Snow flakes, Emoto effect, and Pollack effect: life at quantum criticality?

Suppose that solid-liquid solid-vapour critical curves correspond to quantum criticality. Could some kind of life forms be associated with these quantum criticalities?

1. Snowflakes (see this) are amazingly ordered structures and appear in freezing and direct solidification of water vapour. Snow flakes do not have metabolism. Could snowflakes be "corpses" of life forms emerging at quantum criticality?

   The experiments of Masaru Emoto, discussed from the TGD point of view here, demonstrate that if water at freezing point is subject to sound signals, it generates freezing patterns, which can be extremely beautiful or ugly depending on the emotional content than human would associate to the signal. Emoto suggests an interpretation in terms of expression of emotions generated by the sounds.

2. In the TGD framework, a model of harmony leads to a model of genetic code (see this and this). Genetic codons would consist of 6-bit codons realized also as 3-chords represented by 3 dark photons and by dark 3-proton states. The harmony is defined by 3 icosahedral Hamiltonian cycles, each representing a 12-note scale, plus the unique tetrahedral Hamiltonian cycle. The 3-chords define a bioharmony with 64-chords realized as dark photon triplets. Since ordinary harmony of music induces and expresses emotions, the proposal is that a given bioharmony defines an analog of mood already at the level of basic information molecules.
3. Could a dark realization of the genetic code be involved with the criticality of water and explain the high information content of snowflakes and the findings of Emoto? Snowflake has a locally violated 6-fold rotational symmetry and looks like a planar tree with branches emanating from the center. That one cannot find two identical snowflakes, can be understood in terms of criticality during their formation.

   Icosahedron and tetrahedron correspond to an icosahedral symmetry group with 60 elements and hexagon to Z₆. All these groups belong to an infinite hierarchy of discrete and finite subgroups of SU(2) associated with the inclusions of von Neumann algebras known as hyper-finite factors of type II₁ (see this and this). M⁸-H duality allows us to interpret SU(2) as a covering group of the automorphism group of quaternions.

4. The dark proton realization genetic code would be in terms of icosa-tetrahedral tessellation of hyperbolic 3-space H³ (light-cone proper time constant surface) (see this). Ordinary ice I_h consists of hexagonal layers (see this): could a hexagonal tessellation at the level of H³ could be involved. This suggests that if the genetic code is realized at the level of MB, a symmetry breaking leading from an icosa-tetrahedral tessellation to a hexagonal tessellation at the level of ordinary matter takes place in the freezing of water.

5. Intriguingly, the size scale of the snowflake hexagon is of order .45 cm, which happens to be the gravitational Compton length Λ_gr= GM_E/v₀ in the gravitational field of Earth for v₀=c determined from other arguments (see this)! This scale is huge as compared with the size of order 1 Angstr\"om of the ice crystal hexagon. Quantum fluctuations at quantum criticality involve however large values of h_eff meaning scaled up sizes for the basic structures. For h_eff=h_gr the minimum size would naturally be Λ_gr! Note that the thickness of human cortex varies in the range .1-.45 cm.
6. The fourth phase of water, as Pollack called it, is formed in the Pollack effect (for the TGD view see this) and consists of hexagonal layers connected by hydrogen bonds. The effective stoichiometry is H_1.5O so that every fourth proton goes somewhere and a negatively charged exclusion zone (EZ) is formed. In the TGD based model, every fourth proton becomes a dark proton at flux tube so that the stoichiometry becomes H_1.5O.

   Dark protons with h_eff=h_gr would not be present for snowflakes nor for the crystal-like structures studied by Emoto. However, at the quantum criticality for freezing they could emerge and be associated with quantum gravitational hydrogen bonds (flux tubes) containing dark protons delocalized in the Earth size scale (see this).

   The basic claim of Emoto is that water at criticality has emotions and expresses them. If bioharmony determines emotions and is realized in terms of dark proton and dark photon sequences at quantum criticality, the question arises whether a dark realization of the genetic code for snow flakes and whether the MB controls and communicates with water using dark 3-photons. Conditioned learning is based on emotions: could water at criticality be able to learn in this way?

