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Year 2015

Is non-associative physics and language possible only in many-sheeted space-time?

In Thinking Allowed Original there was very interesting link added by Ulla about the possibility of non- associative quantum mechanics.

Also I have been forced to consider this possibility.

  1. The 8-D imbedding space of TGD has octonionic tangent space structure and octonions are non-associative. Octonionic quantum theory however has serious mathematical difficulties since the operators of Hilbert space are by definition associative. The representation of say octonionic multiplication table by matrices is possible but is not faithful since it misses the associativity. More concretely, so called associators associated with triplets of representation matrices vanish. One should somehow transcend the standard quantum theory if one wants non-associative physics.
  2. Associativity therefore seems to be fundamental in quantum theory as we understand it recently. Associativity is indeed a fundamental and highly non-trivial constraint on the correlation functions of conformal field theories. In TGD framework classical physics is an exact part of quantum theory so that quantum classical correspondence suggests that associativity could play a highly non-trivial role in classical TGD.

    The conjecture is that associativity requirement fixes the dynamics of space-time sheets - preferred extremals of Kähler action - more or less uniquely. One can endow the tangent space of 8-D imbedding H=M4× CP2 space at given point with octonionic structure: the 8 tangent vectors of the tangent space basis obey octonionic multiplication table.

    Space-time realized as n-D surface in 8-D H must be either associative or co-associative: this depending on whether the tangent space basis or normal space basis is associative. The maximal dimension of space-time surface is predicted to be the observed dimension D=4 and tangent space or normal space allows a quaternionic basis.

  3. There are also other conjectures (see this) about what the preferred extremals of Kähler action defining space-time surfaces are.
    1. A very general conjecture states that strong form of holography allows to determine space-time surfaces from the knowledge of partonic 2-surfaces and 2-D string world sheets.
    2. Second conjecture involves quaternion analyticity and generalization of complex structure to quaternionic structure involving generalization of Cauchy-Riemann conditions.
    3. M8-M4× CP2 duality stating that space-time surfaces can be regarded as surface in either M8 or M4× CP2 is a further conjecture.
    4. Twistorial considerations select M4× CP2 as a completely unique choice since M4 and CP2 are the only spaces allowing twistor space with Kähler structure. The conjecture is that preferred extremals can be identified base spaces of 6-D sub-manifolds of the product CP3× SU(3)/U(1)× U(1) of twistor spaces of M4 and CP2 having the property that it makes sense to speak about induced twistor structure.
    The "super(optimistic)" conjecture is that all these conjectures are equivalent.
One must be of course very cautious in order to not draw too strong conclusions. Above one considers quantum physics at the level of single space-time sheet. What about many-sheeted space-time? Could non-associative physics emerge in TGD via many-sheeted space-time? To answer this question one must first understand what non-associativity means.
  1. In non-associative situation brackets matter. A(BC) is different from (AB)C. From schooldays or at least from the first year calculus course one recalls the algorithm: when calculating the expression involving brackets one first finds the innermost brackets and calculates what is inside them, then proceed to the next innermost brackets, etc... In computer programs the realization of the command sequences involving brackets is called parsing and compilers perform it. Parsing involves decomposition of program to modules calling modules calling.... Quite generally, the analysis of linguistic expressions involves parsing. Bells start to ring as one realizes that parsings form a hierarchy as also do the space-time sheets!
  2. More concretely, there is hierarchy of brackets and there is also a hierarchy of space-time sheets, perhaps labelled by p-adic primes. B and C inside brackets form (BC), something analogous to a bound state or chemical compound. In TGD this something could correspond to a "glueing" space-time sheets B and C at the same larger space-time sheet. More concretely, (BC) could correspond to braided pair of flux tubes B and C inside larger flux tube, whose presence is expressed as brackets (..). As one forms A(BC) one puts flux tube A and flux tube (BC) containing braided flux tubes B and C inside larger flux tube. For (AB)C flux one puts tube (AB) containing braided flux tubes A and B and tube C inside larger flux tube. The outcomes are obviously different. A
  3. Non-associativity in this sense would be a key signature of many-sheeted space-time. It should show itself in say molecular chemistry, where putting on same sheet could mean formation of chemical compound AB from A and B. Another highly interesting possibility is hierarchy of braids formed from flux tubes: braids can form braids, which in turn can form braids,... Flux tubes inside flux tubes inside... Maybe this more refined breaking of associativity could underly the possible non-associativity of biochemistry: biomolecules looking exactly the same would differ in subtle manner.
  4. What about quantum theory level? Non-associativity at the level of quantum theory could correspond to the breaking of associativity for the correlation functions of n fields if the fields are not associated with the same space-time sheet but to space-time sheets labelled by different p-adic primes. At QFT limit of TGD giving standard model and GRT the sheets are lumped together to single piece of Minkowski space and all physical effects making possible non-associativity in the proposed sense are lost. Language would be thus possible only in TGD Universe! My nasty alter ego wants to say now something - my sincere apologies: in superstring Universe communication of at least TGD has indeed turned out to be impossible! If superstringy universe allows communications at all, they must be uni-directional!
Non-associativity is an essentially linguistic phenomenon and relates therefore to cognition. p-Adic physics labelled by p-adic primes fusing with real physics to form adelic physics are identified as the physics of cognition in TGD framework.
  1. Could many-sheeted space-time of TGD provides the geometric realization of language like structures? Could sentences and more complex structures have many-sheeted space-time structures as geometrical correlates? p-Adic physics as physics of cognition would suggests that p-adic primes label the sheets in the parsing hierarchy. Could bio-chemistry with hierarchy of magnetic flux tubes added, realize the parsing hierarchies?
  2. DNA is a language and might provide a key example about parsing hierarchy. The mystery is that human DNA and DNAs of most simplest creatures do not differ much. Our cousins have almost identical DNA with us. Why do we differ so much? Could the number of parsing levels be the reason- p-adic primes labelling space-time sheets? Could our DNA language be much more structured than that of our cousins. At the level of concrete language the linguistic expressions of our cousin are indeed simple signals rather than extremely complex sentences of old-fashioned German professor forming a single lecture each. Could these parsing hierarchies realize themselves as braiding hierarchies of magnetic flux tubes physically and more abstractly as the parsing hierarchies of social structures. Indeed, I have proposed that the presence of collective levels of consciousness having hierarchy of magnetic bodies as a space-time correlates distinguishes us from our cousins so that this explanation is consistent with more quantitative one relying on language.
  3. I have also proposed that intronic portion of DNA is crucial for understanding why we differ so much from our cousins (see this and this). How does this view relate to the above proposal? In the simplest model for DNA as topological quantum computer introns would be connected by flux tubes to the lipids of nuclear and cell membranes. This would make possible topological quantum computations with the braiding of flux tubes defining the topological quantum computer program.

