients of a polynomial determining the space-time surface are in extension of rationals is very powerful condition and might prevent the extension. As a matter fact, SH becomes at the level of M⁸ even stronger: discrete set of points naturally identifiable as the set of singular points and thus poles of analytic function basically would determine the space-time surface. If fermion lines correspond to cuts, this super-strong form of SH would weaken. For polynomials considerws here cuts are however not possible and they should be generated in the map from H to M⁴× CP₂.
   
   

For details and background see the article Some Questions Related to the Twistor Lift of TGD or the chapter of "Towards M-matrix" with the same title.

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

Articles and other material related to TGD.

Interpretation of the experiments of Montagnier et al

One can make the model of MB more detailed by applying it the experiments of Montagnier et al discussed already earlier from TGD viewpoint (see this). I have developed in collaboration with Peter Gariaev a model for analogous observations by this group (see this).

Consider first a very rough sketch of the experiments.

1. A fragment of DNA was amplified by PCR. It was diluted to say 10^-6 by adding pure water and found to generate EMS at ULF frequency range .5-3 kHz. Call this sample A.
   
   
2. Dilution was put in mu-mental container, which does not allow ULF radiation to get out. In its vicinity another tube, call it B, containing pure water was placed. The water content of each tube was filtered through 450 nm and 20 nm filters. Filtering does not allow particles with size smaller than 20 nm to go through. The samples were diluted to 10^-15 by adding pure water. During each dilution a mechanical agitation of water by generating a vortex was performed.
   
   
3. Copper solenoid producing 7 Hz current was added around the samples. Eventually EMS was found in both A and B. In B there was primer, DNA polymerase, and free nucleotides but not the template complementary strand as in ordinary polymerase chain reaction.
   
   

The TGD interpretation for what happened in sample A would be following.

1. As explained ordinary DNA strand is paired with dark DNA strand for which dark proton triplets at flux tube parallel to ordinary DNA strand represent the codons. This is analog of pairing of DNA strand and its conjugate.
   
   
2. The cyclotron transitions of dark protons (possibly also those changing the direction of spin) generate the ULF radiation as classical em fields accompanied dark photons transformed to ordinary photons. The energies of dark photons are given by E= h_grf and should be above thermal energy at physiological temperatures. The transformations of dark photons to ordinary photons give rise to bio-photons with energies in visible and UV, and possibly also below this range.
   
   
3. Dilution eliminated ordinary DNA from A but left some dark DNA strands to the water. This is nothing but the phantom DNA phenomenon discovered by Gariaev and collaborators. In case of water memory one has phantoms of bio-active molecules. I have applied TGD also to other experimental findings and ideas by Gariaev et al. In particular there are articles written in collaboration about the TGD realization of identification of DNA as hologram and about DNA remote replication analogous to what happens in Montagnier's experiments (see this).
   
   
4. The interpretation of the agitation carried out also in the preparation of homeopathic remedies is that it provided metabolic energy needed to generate large h_eff. Quite generally, the energy of dark variant is larger than that of ordinary state: for instance, cyclotron energy is proportional to h_eff and atomic binding energies to 1/h_eff² so that metabolic energy is needed.
   

   The analogy with ordinary DNA and the idea that DNA replication is a shadow of the replication of dark DNA suggests that dark DNA replicated and a population of dark DNA mimicking ordinary DNA was generated in the diluted water sample A. More generally, water would perform mimicry of bio-active molecule by using dark protons at its magnetic body to generate the cyclotron frequency spectrum of the molecule. An interesting possibility is that dark proton sequences - dark nuclei - perform this mimicry.
   
   

5. The general model suggests that dark DNA generate transversal flux tubes at transversal sheets going through it. One could start by saying loosely that dark photon cyclotron radiation propagated along these flux tubes to the pure water sample, where there was flux tube receiving this radiation. But what the precise meaning of this statement could be, becomes more clear in the following.
   
   

What happened in the pure water sample?

1. Dark photon radiation at ULF frequencies should have caused the generation of dark DNA strands also in pure water sample. The water in the pure water sample mimicked the dark photon radiation by the basic homeopathic mechanism and generated dark DNA strands with transversal flux tubes at transversal flux sheets carrying magnetic fields corresponding to the cyclotron frequencies of dark DNA nucleotides.
   