   If quantum criticality is the prerequisite of life, one can ask whether snowflakes of the crystal structures of Emoto could be "revived" by bringing the water to criticality.

7. At least for water, silicon, gallium, germanium, bismuth, and plutonium, the density is higher for liquid phase than solid phase above criticality. Could all substances with this property show analogs of Pollack and Emoto effects? Or could these effects appear universally at melting and sublimation curves. What about the analogs of snowflakes with size Λ_gr≈ .45 cm? Note that the thickness of human cortex varies in the range .1-.45 cm.

See the article Comparison of Orch-OR hypothesis with the TGD point of view or the chapter Quantum gravitation and quantum biology in TGD Universe.

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

Articles related to TGD

Pythagorean number mysticism, music harmony, and genetic code

The discussion with Marko Manninen renewed my interest in the ideas of Pythagoras related to mystics and mathematics and its role in music.

Rational Platonia

Pythagoras believed that rationals are all that is needed for a Universe and for him the discovery of \sqrt{2} represented geometrically by the diagonal of a unit square was probably a shock.

It is interesting that in the TGD framework the rationals appear naturally. In its simplest form, Galois confinement (see this and this) states that the total 4-momenta of physical states are Galois singlets invariant under Galois group permuting roots of a given polynomial (the notion generalizes if one considers functions in momentum space). This would allow only momenta with components, which are integers when a physical natural momentum unit is used. Platon would have been right in a certain sense!

However, Galois singlets would at fundamental level consist of quarks (in particular leptons and bosons would do so) having 4-momenta with components, which are algebraic integers in the extension of rationals defined by the polynomial defining the space-time region considered (see this and this). One could regard the algebraic integer valued momenta as virtual momenta characterizing the building bricks of physical states.

Special role of primes 2, 3 and 5

The number mysticism of Pythagoras involves the idea that the numbers 2 and 3 are very special. Using the language of modern number theory, one could say numbers 2 and 3 span a group with respect to multiplication consisting of numbers 2^m3ⁿ, where m and n are integers. One could call this group B(2,3). If m and n are restricted to non-negative integers, the inverses do not exist and only a semigroup is obtained. This object could be called A(2,3).

If Pythagoras identified rational numbers as a kind of Platonia, this group might be said to define an important province of Platonia. A more general object would be ideal consisting of all integers proportional to, say, 6=2× 3 closed with respect to multiplication by any integer.

It should be noticed that any set (p₁,...,p_n) of primes and even integers defines a group with respect to multiplication as the group B(m₁,m₂,...,m_n) of integers. Especially interesting example is the group B(2,3,5) containing B(2,3) and B(3/2).

p-Adic length scale hypothesis states that powers of small primes near to prime define important p-adic length scales. Powers of 2 are of special importance in p-adic mass calculations (see this and this) but there exists also evidence for powers of 3 (see this).

Decimal system is the decimal system used in everyday life and very often numerologists freely change the position of a decimal number and get results, which make sense only if the decimal system is in a special role. Could this be the case? If so, then the decimal system would not reflect only the fact that we have 10 fingers, and also the algebras B(2,5) and B(10) could be special.

There are some indications that this might be the case.

1. The faces of icosahedron resp. dodecahedron are triangles resp. pentagons so that numbers of 3 and 5 are natural.

2. DNA is a helical structure with a twist angle 2\pi/10 between to codons so that 10 codons make a 6\pi twist and define length scale 10 nm which is the p-adic length scale associated with Gaussian Mersenne prime M_G,151= (1+i)¹⁵¹-1, one of the 4 Gaussian Mersennes defining p-adic length scales in the range 10 nm, 2.5 μm. These scales are a number theoretic miracle. Numbers 2,3, and 5 relate to the geometry of DNA.