    Ordinary computer programs rely on computer language. Same should be true about quantum computer programs realized as braidings. Now the hierarchical structure of parsings would correspond to that of braidings: one would have braids, braids of braids, etc... This kind of structure is also directly visible as the multiply coiled structure of DNA. The braids beginning from the intronic portion of DNA would form braided flux tubes inside larger braided flux tubes inside.... defining the parsing of the topological quantum computer program.

    The higher the number of parsing levels, the higher the position in the evolutionary hierarchy. Each braiding would define one particular fundamental program module and taking this kind of braided flux tubes and braiding them would give a program calling these programs as sub-programs.

  4. The phonemes of language would have no meaning to us (at our level of self hierarchy) but the words formed by phonemes and involving at basic level the braiding of "phoneme flux tubes" would have. Sentences and their substructures would in turn involve braiding of "word flux tubes". Spoken language would correspond to a temporal sequence of braidings of flux tubes at various hierarchy levels.
  5. The difference between us and our cousins (or other organisms) would not be at the level of visible DNA but at the level of magnetic body. Magnetic bodies would serve as correlates also for social structures and associated collective levels of consciousness. The degree of braiding would define the level in the evolutionary hierarchy. This is of course the basic vision of TGD inspired quantum biology and quantum bio-chemistry in which the double formed by organism and environment is completed to a triple by adding the magnetic body.
p-Adic hierarchy is not the only hierarchy in TGD Universe: there is also the hierarchy of Planck constants heff=n× h giving rise to a hierarchy of intelligences. What is the relationship between these hierarchies?
  1. I have proposed that speech and music are fundamental aspects of conscious intelligence and that DNA realizes what I call bio-harmonies in quite concrete sense (see this and this): DNA codons would correspond to 3-chords. DNA would both talk and sing. Both language and music are highly structured. Could the relation of heff hierarchy to language be same as the relation of music to speech?
  2. Are both musical and linguistic parsing hierarchies present? Are they somehow dual? What does parsing mean for music? How musical sounds could combine to form the analog of two braided strand? Depending on situation we hear music both as separate notes and as chords as separate notes fuse in our mind to a larger unit like phonemes fuse to a word.

    Could chords played by single instrument correspond to braidings of flux tubes at the same level? Could the duality between linguistic and musical intelligence (analogous to that between function and its Fourier transform) be very concrete and detailed and reflect itself also as the possibility to interpret DNA codons both as three letter words and as 3-chords (see this)?

See the new chapter Is Non-Associative Physics and Language Possible Only in Many-Sheeted Space-Time?.

Does also low Tc superconductivity rely on magnetic flux tubes in TGD Universe?

Discussions with Hans Geesink have inspired sharpening of the TGD view about bio-superconductivity (bio-SC), high Tc superconductivity (SC) and relate the picture to standard descriptions in a more detailed manner. In fact, also standard low temperature super-conductivity modelled using BCS theory could be based on the same universal mechanism involving pairs of magnetic flux tubes possibly forming flattened square like closed flux tubes and members of Cooper pairs residing at them.

A brief summary about strengths and weakness of BCS theory

First I try to summarise some basics about BCS theory.

  1. BCS theory is successful in 3-D superconductors and explains a lot: supracurrent, diamagnetism, and thermodynamics of the superconducting state, and it has correlated many experimental data in terms of a few basic parameters.
  2. BCS theory has also failures.
    1. The dependence on crystal structure and chemistry is not well-understood: it is not possible to predict, which materials are super-conducting and which are not.
    2. High-Tc SC is not understood. Antiferromagnetism is known to be important. The quite recent experiment demonstrates conductivity- maybe even conductivity - in topological insulator in presence of magnetic field (see this). This is compete paradox and suggests in TGD framework that the flux tubes of external magnetic field serve as the wires (see previous posting).

  3. BCS model based on crystalline long range order and k-space (Fermi sphere). BCS-difficult materials have short range structural order: amorphous alloys, SC metal particles 0-down to 50 Angstroms (lipid layer of cell membrane) transition metals, alloys, compounds. Real space description rather than k-space description based on crystalline order seems to be more natural. Could it be that the description of electrons of Cooper pair is not correct? If so, k-space and Fermi sphere would be only appropriate description of ordinary electrons needed to model the transition to to super-conductivity? Super-conducting electrons could require different description.
  4. Local chemical bonding/real molecular description has been proposed. This is of course very natural in standard physics framework since the standard view about magnetic fields does not provide any ideas about Cooper pairing and magnetic fields are only a nuisance rather than something making SC possible. In TGD framework the situation is different.

TGD based view about SC

TGD proposal for high Tc SC and bio-SC relies on many-sheeted space-time and TGD based view about dark matter as heff=n× h phase of ordinary matter emerging at quantum criticality (see this).

Pairs of dark magnetic flux tubes would be the wires carrying dark Cooper pairs with members of the pair at the tubes of the pair. If the members of flux tube pair carry opposite B:s, Cooper pairs have spin 0. The magnetic interaction energy with the flux tube is what determines the critical temperature. High Tc superconductivity, in particular the presence of two critical temperatures can be understood. The role of anti-ferromagnetism can be understood.

TGD model is clearly x-space model: dark flux tubes are the x-space concept. Momentum space and the notion of Fermi sphere are certainly useful in understanding the transformation ordinary lattice electrons to dark electrons at flux tubes but the super conducting electron pairs at flux tubes would have different description.

Now come the heretic questions.

  1. Do the crystal structure and chemistry define the (only) fundamental parameters in SC? Could the notion of magnetic body - which of course can correlate with crystal structure and chemistry - equally important or even more important notion?
  2. Could also ordinary BCS SC be based on magnetic flux tubes? Is the value of heff=n× h only considerably smaller so that low temperatures are required since energy scale is cyclotron energy scale given by E= heff=n× fc, fc = eB/me. High Tc SC would only have larger heff and bio-superconductivity even larger heff!
  3. Could it be that also in low Tc SC there are dark flux tube pairs carrying dark magnetic fields in opposite directions and Cooper pairs flow along these pairs? The pairs could actually form closed loops: kind of flattened O:s or flattened squares.
One must be able to understand Meissner effect. Why dark SC would prevent the penetration of the ordinary magnetic field inside superconductor?
  1. Could Bext actually penetrate SC at its own space-time sheet. Could opposite field Bind at its own space-time sheet effectively interfere it to zero? In TGD this would mean generation of space-time sheet with Bind=-Bext so that test particle experiences vanishing B. This is obviously new. Fields do not superpose: only the effects caused by them superpose.