   
2. Did a pairing of dark DNA in A and its conjugate in B analogous to the pairing of DNA and its conjugate take place? As in the ordinary DNA pairing the pairing would be favored by the minimization of interaction energy. The flux tubes connecting the members of the pair would be like stretched hydrogen bonds between DNA strand and its conjugate so that it would be very long, of order cyclotron wavelength of proton in the magnetic field of flux tube. TGD indeed predicts that hydrogen bonds have length spectrum corresponding to various values of h_eff. In this case however rather small values are involved. Now the values would be very large by h_eff=h_gr.
   
   
3. Did the transversal flux tubes attach to the dark DNA flux tubes directly and have length of the order of distance between samples? Or did the flux tubes from water sample combine to many-sheeted gravitational flux tube with length of the order of cyclotron frequency of proton? The latter option is favored.
   

   The dark photons assignable to the frequency range .5-3 kHz should have energies above thermal energy at physiological temperature in order to have physiological effects. This requires h_eff≥ 6× 10¹⁰: f=.5 kHz would correspond to a thermal energy of photon for most probable wavelength about 10 μm.
   

   A reasonable estimate for the length of the flux tubes involved comes from the cyclotron wavelength of proton. The cyclotron frequency .5-3.0 kHz for proton requires magnetic field about .3 -2.0 Gauss somewhat stronger than B_end=.2 Gauss (B_E=.5 Gauss). The cyclotron wavelength would be in the range .1-.6 Mm (Earth radius is 6.4 Mm) so that the analogs of hydrogen bonds would be very long!
   
   

4. The generation of ordinary DNA strands in this sample would have been by the analog of DNA - dark DNA pairing that should occur in standard biology. The DNA fragment in pure water sample was reproduced as if the complementary strand would have been present.
   
   
5. As already explained, the dark protons are at single sheeted ordinary flux tubes accompanying DNA. n_gr flux tubes from various positions would combine n_gr-sheeted flux tube with same M⁴ projection as ordinary flux tube: they were on top of each other in M⁴× CP₂. Why the protons deserved to be called dark is that the proton sequences at n_gr separate flux tubes form single quantum coherent many-proton states somewhat analogous to Bose-Einstein condensate. Cyclotron energy is therefore naturally n_gr times the cyclotron energy of single state. This is essentially quantum non-locality made possible by the locality at the gravitational flux tube quantum controlling the system. Also dark photons having n_gr-fold energy non-local many-photon states with one photon at each flux tube with same energy and momentum.
   
   
6. Also 7 Hz frequency is necessary for the effect to occur. A natural guess is that this frequency is related to Schumann resonances (see this), which are associated with collective oscillations in the Earth's magnetic field in the cavity bounded by Earth's surface and ionosphere in which em waves cannot propagate. Schumann resonances dominate the frequency spectrum from 3 Hz to 60 Hz - a considerable part of EEG - and there are distinct peaks at frequencies resonance 7.81, 14.3, 20.8, 27.3 and 33.8 Hz.
   

   In the linear model Schumann resonances treating atmosphere as vacuum Schumann resonance frequencies f_n= (n(n+1))^1/2c/2π R_E are determined by the geometry alone with lowest resonance at 7.41 Hz for R_E= 6371 km. The finite conductivity of atmosphere lowers the propagation velocity of light and the frequencies are reduced. This can bring the resonance frequency 7.81 Hz nearer to 7 Hz, and there is of course also the continuum besides the resonance peaks.
   

   In TGD picture the quasi-continuum would relate to the many-sheetedness of the space-time surface making it possible for light to propagate along large number of flux tube paths so that the effective light-velocity would vary. A more precise model give also a resonance at 4.11 Hz. This resonance frequency however varies due to the several factors.
   

   The interpretation of Schumann resonances 7.81, 14.3, 20.8, 27.3 and 33.8 Hz and higher resonances as resonance frequencies of EEG is highly attractive. At higher frequencies the resonances appear approximately with 6.5 Hz intervals. Next resonance would be at 40.3 Hz, which is the familiar thalamo-cortical resonance frequency to which consciousness was once assigned. 8:th partial wave has resonance frequency 60 Hz which happens to be the frequency appearing in the experiments of Li and Heroux. 4 Hz frequency in turn is theta resonance frequency in EEG.
   