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Pythagorean scale

Pythagoras also studied music and introduced the notion of Pythagorean scale for which the frequencies of notes are in rational ratios. A standard manner to realized this scale is by quint cycle, which means that one forms the multiples (3/2)ⁿf₀ of fundamental frequency f₀ and identifies them by octave equivalence with a frequency in the basic octave [f₀,2f₀]. The quint cycle appears very often in jazz.

For n=12 the frequency obtained is almost a full number of octaves but quite not. This imperfectness of Platonia troubled Pythagoras a lot. In an equal tempered scale one introduces powers 2^m/2nf₀ and avoids this problem. This means replacement of rationals by its algebraic extension generated by 2^1/12.

Obviously, the Pythagorean scale is very natural in the framework of group B(3/2). Pythagoras also had ideas about the relationship of music scale and Platonic solids.

Pythagorean scale and genetic code

In the TGD framework, the idea about a possible connection between music and Platonic solids inspired the proposal about realization of the 12-note scale as a Hamiltonian cycle at icosahedron. The Hamiltonian cycle is a closed curve connecting only neighboring points of the icosahedron and going through all its 12 vertices. There are quite a large number of icosahedral cycles and they assign to the 20 triangles of icosahedron 3-chords proposed to define icosahedral harmony with 20 chords. The non-chaotic icosahedral cycles have symmetry groups Z₆, Z₄, and Z₂, which can act as a rotation or reflection.

The big surprise was that the model of icosahedral harmony leads to a model of genetic code. The code would involve a fusion of 3 different icosahedral harmonies with symmetry groups Z₆, Z₄, and Z₂ giving 60 codons plus tetrahedral code giving 4 codons. The counterparts of amino-acids would correspond to the orbits of these symmetry groups: 3 orbits with 6 triangles and 1 with 2 triangles as orbits for Z₆, 4 orbits with 4 triangles for Z₄ and 10 orbits with 2 triangles for Z₂. The number of triangles at the orbit is the number of DNA codons. Tetrahedron would give the missing 4 codons and stop codons and one missing amino acid.

For a given choice of the 3 Hamiltonian cycles, the realization would be in terms of 3-chords of light defining harmony for a music of light (and possibly also sound). Since music expresses and generates emotions, the proposal was that this realization of the genetic code expresses emotions already at the molecular level and that emotional intelligence corresponds to this realization whereas bit intelligence would correspond to the interpretation of codons as 6-bit sequences.

It should be mentioned that Hamiltonian cycles are solutions to the travelling salesman problem at the icosahedron: cities would correspond to the vertices. In the case of dodecahedron, which is dual of icosahedron, there is only one Hamiltonian cycle so that the harmony is now unique. If this corresponds to harmony, the first guess is that there would be a 20-note scale and 12 5-chords.

What about dodecahedral harmony and analog of genetic code?

Could also dodecahedron define a bioharmony and an analog of genetic code?

1. The first guess is that dodecahedral harmony has 20 notes per octave and perhaps corresponds to the scale defined by micro-octaves used in Eastern music. There would be 12 5-chords and the harmony would be unique. There would exist only a single emotional mood, a kind of enlightened state.
2. Since the harmony is unique, and there are no other Platonic solids with pentagons as faces. The analog of genetic code should correspond to dodecahedral harmony. The 5-chords would define 12 analogs of DNA codons.

   The dodecahedral cycle Z₃ acts as a symmetry group (\url{https://jrh794.wordpress.com/2021/04/01/the-original-hamiltonian-cycle-continued/}). This means that there are 4 orbits of Z₃ with 3 codons at each and they would correspond to 4 different analogs of amino-acids.

3. Could one consider instead of an icosahedral quint cycle with scaling 3/2 replaced with scaling 5/2? The tempered system would use powers of 2^1/20 to generate a 20-note scale. A single step along Hamilton's cycle connecting neighboring vertices of dodecahedron would correspond to a scaling f\rightarrow 5/2f plus octave equivalence.

   By octave equivalence the scaling b y 5/2 would correspond to a transition from say C to a note between E_b and E. The microintervals between this note and either E_b or E appears in blues, jazz etc as a blue note. This interval is between minor and major.