    Could dark or ordinary flux tube pairs carrying Bind be created such that the first flux tube portion Bind in the interior cancels the effect of Bext on charge carriers. The return flux of the closed flux tube of Bind would run outside SC and amplify the detected field Bext outside SC. Just as observed.

  2. What happens, when Bext penetrates to SC? heff→ h must take place for dark flux tubes whose cross-sectional area and perhaps also length scale down by heff and field strength increases by heff. If also the flux tubes of Bind are dark they would reduce in size in the transition heff→ h by 1/heff factor and would remain inside SC! Bext would not be screened anymore inside superconductor and amplified outside it! The critical value of Bext would mean criticality for this heff → h phase transition.
  3. Why and how the phase transition destroying SC takes place? Is it energetically impossible to build too strong Bind? So that effective field Beff=Bdark+ Bind+Bext experienced by electrons is reduced so that also the binding energy of Cooper pair is reduced and it becomes thermally unstable. This in turn would mean that Cooper pairs generating the dark Bdark disappear and also Bdark disappears. SC disappears.

See the chapter Quantum model for bio-superconductivity: II

What music can teach about consciousness?

Recently I have been reading the of Oliver Sacks titled "Musicophilia" dealing with various aspects of music experience. Humans as a species indeed have a very special relation to music. But is it really genuine characteristic of human consciousness? One can even ask whether consciousness emerges only in higher species or whether it could be in some form a characteric of any living or even inanimate system? I am not the only quantum consciousness theorists forced to consider panpsychism in some form. In this framework one can ask whether music like aspects of conscious experience could be universal and only especially highly developed in humans?

In this chapter I restrict the consideration to those stories of Musicophilia, which I find of special interest from the point of view of TGD inspired theory of consciousness. The outcome is a more precise formulation for the general TGD inspired vision about brain based on basic ideas of quantum TGD.

Zero Energy Ontology (ZEO) implies a new view about the relation between geometric and experienced time and allowing to generalize quantum measurement theory to a theory of consciousness.

Strong form of holography implies the analog of AdS/CFT duality between 2-D representation of physics based on string world sheets and partonic 2-surfaces and 4-D space-time representations. This duality is not tautology and this inspires the idea that these two representations correspond to two modes for consciousness motivating "Left brain talks, right brain sings" metaphor.

  1. Language and music could relate to two dual representations of conscious information - local and holistic, cognitive and sensory. Discretization of function/its Fourier transform as a collection of its values at discrete set values of time/frequencies would correspond local/holistic approximations of function. In principle any conscious entity - self- could utilize these two representational modes at appropriate quantum criticality.
  2. The holistic "musical consciousness" is assignable to right brain hemisphere and according to the stories of Sacks seems to characterized by episodal sensory memories. TGD based view about memories relies on ZEO: the memories would be mental images with sensory input from geometric past, genuine sensory experiences of time reversed sub-selves! This picture simplifies considerably and one can see all memories - sensory, cognitive, or emotional - as analogs of phantom pain, which would be also a sensory memory and even more a genuine sensory experience. It is even possible that our biological bodies are used by two selves: right brain hemisphere sleeps when we are awake and vice versa. Even the experiences of epileptics about having double consciousness could be understood.
  3. A more concrete realization of "Left brain talks, right brain sings" metaphor relies on the assumption that "magneto-anatomy" is universal. Only the "magneto-physiology" characterized by the values of heff characterizing quantum criticality and defining a kind of intelligence quotient dictating the span of long term memory and planned action varies.

    heff would differ for the magnetic bodies of various brain areas, and the spectrum of heff for right and left brain would differ and characterize their specializations. For instance, the value of heff would be large (small) for the cognitive areas of left (right) brain and small (large) for some higher sensory areas of right (left) brain. Magnetic bodies form a fractal hierarchy and one can characterize even individual cells and neurons by the value of heff associated with them. The spectrum for heff allows also to distinguish between members of the same species since it defines the skill profile. This obviously goes far beyond the genetic determinism.

See the chapter What music can teach about consciousness? or the article What music can teach about consciousness?


A new control mechanism of TGD inspired quantum biology

The idea that TGD Universe is quantum critical, is the key idea of quantum TGD and fixes the theory more or less uniquely since the only coupling constant parameter of the theory - Kähler coupling strength - is analogous to critical temperature. Also more than one basic parameters are in principle possible - maximal quantum criticality fixes the values of all of them - but it seems that only Kähler coupling strength is needed. TGD Universe is a quantum critical fractal: like a ball at the top of hill at the top of hill at.... Quantum criticality allows to avoid the fine tuning problems plaguing as a rule various unified theories.

Quantum criticality

The meaning of quantum criticality at the level of dynamics has become only gradually clearer. The development of several apparently independent ideas generated for about decade ago have led to the realization that quantum criticality is behind all of them. Behind quantum criticality are in turn number theoretic vision and strong forms of general coordinate invariance and holography.

  1. The hierarchy of Planck constants defining hierarchy of dark phases of ordinary matter corresponds to a hierarchy of quantum criticalities assignable to a fractal hierarchy of sub-algebras of super-symplectic algebra for which conformal weights are n-ples of those for the entire algebra, n corresponds to the value of effective Planck constant heff/h=n. These algebras are isomorphic to the full algebra and act as gauge conformal algebras so that a broken super-conformal invariance is in question.
  2. Quantum criticality in turn reduces to the number theoretic vision about strong form of holography. String world sheets carrying fermions and partonic 2-surfaces are the basic objects as far as pure quantum description is considered. Also space-time picture is needed in order to test the theory since quantum measurements always involve also the classical physics, which in TGD is an exact part of quantum theory.

    Space-time surfaces are continuations of collections of string world sheets and partonic 2-surfaces to preferred extremals of Kähler action for which Noether charges in the sub-algebra of super-symplectic algebra vanish. This condition is the counterpart for the reduction of the 2-D criticality to conformal invariance. This eliminates huge number of degrees of freedom and makes the strong form of holography possible.

  3. The hierarchy of algebraic extensions of rationals defines the values of the parameters characterizing the 2-surfaces, and one obtains a number theoretical realization of an evolutionary hierarchy. One can also algebraically continue the space-time surfaces to various number fields - reals and the algebraic extensions of p-adic number fields. Physics becomes adelic. p-Adic sectors serve as correlates for cognition and imagination. One can indeed have string world sheets and partonic 2-surfaces, which can be algebraically continued to preferred extremals in p-adic sectors by utilizing p-adic pseudo constants giving huge flexibility. If this is not possible in the real sector, figment of imagination is in question! It can also happen that only part of real space-time surface can be generated: this might relate to the fact that imaginations can be seen as partially realized motor actions and sensory perceptions.