   This supports the view that water entrains to Schumann frequencies by tuning to cyclotron frequencies by varying the thickness of flux tubes of its MB so that the coupling of living matter to the oscillations of Earth's magnetic field would play fundamental role in biology and neuroscience. The testable prediction is the correlation of EEG with the local Schumann resonance spectrum of Earth independent of individual.
   

   Dr. Phil Callahan claims on basis of intensive experimental work that there is a tendency of political strifes and wars to concentrate on regions where Schumann resonances are weak. In the proposed picture this would not be surprising. The reduction in the level of consciousness would imply strifes and wars at the level of society and cancer at the level of cell community.
   
   

For details see the article Could Cancer be a Disease of Magnetic Body? by Dana Flavin and me or alternatively the chapter of "Biosystems as Conscious holograms" with the same title.

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

Articles and other material related to TGD.

Understanding the dark magnetic bodies of biomolecules: concrete view about bio-quantum coherence

In previous posting I told about a model of cancer identifying it as a disease of magnetic body (MB) basically MB of water containing charged particles characterizing living matter.

The model for how cancer could be seen as a disease of magnetic body (MB) hardly mentions biochemistry or even cell membrane. Basically a disease of MB of water would be in question. Water of course contains basic ions, biomolecules, and cells and the cyclotron frequencies and masses of ions affect the detailed anatomy of MB. If MB is indeed the boss and biochemistry is mere shadow dynamics. The implications are not restricted to cancer but also other diseases.

The basic cure would be analogous to homeopathy. Irradiate water with the frequencies crucial for communication to and control by MB so that the lost frequencies are re-established.

This is achieved because MB entrains to external frequencies by varying the thickness of its "body parts", flux tubes. MB is like living radio set able to tune itself. This can also lead to problems when some important frequency is tuned to some frequency near it and MB goes out of synch. The negative health effects of the mobile phones (also cancer) might be due this kind of distraction of MB's attention from biological body to the frequencies produce by phone.

This led also to a second flux of big ideas due to a more precise vision about the anatomy of MB. Flux tubes from identical basic units (cells, DNA, identical proteins, etc) combine to from many-sheeted flux tube so that the incoming flux tubes have same M^4 projection being on top of each other in CP_2 direction! This super cable is like umbilical chord! The structures form a Bose-Einstein condensate in abstract topological sense.

This opens fascinating possibilities in understanding of dark DNA which is one of the basic notions of TGD inspired biology.

1. Cells have identical DNAs. Earlier I have assumed that magnetic flux sheets go through DNA in transversal direction and that dark DNA in some sense is sequence of dark proton triplets associated with flux tubes. Furthermore, DNA transcription requires that there are transversal flux tubes emerging from codons or perhaps even nucleotides. A lot of flux tubes!
   

   How to combine these views together with new view about combination of the DNAs flux tube to larger superstructure, one DNA from each cell in structure?
   
   

2. For single DNA each codon would correspond to 3-proton units organized linearly into a sequence. Each 3-proton unit must have a flux tube transversal flux to DNA strand and located at 2-D sheet. This brings in mind the structure of spine as anatomical and neurobiological analogy. This suggests that dark DNA codons formed by 3-proton units should be associated with these horizontal flux tubes in 2-D locally planar surface going through DNA.
   
   
3. These structures from n_gr= h_gr/h₀ = h_eff/h₀ separate cells should combine to single n_gr-sheeted gravitational flux tube with sheets on top of each other with same M⁴ projection. This would be dark DNA at the level of MB. It would seem that given codon of each DNA must contribute a dark proton triplet so that there would be n_gr dark proton triplets at given flux tube which is however very long. The size scale - that is the length of the flux tube - is that of Earth typically and fixed by the cyclotron wave length
   

   This would give a concrete topological meaning to quantum quantum coherence at the level of MB of bio-system. Also a view about how lower level conscious entities integrate to larger ones. Same should apply to other basic biological structures: cells, proteins, RNA, tRA. Dark realization of the genetic code predicts the dark variants of these biomolecules.
   

This raises a long series of questions.

1. How do DNA and its conjugate relate at this level: do DNA and conjugate correspond to single closed long flux tube forming part of the "umbical chord" far from biological body?
   
   
2. What replication of DNA could mean topologically at the level of this super-DNA? What about description of transcription and translation at these super-levels. Are the ordinary replication, etc.. induced from this super level as mere shadow processes: this would explain their mysterious coherence?
   
