**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.

- 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 h
_{eff}/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.

- 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.

- 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.

- 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.

- Self corresponds to a sequence state function reductions to the same boundary of CD and h
_{eff}does not change during that period. The increase of h_{eff}(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.

- 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.

- 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≅ 10

^{5}if conduction electron is to be transferred to the cyclotron orbit.

- 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.

- 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, h

_{eff}/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.

- 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=h
_{eff}f in the range of bio-photon energies make the necessary signalling possible.

- 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.

- 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. h
_{eff}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 h_{eff}=h_{gr}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.

- 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.

- 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 h
_{eff}/h=n cannot be larger than N.

See the chapter Criticality and Dark Matter of "Hyper-finite Factors and Hierarchy of Planck Constants" or the article A new control mechanism of TGD inspired quantum biology.

For a summary of earlier postings see Links to the latest progress in TGD.

## 2 comments:

So, Matti, What then is magnetism other than anyone who has played with magnets and can see and feel what is really sort of invisible? We can see the magnetic lines form say from powdered iron filings. But is this the magnetism itself no matter how we make hierarchies or expand our flux tubes in the imagined dark and negative spaces? I could agree that such tubes are real and material in effect and yes something limits this process if seen as quantum or relativistic in the space. The representation of a series of sheets is one form of a few models but the deep calculation still escapes us. Some things seem as much fixed as critical. With a more general theory it seems reasonable to say light itself may work rather well in redesigning or healing our biological systems, as well as where there can be an observation and unique diagnosis. These are important thoughts, mainstream or not, and have a role in the Bigger Picture...it is not even sufficient to say we cannot exceed N unless we understand better the prime calculation and environs from one of our perspectives we assume a necessity.

Our sensory percepts about magnetism give only an extremely narrow glimpse about what it is involved. It gives only consistency conditions on theories. Maxwell's theory is simple linear theory but not enough - even its generalisation to standard model is not enough.

TGD is the next step in which Maxwel's fields and also other fields are geometrized: extremely non-linear structure is the outcome but it simplifies physics enormously: four imbedding space coordinates become the fundamental field degrees of freedom. At the level of single space-time sheet things are ridiculously simple. Many-sheetedness having approximate description using standard model is what masks this simplicity. Here is the next step of reduction and has already begun - mainstreamers have of course not yet realised that this has happened.

Quantitative testing of theories means expanding of our sensory perception. At this moment we are at the verge of expanding it so that we can "see" also dark matter. This SmBr6 business is just about that. Condensed matter physicists are taking the lead from particle physicists who have lost their way by sticking to wrong theories.

If things had proceeded in times of Einstein and others, I had proposed in some conference the detection of conductivity in topological insulator made possible by dark magnetic flux tubes - very dramatic and paradoxical prediction: insulator behaving like conductor! Some group would have worked for few years and announced in some conference that dark currents have been found!

Imagination is necessary when we do not know or cannot yet measure. Imaginations must be testable and be tested and this evolutionary pressure gradually selects the imaginations which we begin to call reality. One of the most charming applications of the adelic vision about strong holography is understanding of what imagination is. Physics is now reaching the same level as mathematics achieved thanks to Godel: it can also say something about physicist.

A more familiar example about similar expansion of perception is provided by hadron physics. Now we "see" quarks. This is a complex process involving all aspects of human consciousness (and perhaps even that above human consciousness;-).

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