Quantum criticality and TGD inspired quantum biology

In TGD inspired quantum biology quantum criticality is in crucial role. First some background.

  1. Quantum measurement theory as a theory of consciousness is formulated in zero energy ontology (ZEO) and defines an important aspect of quantum criticality. Strong form of NMP states that the negentropy gain in the state function reduction at either boundary of causal diamond (CD) is maximal. Weak form of NMP allows also quantum jumps for which negentropic entanglement is not generated: this makes possible ethics (good and evil) and morally responsible free will: good means basically increase of negentropy resources.
  2. Self corresponds to a sequence state function reductions to the same boundary of CD and heff does not change during that period. The increase of heff (and thus evolution!) tends to occur spontaneously, and can be assigned to the state function reduction to the opposite boundary of CD in zero energy ontology (ZEO). The reduction to the opposite boundary means death of self and living matter is fighting in order to avoid this even. To me the only manner to make sense about basic myth of Christianity is that death of self generates negentropy.
  3. Metabolism provides negentropy resources for self and hopefully prevents NMP to force the fatal reduction to the opposite boundary of CD. Also homeostasis does the same. In this process self makes possible evolution of sub-selves (mental images dying and re-incarnating) state function by state function reduction so that the negentropic resources of the Universe increase.

A new mechanism of quantum criticality

Consider now the mechanisms of quantum criticality. The TGD based model (see this) for the recent paradoxical looking finding (see this) that topological insulators can behave like conductors in external magnetic field led to a discovery of a highly interesting mechanism of criticality, which could play a key role in living matter.

  1. The key observation is that magnetic field is present. In TGD framework the obvious guess is that its flux tubes carry dark electrons giving rise to anomalous currents running in about million times longer time scales and with velocity, which is about million times higher than expected. Also supra-currents can be considered.

    The currents can be formed of the cyclotron energies of electrons are such that they correspond to energies near the surface of the Fermi sphere: recall that Fermi energy for electrons is determined by the density of conduction electrons and is about 1 eV. Interestingly, this energy is at the lower end of bio-photon energy spectrum. In the field of 10 Tesla the cyclotron energy of electron is .1 mV so that the integer characterizing cyclotron orbit must be n≅ 105 if conduction electron is to be transferred to the cyclotron orbit.

  2. The assumption is that external magnetic field is realized as flux tubes of fixed radius, which correspond to space-time quanta in TGD framework. As the intensity of magnetic field is varied, one observes so called de Haas-van Alphen effect used to deduce the shape of the Fermi sphere: magnetization and some other observables vary periodically as function of 1/B.

    This can be understood in the following manner. As B increases, cyclotron orbits contract. For certain increments of 1/B n+1:th orbit is contracted to n:th orbit so that the sets of the orbits are identical for the values of 1/B, which appear periodically. This causes the periodic oscillation of say magnetization.

  3. For some critical values of the magnetic field strength a new orbit emerges at the boundary of the flux tube. If the energy of this orbit is in the vicinity of Fermi surface, an electron can be transferred to the new orbit. This situation is clearly quantum critical.

    If the quantum criticality hypothesis holds true, heff/h=n dark electron phase can generated for the critical value of magnetic fields. This would give rise to the anomalous conductivity perhaps involving spin current due to the spontaneous magnetization of the dark electrons at the flux tube. Even super-conductivity based on the formation of parallel flux tube pairs with either opposite or parallel directions of the magnetic flux such that the members of the pair are at parallel flux tubes, can be considered and I have proposed this a mechanism of bio-superconductivity and also high Tc super-conductivity

A new mechanism of quantum criticality and bio-control

The quantum criticality of the process in which new electron orbit emerges near Fermi surface suggests a new mechanism of quantum bio-control by generation of super currents or its reversal.

  1. In TGD inspired quantum biology magnetic body uses biological body as motor instrument and sensory receptor and EEG and its fractal variants with dark photons with frequencies in EEG range but energy E=hefff in the range of bio-photon energies make the necessary signalling possible.
  2. Flux tubes can become braided and this makes possible quantum computation like processes. Also so called 2-braids - defined by knotted 2-surfaces imbedded in 4-D space-time surface - are possible for the string world sheets defined by flux tubes identified to be infinitely thin, are possible. As a matter fact, also genuine string world sheets accompany the flux tubes. 2-braids and knots are purely TGD based phenomenon and not possible in superstring theory or M-theory.
  3. It is natural to speak about motor actions of the magnetic body. It is assumed that the flux tubes of the magnetic body connect biomolecules to form a kind of Indra's web explaining the gel like character of living matter. heff reducing phase transitions contract flux tubes connecting biomolecules so that they can find each other by this process and bio-catalysis becomes possible. This explains the mysterious looking ability of bio-molecules to find each other in the dense molecular soup. In fact the dark matter part is far from being soup! The hierarchy of Planck constants and heff=hgr hypothesis imply that dark variants of various particles with magnetic moment are neatly at their own flux tubes like books in shelf.

    Reconnection of the U-shaped flux tubes emanating from two subsystems generates a flux tube pair between them and gives rise to supracurrents flowing between them. Also cyclotron radiation propagating along flux tubes and inducing resonant transitions is present. This would be the fundamental mechanism of attention.

  4. I have proposed that the variation of the thickness of the flux tubes could serve as a control mechanism since it induces a variation of cyclotron frequencies allowing to get in resonance or out of it. For instance, two molecules could get in flux tube contact when the cyclotron frequencies are identical and this can be achieved if they are able to vary their flux tube thickness. The molecules of immune system are masters in identifying alien molecules and the underlying mechanism could be based on cyclotron frequency spectrum and molecular attention. This would be also the mechanism behind water memory and homeopathy (see this), which still is regarded as a taboo by mainstreamers.
  5. Finally comes the promised new mechanism of bio-control! The variation of the magnetic field induced by that of flux tube thickness allows also to control whether there is quantum criticality for the generation of dark electron supra currents of electrons. The Fermi energy of the conduction electrons at the top of Fermi sphere is the key quantity and dictated by the density of these electrons. This allows to estimate the order of magnitude of the integers N characterizing cyclotron energy for ordinary Planck constant and the maximal value of heff/h=n cannot be larger than N.