   
3. What sexual reproduction and associated recombination of chromosomes could mean at super level? What does the growth of organisms mean at super level? Addition of new sheets to super DNA and its variants so that n_gr = number of basic units grows and organism becomes more and more quantum intelligent?
   
   

Fantastic challenges for visual imagination!

For details see the article Could Cancer be a Disease of Magnetic Body? by Dana Flavin and me or alternatively the chapter of "Biosystems as Conscious holograms" with the same title.

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

Articles and other material related to TGD.

Could cancer be a disease of magnetic body?

Li and Heroux have made a highly interesting discovery. The treatment of cancer cell population by 60 Hz oscillating magnetic field with extremely small strength above 25 nT leads to a reduction of the abnormally large chromosome number of the mitochondria of cancer cells and eventually the cancer cells return to the normal state.

TGD based explanation for the findings relies on the basic notions of TGD inspired quantum biology. The basic notions are magnetic body (MB) and hierarchy of Planck constants h_eff=n× h₀ (h=6h_0) emerging from the adelic physics as a prediction but originally proposed on basis of anomalous effects of ELF em fields in living matter. The value of n can be relatively small or very large corresponding to flux tubes mediating em and gravitational interactions. The anatomy of MB has remained unclear hitherto but in this article a detailed model is developed allowing to understand the formula h_gr =h_eff = n_grh₀ for gravitational Planck constant and leading to a further formula for h_gr relating magnetism and gravitation.

A further central notion is TGD based model for water memory as the ability of the MB of water to control the thickness of its flux tubes to entrain with external frequencies and reproduce them. This is a central element in the TGD based view about immune systems and homeopathic effects. Cancer would reduce to a disease of the MB of the system, to a high degree determined by MB of water and homeopathy like treatment based on irradiated water could serve as a cure.

For details see the article Could Cancer be a Disease of Magnetic Body? by Dana Flavin and me or alternatively the chapter of "Biosystems as Conscious holograms" with the same title.

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

Articles and other material related to TGD.

Could dark protons and electrons be involved with di-electric breakdown and conduction in electrolytes?

I have had long time the intuitive feeling that electrolytes are not really understood in standard chemistry and physics and I have expressed this feeling in the TGD model of "cold fusion" (see this). This kind of feeling of course induces immediate horror reaction turning stomach around. Not a single scientist in the world seems to be challenging the age-old chemical wisdom. Who am I to do this? Perhaps I really am the miserable crackpot that colleagues have for four decades told me to be. Do I realize only at the high age of 68 that my wise colleagues have have been right all the time?

The question of my friend related to di-electric breakdown in gases led me to consider this problem more precisely. I will first consider di-electric breakdown and then ionic conduction in electrolytes from TGD point of view to see whether the hypothesis stating that dark matter consists of phases of ordinary matter with non-standard Planck constant h_eff=nh₀ (see this) following from adelic physics (see this) could provide concrete insights to these phenomena.

Ionization in di-electric breakdown in gases

One can start from a model for the dielectric breakdown of gas (see this). The basic idea is that negatively charged cathode emits electrons by tunnelling in electric field and these accelerate in the electric field and ionize atoms provided they travel a distance longer than the free path l= 1/nσ before collision. Here n is number density of atoms and σ collision cross section, in geometric approximation the cross sectional area of gas atom. This implies a lower bound on the number density n of gas atoms. On the other hand, too low density makes also ionizations rare.

The positive ions in turn are absorbed by cathode and more electrons are liberated. In gas dielectric breakdown results if the field strength is above critical value E_cr. For air this one has E_cr=3 kV/mm.

1. Cathode with a sharp tip liberates electrons. The electric field near the tip is very strong an in a reasonable approximation has strength
   

   E= V/r ,
   

   where r is radius of curvature of the tip and V is the voltage with respect to earth. If r is small enough, electron is able to tunnel from the metal.
   
   

2. The tunnelling current from electron can be deduced from a simple model based on Scrödinger equation in
   one-dimensional potential having the form U(x) =-Φ_w+ Vx/r in the non-allowed region.
   One assumes that one can describe the electron using analog of plane wave exp(ikx) with kx replaced with ∫₀^x k(x)dx=i∫₀^xp(x) dx/ℏ with imaginary momentum p(x)= i(2m|E-U(x)|)^1/2 in the non-allowed region. Tunnelling current is proportional to the exponential factor
   

   R= exp(i∫ k(x)dx)
   

   having interpretation as tunneling probability.
   