See the chapter Quantum Model for Bio-Superconductivity: II or the article A new control mechanism of TGD inspired quantum biology


Does the physics of SmB6 make the fundamental dynamics of TGD directly visible?

The group of Suchitra Sebastian has discovered very unconventional condensed matter system which seems to be simultaneously both insulator and conductor of electricity in presence of magnetic field. Science article is entitled "Unconventional Fermi surface in an insulating state". There is also a popular article "Paradoxical Crystal Baffles Physicists" in Quanta Magazine summarizing the findings. I learned about the finding first from the blog posting of Lubos (I want to make absolutely clear that I do not share the racistic attitudes of Lubos towards Greeks. I find the discussions between Lubos and same minded blog visitor barbarians about the situation in Greece disgusting).


The crystal studied at superlow temperatures was Samarium hexaboride - briefly SmB6. The high resistance implies that electron cannot move more that one atom's width in any direction. Sebastian et al however observed electrons traversing over a distance of millions of atoms- a distance of orde 10-4 m, the size of a large neuron. So high mobility is expected only in conductors. SmB6 is neither metal or insulator or is both of them! The finding is described by Sebastian as a "big schock and as a "magnificent paradox by condensed matter theorists Jan Zaanen. Theoreticians have started to make guesses about what might be involved but according to Zaanen there is no even remotely credible hypothesis has appeared yet.

On basis of its electronic structure SmB6 should be a conductor of electricity and it indeed is at room temperature: the average number conduction electrons per SmB6 is one half. At low temperatures situation however changes. At low temperatures electrons behave collectivly. In superconductors resistance drops to zero as a consequence. In SmB6 just the opposite happens. Each Sm nucleus has the average 5.5 electrons bound to it at tight orbits. Below 223 degrees of Celsius the conduction electrons of SmB6 are thought to "hybridize" around samarium nuclei so that the system becomes an insulator. Various signatures demonstrate that SmB6 indeed behaves like an insulator.

During last five years it has been learned that SmB6 is not only an insulator but also so called topological insulator. The interior of SmB6 is insulator but the surface acts as a conductor. In their experiments Sebastian et al hoped to find additional evidence for the topological insulator property and attempted to measure quantum oscillations in the electrical resistance of their crystal sample. The variation of quantum oscillations as sample is rotated can be used to map out the Fermi surface of the crystal. No quantum oscillations were seen. The next step was to add magnetic field and just see whether something interesting happens and could save the project. Suddenly the expected signal was there! It was possible to detect quantum oscillations deep in the interior of the sample and map the Fermi surface! The electrons in the interior travelled 1 million times faster than the electrical resistance would suggest. Fermi surface was like that in copper, silver or gold. A further surprise was that the growth of the amplitude of quantum oscillations as temperature was decreased, was very different from the predictions of the universal Lifshitz-Kosevich formula for the conventional metals.

Could TGD help to understand the strange behavior of SmB6?

There are several indications that the paradoxical effect might reveal the underlying dynamics of quantum TGD. The mechanism of conduction must represent new physics and magnetic field must play a key role by making conductivity possible by somehow providing the "current wires". How? The TGD based answer is completely obvious: magnetic flux tubes.

One should also understand topological insulator property at deeper level, that is the conduction along the boundaries of topological insulator. One should understand why the current runs along 2-D surfaces. In fact, many exotic condensed matter systems are 2-dimensional in good approximation. In the models of integer and fractional quantum Hall effect electrons form a 2-D system with braid statistics possible only in 2-D system. High temperature super-conductivity is also an effectively 2-D phenomenon.One should also understand topological insulator property at deeper level, that is the conduction along the boundaries of topological insulator.

  1. Many-sheeted space-time is second fundamental prediction TGD. The dynamics of single sheet of many-sheeted space-time should be very simple by the strong form of holography implying effective 2-dimensionality. The standard model description of this dynamics masks this simplicity since the sheets of many-sheeted space-time are replaced with single region of slightly curved Minkowski space with gauge potentials sums of induced gauge potentials for sheets and deviation of metric from Minkowski metric by the sum of corresponding deviations for space-time sheets. Could the dynamics of exotic condensed matter systems give a glimpse about the dynamics of single sheet? Could topological insulator and anyonic systems provide examples of this kind of systems?
  2. Second basic prediction of TGD is strong form of holography: string world sheets and partonic 2-surfaces serve as kind of "space-time genes" and the dynamics of fermions is 2-D at fundamental level. It must be however made clear that at QFT limit the spinor fields of imbedding space replace these fundamental spinor fields localized at 2-surface. One might argue that the fundamental spinor fields do not make them directly visible in condensed matter physics. Nothing however prevents from asking whether in some circumstances the fundamental level could make itself visible.

    In particular, for large heff dark matter systems (, whose existence can be deduced from the quantum criticality of quantum TGD) the partonic 2-surfaces with CP2 size could be scaled up to nano-scopic and even longer size scales. I have proposed this kind of surfaces as carriers of electrons with non-standard value of heff in QHE and FQHE.

    The long range quantum fluctuations associated with large, heff=n× h phase would be quantum fluctuations rather than thermal ones. In the case of ordinary conductivity thermal energy makes it possible for electrons to jump between atoms and conductivity becomes very small at low temperatures. In the case of large scale quantum coherence just the opposite happens as observed. One therefore expects that Lifshitz-Kosevich formula for the temperature dependence of the amplitude does not hold true.

    The generalization of Lifschitz-Kosevich formula to quantum critical case deduced from quantum holographic correspondence by Hartnoll and Hofman might hold true qualitatively also for quantum criticality in TGD sense but one must be very cautious.

    The first guess is that by underlying super-conformal invariance scaling laws typical for critical systems hold true so that the dependence on temperature is via a power of dimensionless parameter x=T/mu;, where μ is chemical potential for electron system. As a matter fact, exponent of power of x appears and reduces to first power for Lifshitz-Konsevich formula. Since magnetic field is important, one also expects that the ratio of cyclotron energy scale Ec∝ ℏeff eB/me to Fermi energy appears in the formula. One can even make an order of magnitude guess for the value of heff/h≅ 106 from the facts that the scale of conduction and conduction velocity were millions times higher than expected.

    Strings are 1-D systems and strong form of holography implies that fermionic strings connecting partonic 2-surfaces and accompanied by magnetic flux tubes are fundamental. At light-like 3-surfaces fermion lines can give rise to braids. In TGD framework AdS/CFT correspondence generalizes since the conformal symmetries are extended. This is possible only in 4-D space-time and for the imbedding space H=M4× CP2 making possible to generalize twistor approach.