   

3. Tunneling rate is highest near Fermi energy and at this energy the tunnelling rate is
   

   R= exp(-8π (2mΦ_w³)^1/2/3hE) .
   

   Here m is electron's mass and Φ_w is work function of the metal telling the height of the potential well in which electron resides. In the model of photo-electric effect the energy of photon needed to kick out electron from metal must be above Φ_w. The exponential factor approaches extremely rapidly but for small enough curvature radii and it can be sufficiently near to unity.
   

   Remark: Imaginary momentum does not make sense in classical mechanics. What is interesting that in classical TGD the classical conserved quantities are in general complex numbers and the analogs of virtual particles are on mass shell states with complex moments as also in twistor Grassmannian approach having 8-D generalization in TGD framework. Could tunnelling have classical space-time description in TGD framework?
   
   

4. The electric field needed in the tip cannot be much larger than
   

   
   E_max= Vr ∼ 8π (2mΦ_w³)^1/2/3h
   

   to guarantee that the exponent is not too small. If one has h→ h_eff=n× h₀>h (h=6h₀ is a good guess, see this and this) tunnelling rate increases. This effect might serve as a signature for large value of h_eff. Tunnelling would be to magnetic flux tubes carrying dark electrons.
   
   

What is needed is di-electric breakdown in a manner already described.

1. Electrons ionize atoms and the resulting electrons cause more ionizations. Also the positive ions collide with cathode and generate new electrons. A continual discharge, arc generation, would be the outcome.
   

   A rough criterion for ionization is that the free path l= 1/nσ of electron is so large that the electron gains so large energy in the electric field E that it exceeds ionization energy. The condition is El≥ E_I. Small density increases l but also decreases the number of collisions so that there is some optimal density and pressure for the di-electric breakdown to occur. If electrons are dark they can travel along flux tubes, which would increase the free path in electric field and increase the rate of ionization.
   
   

2. The generation of arc is described by Paschen's law giving the breakdown voltage and discovered 1989 empirically by Paschen (see this).
   
   
   

Do we really understand ionic conduction in electrolytes?

One must now explain why ions can act as charged carriers in relatively weak electric fields. Concerning the production of electrons at electrode the situation remains the same. In electrolyte however the free path is much shorter than in gas since the density n is orders of magnitude higher. Therefore the ionization mechanism in electrolytes must be different - at least in standard physics framework. One can of course ask whether the large value of h_eff might help both in the generation of dark electron at cathode and also help to increase the free path of electron so that they gain higher energy in the electric field of electrolyte typically much lower that in dielectric breakdown.

The mechanism for the dissolution of ions in water involves neither electrodes nor electric field. The ionization of NaCl in water serves as a good example.

1. Na and Cl in NaCl are already ionized since ionic bond is in question. In dissolution giving rise to Na⁺ and Cl^- ions NaCl ionizes into Na⁺ and Cl^- in water. The sizes of ions vary in the range .2- 2 Angstrom. The explanation is that the presence of polar water molecules of size about 3 Angstrom of which some have ionized to OH^- and H⁺ leads to a competition and the presence of OH^- and H⁺ breaks ionic NaCl bonds and dissolves NaCl. Approximating the situation as one-dimensional would suggest that NaCl corresponds to a potential well for e²/r potential. From the distance r between Na and Cl one obtains an estimate for the Coulomb potential energy depending on distance. For r=2 Angstrom it is about 50 eV and therefore rather high.
   
   
2. The presence of OH^- or H⁺ means second potential well. The Coulomb potentials of say Cl^- and OH^- acting on H⁺ sum up and double potential well is created. In the original situation Na⁺ is the potential well of Cl^-. The closer the Cl^- and OH^- (or H⁺ and Na⁺ ions are, the lower the barrier between the two wells is and the higher the tunnelling probability for Na⁺ from the potential well of Cl^- to that of OH^- is. This can make possible tunnelling of Na⁺/Cl^- with subsequent formation of ionic bound state NaOH/HCl.
   

   The tunnelling probability is also now an exponential analogous to that appearing in the previous formula and proportional to 1/h. Ions must however get so close that the potential barrier is low enough. The rate for close encounters must be therefore high enough.
   