  3. Topological insulator property means from the perspective of modelling that the action reduces to a non-abelian Chern-Simons term. The quantum dynamics of TGD at space-time level is dictated by Kähler action. Space-time surfaces are preferred extremals of Kähler action and for them Kähler action reduces to Chern-Simons terms associated with the ends of space-time surface opposite boundaries of causal diamond and possibly to the 3-D light-like orbits of partonic 2-surfaces. Now the Chern-Simons term is Abelian but the induced gauge fields are non-Abelian. One might say that single sheeted physics resembles that of topological insulator.
  4. The effect appears only in magnetic field. I have been talking a lot about magnetic flux tubes carrying dark matter identified as large heff phases: topological quantization distinguishes TGD from Maxwell's theory: any system can be said to possess "magnetic body, whose flux tubes can serve as current wires. I have predicted the possibility of high temperature super-conductivity based on pairs of parallel magnetic flux tubes with the members of Cooper pairs at the neighboring flux tubes forming spin singlet or triplet depending on whether the fluxes are have same or opposite direction.

    Also spin and electric currents assignable to the analogs of spontaneously magnetized states at single flux tube are possible. The obvious guess is that the conductivity in question is along the flux tubes of the external magnetic field. Could this kind of conductivity explains the strange behavior of SmB6. The critical temperature would be that in which the parallel flux tubes are stable. The interaction energy of spin with the magnetic field serves as a possible criterion for the stability if the presence of dark electrons stabilizes the flux tubes.

The following represents an extremely childish attempt of a non-specialist to understand how the conductivity might be understood. The current carrying electrons at flux tubes near the top of Fermi surface are current carriers. heff=n×h and magnetic flux tubes as current wires bring in the new elements. Also in the standard situation one considers cylinder symmetric solutions of Schrödinger equation in external magnetic field and introduces maximal radius for the orbits so that formally the two situations seem to be rather near to each other. Physically the large heff and associated many-sheeted covering of space-time surface providing the current wire makes the situation different since the collisions of electrons could be absent in good approximation so that the velocity of charge carriers could be much higher than expected as experiments indeed demonstrate.

Quantum criticality is the crucial aspect and corresponds to the situation in which the magnetic field attains a value for which a new orbit emerges/disappears at the surface of the flux tube: in this situation dark electron phase with non-standard value of heff can be generated. This mechanism is expected to apply also in bio- superconductivity and to provide a general control tool for magnetic body.

  1. Let us assume that flux tubes cover the whole transversal area of the crystal and there is no overlap. Assume also that the total number of conduction electrons is fixed, and depending on the value of heff is shared differently between transversal and longitudinal degrees of freedom. Large value of heff squeezes the electrons from transversal to longitudinal flux tube degrees of freedom and gives rise to conductivity.
  2. Consider first Schrödinger equation. In radial direction one has harmonic oscillator and the orbits are Landau orbits. The cross sectional area behaves like πR2= nTheff/2mωc giving nT∝1/heff. Increase of the Planck constant scales up the radii of the orbits so that the number of states in cylinder of given radius is reduced.

    Angular momentum degeneracy implies that the number of transversal states is NT= nT2∝ 1/heff2. In longitudinal direction one has free motion in a box of length L with states labelled by integer nL. The number of states is given by the maximum value NL of nL.

  3. If the total number of states is fixed to N = NLNT is fixed and thus does not depend on heff, one has NL ∝ heff2. Quanta from transversal degrees of freedom are squeezed to longitudinal degrees of freedom, which makes possible conductivity.
  4. The conducting electrons are at the surface of the 1-D "Fermi-sphere", and the number of conduction electrons is Ncond≅ dN/dε × δ ε≅dN/dε T= NT/2εF ∝ 1/heff4. The dependence on heff does not favor too large values of heff. On the other hand, the scattering of electrons at flux tubes could be absent. The assumption L∝heff increases the range over which current can flow.
  5. To get a non-vanishing net current one must assume that only the electrons at the second end of the 1-D Fermi sphere are current carriers. The situation would resemble that in semiconductor. The direction of electric field would induce symmetry breaking at the level of quantum states. The situation would be like that for a mass in Earth's gravitational field treated quantally and electrons would accelerate freely. Schrödinger equation would give rise to Airy functions as its solution.

What about quantum oscillations in TGD framework?

  1. Quantum oscillation refers to de Haas-van Alphen effect - an oscillation of the induced magnetic moment as a function of 1/B with period τ= 2πe/ℏS, where S is the momentum space area of the extremal orbit of the Fermi surface, in the direction of the applied field. The effect is explained to be due to the Landau quantization of the electron energy. I failed to really understand the explanation of this source and in my humble opinion the following arguments provide a clearer view about what happens.
  2. If external magnetic field corresponds to flux tubes Fermi surface decomposes into cylinders parallel to the magnetic field since the motion in transversal degrees of freedom is along circles. In the above thought experiment also a quantization in the longitudinal direction occurs if the flux tube has finite length so that Fermi surface in longitudinal direction has finite length. One expects on basis of Uncertainty Principle that the area of the cross section in momentum space is given by S∝ heff2/πR2, where S is the cross sectional area of the flux tube. This follows also from the equation of motion of electron in magnetic field. As the external magnetic field B is increased, the radii of the orbits decrease inside the flux tube, and in momentum space the radii increase.

  3. Why does the induced magnetic moment (magnetization) and other observables oscillate?
    1. The simplest manner to understand this is to look at the situation at space-time level. Classical orbits are harmonic oscillator orbits in radial degree of freedom. Suppose that that the area of flux tube is fixed and B is increased. The orbits have radius rn2= (n+1/2) × hbar/eB and shrink. For certain field values the flux eBA =n×hbar corresponds to an integer multiple of the elementary flux quantum - a new orbit at the boundary of the flux tube emerges if the new orbit is near the boundary of Fermi sphere providing the electrons. This is clearly a critical situation.
    2. In de Haas- van Alphen effect the orbit n+1 for B has same radius as the orbit n for 1/B+Δ (1/B): rn+1(1/B) =rn(1/B+Δ (1/B)). This gives approximate differential equation with respect to n and one obtains (1/B)(n)= (n+1/2)× Δ (1/B) . Δ (1/B) is fixed from the condition the flux quantization. When largest orbit is at the surface of the flux, tube the orbits are same for B(n) and B(n+1), and this gives rise to the de Haas - van Alphen effect.
    3. It is not necessary to assume finite radius for the flux tube, and the exact value of the radius of the flux tube does not play an important role. The value of flux tube radius can be estimated from the ratio of the Fermi energy of electron to the cyclotron energy. Fermi energy about .1 eV depending only on the density of electrons in the lowest approximation and only very weakly on temperature. For a magnetic field of 1 Tesla cyclotron energy is .1 meV. The number of cylinders defined by orbits is about n=104.
  4. What happens in TGD Universe in which the areas of flux tubes identifiable as space-time quanta are finite? Could quantum criticality of the transition in which a new orbit emerges at the boundary of flux tube lead to a large heff dark electron phase at flux tubes giving rise to conduction?
    1. The above argument makes sense also in TGD Universe for the ordinary value of Planck constant. What about non-standard values of Planck constant? For heff/h =n the value of flux quantum is n-fold so that the period of the oscillation in de Haas - van Alphen effect becomes n times shorter. The values of the magnetic field for which the orbit is at the surface of the flux tube are however critical since new orbit emerges assuming that the cyclotron energy corresponds is near Fermi energy. This quantum criticality could give rise to a phase transition generating non-standard value of Planck constant.

      What about the period for Δ (1/B)? For heff/h=n? Modified flux quantization for extremal orbits implies that the area of flux quantum is scaled up by n. The flux changes by n units for the same increment of Δ (1/B) as for ordinary Planck constant so that de Haas -van Alphen effect does not detect the phase transition.

    2. If the size scale of the orbits is scaled up by n1/2 as the semiclassical formula suggests the number of classical orbits is reduced by a factor 1/n if the radius of the flux tube is not changed in the transition h→ heff to dark phase. n-sheetedness of the covering however compensates this reduction.
    3. What about possible values of heff/h? The total value of flux seems to give the upper bound of heff/h=nmax, where nmax is the value of magnetic flux for ordinary value of Planck constant. For electron and magnetic field for B=10 Tesla and has n≤ 105. This value is of the same order as the rough estimate from the length scale for which anomalous conduction occurs.
    Clearly, the mechanism leading to anomalously high conductivity might be the transformation of the flux tubes to dark ones so that they carry dark electrons currents. The observed effect would be dark, quantum critical variant of de Haas-van Alphen effect!

    Also bio-superconductivity is quantum critical phenomenon and this observation would suggests sharpening of the existing TGD based model of bio-super-conductivity. Super-conductivity would occur for critical magnetic fields for which largest cyclotron orbit is at the surface of the flux tube so that the system is quantum critical. Quantization of magnetic fluxes would quantify the quantum criticality. The variation of magnetic field strength would serve as control tool generating or eliminating supra currents. This conforms with the general vision about the role of dark magnetic fields in living matter.

To sum up, a breaktrough of TGD is taking place. I have written about thirty articles during this year - more than one article per week. There is huge garden there and trees contain fruits hanging low! It is very easy to pick them: just shatter and let them drop to the basket! New experimental anomalies having a nice explanation using TGD based concepts appear on weekly basis and the mathematical and physical understanding of TGD is taking place with great leaps. It is a pity that I must do all alone. I would like to share. I can only hope that colleagues could take the difficult step: admit what has happened and make a fresh start.

See the chapter Quantum Model for Bio-Superconductivity: II or the article Does the physics of SmB6 make the fundamental dynamics of TGD directly visible?

Aromatic rings as the lowest level in the molecular self hierarchy?

I had the opportunity to participate the conference Towards Science of Consciousness 2015 held in Helsinki June 8-13. Of special interest from TGD point of view were the talks of Hameroff and Bandyopadphyay, who talked about aromatic rings (ARs) (see this).

I have also wondered whether ARs might play key role with motivations coming from several observations.

  1. In photosynthesis ARs are a central element in the energy harvesting system , and it is now known that quantum effects in longer length and time scales than expected are involved. This suggests that the ARs involved fuse to form a larger quantum system connected by flux tubes, and that electron pair currents follow along the flux tubes as supra currents.

    DNA codons involve ARs with delocalized pi electrons, neurotransmitters and psychoactive drugs involve them, 4 amino-acids Phe, trp, tyr and his involve them and they are all hydrophobic and tend to be associated with hydrophobic pockets. Phe and trp appear in hydrophobic pockets of microtubules.

  2. The notion of self hierarchy suggests that at molecular level ARs represent the basic selves. ARs would integrate to larger conscious entities by a reconnection of the flux tubes of their magnetic bodies (directing attention to each other!). One would obtain also linear structures such as DNA sequence in this manner. In proteins the four aromatic amino-acids would represent subselves possibly connected by flux tubes. In this manner one would obtain a concrete molecular realization of self hierarchy allowing precise identification of the basic conscious entities as aromatic rings lurking in hydrophobic pockets.
  3. Given AR would be accompanied by a magnetic flux tube and the current around it would generate magnetic field. The direction of the current would represent a bit (or perhaps even qbit). In the case of microtubules the phe-trp dichotomy and direction of current would give rise to 4 states identifiable as a representation for four genetic letters A,T,C,G. The current pathways proposed by Hameroff et al consisting of sequences of current rings (see this) could define the counterparts of DNA sequences at microtubule level.

    For B type microtubules 13 tubulins, which correspond to single 2π rotation, would represent basic unit followed by a gap. This unit could represent a pair of helical strands formed by flux tubes and ARs along them completely analogous to DNA double strand. This longitudinal strand would be formed by a reconnection of magnetic flux tubes of the magnetic fields of ARs and reconnection occurring in two different manners at each step could give rise to braiding.

  4. The magnetic flux tubes associated with the magnetic fields of nearby aromatic rings could suffer reconnection and in this manner a longitudinal flux tubes pair carrying supra current could be generated by the mechanism of bio-superconductivity discussed (see this) and working also for the ordinary high Tc super conductivity. The interaction of microtubule with frequencies in the scales kHz, GHz, and THz scales would induce longitudinal superconductivity as a transition to phase A from phase B meaning generation of long super-conducting wires.

    This view suggests that also DNA is superconductor in longitudinal direction and that oscillating AC voltage induces the superconductivity also now. Bandyopadphyay indeed observed the 8 AC resonance frequencies first for DNA with frequency scales of GHz, THz, PHz, which suggests that dark photon signals or AC voltages at these frequencies induce DNA superconductivity. According to the model of DNA as topological quantum computer DNA is superconductor also in the transversal degrees of freedom meaning that there are flux tubes connecting DNA to a lipid layer of the nuclear or cell membrane (see this and this).