   Is this really the case or could h_eff come in rescue? Could the dark protons H⁺ with h_eff=n× h at magnetic flux tubes possibly formed in the ionization of water molecules to OH^- and H⁺ play some role. Could also dark valence electrons assignable to OH play a role. Could one think that dark H⁺ and e^- of H₂O can reside at long flux tubes assignable to H₂O so that H₂O would look like OH^- +H⁺.
   

   As a matter fact, a more realistic model replaces flux tubes with flux tube pairs since there are reasons to assume that the flux tubes carry monopole flux and they must form closed units (see this). Flux tube pairs are also central for the TGD based model of high Tc superconductivity (see this and this).
   

   Same would apply to HCl and NaOH. This leads to several variants of these molecules in which proton or electron or both are dark and resides at long flux tube. External electric field could induce lengthening of this flux flux tube pairs or at least the motion of dark proton and electron along it. These molecules would look like having long charged tentacles formed by flux tube pairs parallel or antiparallel to the direction of electric field. Electric field would force the charged flux tube pair to move so that it would point to the direction to which charged particle moves in the field.
   
   

3. According to standard physics this process generates only different ionic bound states HCl and NaOH are formed from NaCl and H₂O and vice versa. One does not obtain Na⁺ and Cl^- serving as charge carriers. How could the presence of the relatively weak electric field in electrolyte make possible electric currents if there are no charge carriers?
   
   
4. Are HCl and NaOH in water really what they would be in gas? Could HCl in water be a bound state of H⁺ and Cl^- such that H⁺ has a large value of h_eff. Could also Cl^- be Cl for which electron could be dark electron at flux tube? This would make the size of HCl much larger than in gas and the ions involved look like free charge carriers in much longer scale. Could same apply also to NaOH, NaCl ad H₂O.
   

   Could the fundamental current carriers be dark protons and dark electrons at dark flux tubes pairs? Consider a long tentacle formed by a long flux tube pair carrying dark proton or electron with the direction of flux tube pair determined by the sign of the electric force on the charge. This tentacle could reconnect with a neutral tentacle and the charge would be transferred to the latter. This flux tube pair would be in turn driven by by the field perhaps also inducing the increase of h_eff (requiring energy provided by the field) and therefore flux tube length so that it points to the same direction as the original long tentacle. The outcome would be conduction based on the hopping of protons and electrons over a distance of the order of tentacle length. This hopping mechanism could serve as a universal mechanism of conduction in electrolytes and also in living matter.
   
   

For TGD view about "cold fusion" see the article Cold fusion, low energy nuclear reactions, or dark nuclear synthesis?, the shorter article Could dark protons and electrons be involved with di-electric breakdown in gases and conduction in electrolytes?, or the chapter Cold fusion again of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".

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

Articles and other material related to TGD.

Sensory perception and motor action as time reversals of each other: a royal road to the understanding of other minds?

The notion of mirror neuron is extremely attractive because it could allow the understanding of the observed goal directed behaviors of living systems by inducing corresponding imagined or even real actions. The sensory input about behavior would automatically induce the neural activity representing intention about the behavior or imagined behavior. Mirror neuron hypothesis was derived originally for monkeys but has been considerably generalized. For instance, in the case of humans mirro neurons could allow an almost automatic understanding of intentions and emotions of other people.

In TGD framework the objections against mirror neuron hypothesis motivate its replacement with what I call time mirror hypothesis inspired by zero energy ontology, and stating that motor action and sensory perception are in a well-defined sense time reversals of each other. This hypothesis could explain the time anomalies assignable to mirror neurons if they are indeed involved (reactions tend assigned to mirror neurons tend to be "too fast") and also Libet's findings. This inspires the notion of quantum monadology: parts of brain would be continually time mirroring each other. Also magnetic body would be involved. The time mirror relationship could correspond to directed attention having as space-time correlates magnetic flux tubes carrying dark photon signals in both time directions. Time mirror hypothesis is applied to the entrainment of the speech motor regions with auditory areas at the opposite side of brain occurring at resonance frequency 4.5 Hz as discovered by Poeppel and Assaneo.

See the article Sensory perception and motor action as time reversals of each other: a royal road to the understanding of other minds? or the chapter of "TGD and EEG" having the same title.

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

Articles and other material related to TGD.