  5. Interestingly, the model of Hameroff et al for the helical pathway (see this) assumes that there are three aromatic rings per d=1 nm length along microtubule. This number is same as the number of DNA codons per unit length. It is however mentioned that the distance between aromatic rings trp and phe in MT is about d=2 nm. Does this refer to average distance or is d=1 nm just an assumption. In TGD framework the distance would scale as heff so that also scaling of DNA pathway by a factor 6 could be considered. In this case single tubulin could correspond to genetic codon.

    If d=1 nm is correct, these helical pathways might give rise to a representation of memetic codons representable as sequences of 21 genetic codons meaning that there are 2126 different memetic codons this. DNA would represent the lowest level of hierarchy of consciousness and microtubules the next level. Note that each analog of DNA sequences corresponds to different current pathway.

  6. What is especially interesting, that codon and its conjugate have always altogether 3 aromatic cycles. Also phe and trp appearing in MTs have this property as also tyr and his. Could these 3 cycles give rise to 3-braid? The braid group B3, which is covering of permutation group of 3 objects. Since B2 is Abelian group of integers, 3-braid is the smallest braid, which can give rise to interesting topological quantum computation.

    B3 is also the knot group of trefoil knot, and the universal central extension of the modular group PSL(2,Z) (a discrete subgroup of Lorentz group playing a key role in TGD since it defines part of the discrete moduli space for the CDs with other boundary fixed (see this). Quite generally, B(n) is the mapping class group of a disk with n punctures fundamental both in string model: in TGD where disk is replaced with partonic 2-surface.

For details see the chapter Quantum model for nerve pulse or the article Impressions created by TSC 2015 conference.

TGD based model for anesthetic action

The mechanism of anesthetic action has remained mystery although a lot of data exist. The Meyer-Overton correlation suggests that the changes occurring at lipid layers of are responsible for anesthesia but this model fails. Another model assumes that the binding of anesthetes to membrane proteins is responsible for anesthetic effects but also this model has problems. The hypothesis that the anesthetes bind to the hydrophobic pockets of microtubules looks more promising.

The model should also explain hyperpolarization of neuronal membranes taking also place when consciousness is lost. The old finding of Becker is that the reduction or reversal of voltage between frontal brain and occipital regions correlates with the loss of consciousness. Microtubules and DNA are negatively charged and the discovery of Pollack that so called fourth phase of water involves generation of negatively charged regions could play a role in the model. Combining these inputs with TGD inspired theory of consciousness and quantum biology one ends up to a microtubule based model explaining the basic aspects of anaestesia.

For details see the article TGD based model for anesthetic action or the chapter Quantum model for nerve pulse.

Quantitative model of high Tc super-conductivity and bio-super-conductivity

I have developed already earlier a rough model for high Tc super conductivity. The members of Cooper pairs are assigned with parallel flux tubes carrying fluxes which have either same or opposite directions. The essential element of the model is hierarchy of Planck constants defining a hierarchy of dark matters.

  1. In the case of ordinary high Tc super-conductivity bound states of charge carriers at parallel short flux tubes become stable as spin-spin interaction energy becomes higher than thermal energy.

    The transition to super-conductivity is known to occur in two steps: as if two competing mechanisms were at work. A possible interpretation is that at higher critical temperature Cooper pairs become stable but that the flux tubes are stable only below rather short scale: perhaps because the spin-flux interaction energy for current carriers is below thermal energy. At the lower critical temperature the stability would is achieved and supra-currents can flow in long length scales.

  2. The phase transition to super-conductivity is analogous to a percolation process in which flux tube pairs fuse by a reconnection to form longer super-conducting pairs at the lower critical temperature. This requires that flux tubes carry anti-parallel fluxes: this is in accordance with the anti-ferro-magnetic character of high Tc super conductivity. The stability of flux tubes very probably correlates with the stability of Cooper pairs: coherence length could dictate the typical length of the flux tube.
  3. A non-standard value of heff for the current carrying magnetic flux tubes is necessary since otherwise the interaction energy of spin with the magnetic field associated with the flux tube is much below the thermal energy.
There are two energies involved.
  1. The spin-spin-interaction energy should give rise to the formation of Cooper pairs with members at parallel flux tubes at higher critical temperature. Both spin triplet and spin singlet pairs are possible and also their mixture is possible.
  2. The interaction energy of spins with magnetic fluxes, which can be parallel or antiparallel contributes also to the gap energy of Cooper pair and gives rise to mixing of spin singlet and spin triplet. In TGD based model of quantum biology antiparallel fluxes are of special importance since U-shaped flux tubes serve as kind of tentacles allow magnetic bodies form pairs of antiparallel flux tubes connecting them and carrying supra-currents. The possibility of parallel fluxes suggests that also ferro-magnetic systems could allow super-conductivity.

    One can wonder whether the interaction of spins with magnetic field of flux tube could give rise to a dark magnetization and generate analogs of spin currents known to be coherent in long length scales and used for this reason in spintronics (see this). One can also ask whether the spin current carrying flux tubes could become stable at the lower critical temperature and make super-conductivity possible via the formation of Cooper pairs. This option does not seem to be realistic.

In the article Quantitative model of high Tc super-conductivity and bio-super-conductivity the earlier flux tube model for high Tc super-conductivity and bio-super-conductivity is formulated in more precise manner. The model leads to highly non-trivial and testable predictions.
  1. Also in the case of ordinary high Tc super-conductivity large value of heff=n× h is required.
  2. In the case of high Tc super-conductivity two kinds of Cooper pairs, which belong to spin triplet representation in good approximation, are predicted. The average spin of the states vanishes for antiparallel flux tubes. Also super-conductivity associated with parallel flux tubes is predicted and could mean that ferromagnetic systems could become super-conducting.
  3. One ends up to the prediction that there should be a third critical temperature not lower than T**= 2T*/3, where T* is the higher critical temperature at which Cooper pairs identifiable as mixtures of Sz=+/- 1 pairs emerge. At the lower temperature Sz=0 states, which are mixtures of spin triplet and spin singlet state emerge. At temperature Tc the flux tubes carrying the two kinds of pairs become thermally stable by a percolation type process involving re-connection of U-shaped flux tubes to longer flux tube pairs and supra-currents can run in long length scales.
  4. The model applies also in TGD inspired model of living matter. Now however the ratio of critical temperatures for the phase transition in which long flux tubes stabilize is roughly by a factor 1/50 lower than that in which stable Cooper pairs emerge and corresponds to thermal energy at physiological temperatures which corresponds also the cell membrane potential. The higher energy corresponds to the scale of bio-photon energies (visible and UV range).

For details see the chapter Quantum model for bio-superconductivity: II or the article Quantitative model of high Tc super-conductivity and bio-super-conductivity.

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