4. One can test this. The cold shower is that (5/2)²⁰ is not near to a power of 2. However, one has (5/2)¹⁹/2²⁵= 1.084 (for the quint cycle in the icosahedral case the deviation that Platon was worried of, is about 1 percent). As if one had a 19-note scale. A completely analogous situation is encountered with bio-harmony. The scales assigned to Z₆,Z₄, and Z₂ give rise to 19 amino-acids as orbits of these groups. One amino-acid is missing and the tetrahedral code gives this amino-acid plus 3 stop codons (see this).

   The icosa-dodecahedral duality suggests that the scale should consist of 19 notes only. Note however that for an equal tempered variant of the scale one does not have this problem.

5. Dodecahedral code predicts 4 analogs of amino acids. Could these "amino acids" correspond to the 4 DNA codons? 3 dodecahedral codons would be needed to code for a single genetic codon.

   Could he dodecahedral codons, which correspond to 5-chords, be realized as dark 5-photons and sequences of dark 5-protons. One should check whether the states of 5 dark protons could give rise to 12 dark dodecahedral codons and whether something analogous to 12 dark RNA codons, dark tRNA codons, and 4 dark amino acids could emerge.

   For the dodecahedral bioharmony, 5-chords would label the codons and they would serve as addresses based on communications relying on cyclotron resonance. Icosahedral harmony would control codons and dodecahedral harmony would code for their letters so that the codes would appear in different scales.

This speculation raises some questions. One can argue that in the transcription and replication the control of both codons and individual letters is important. This suggests that both realizations are needed for both DNA strands and correspond to different control scales. This would be true for the transcribed DNA, at least.

One can however consider alternatives. For instance, could the passive DNA strand correspond to a dodecahedral realization at the level of letters and the active strand to the icosahedral realization at the level of codons. Or could "junk" DNA and introns in promoter regions correspond to the dodecahedral realization with dark dodecahedral DNA controlling single letters.

See the article The realization of genetic code in terms of dark nucleon and dark photon triplets or the chapter with the same title.

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

Articles related to TGD

Could inert neutrinos be dark neutrinos in the TGD sense?

I learned about a new-to-me anomaly related to nuclear physics and possible neutrino physics (see this). The so-called Ga-anomaly is actually well-known but has escaped my attention. Baksan Experiment on Sterile Transitions (BEST) studies the nuclear reaction ν_e+⁷¹Ga→ e⁺+⁷¹Ga in which an electronic neutrino produced in the beta decay of ⁵¹Cr. The reaction rate has been found to be about 20-24 per cent lower than predicted.

The articles by Barinov et al telling of the experiment and published in Phys Rev Letters and Phys Rev C, can be found from arXiv (see this and this). A thorough discussion of standard nuclear physics predictions for the reaction rate of the reaction can be found in the article "The gallium anomaly revisited" by Kostensalo et al (see this).

Gallium anomaly is reported to be consistent with the sterile neutrino explanation stating that part of the electron neutrinos from the beta decay of ⁵¹Cr transform to their sterile counterparts so that the reaction rate is reduced.

The already discussed MicroBoone experiment (see this) however seems to exclude inert/sterile neutrinos.

1. What was reported is the following. Liquid Argon scintillator was used as a target. Several channels denoted by 1eNpMπ where N=0,1 is the number of protons and M=0,1 is the number of pions, were studied. Also the channel 1eX, where "X" denotes all possible final states was studied. It turned out that the rate for the production of electrons is below or consistent with the predictions for channels 1e1p, 1eNp0π and 1eX.

   Only one channel was an exception and corresponds to 1e0p0π. This anomalous scattering without hadrons in the final state was interpreted in terms of the scattering of ν_e on dark weakly interacting matter. Also the neutrino must be dark and the values of h_eff must be identical for this dark matter and dark neutrino if they interact.

2. The strange scattering in the 0-proton channel would take place from weakly interacting matter, which is dark in the sense that it has non-standard value of effective Planck constant h_eff=nh₀: this proposal has a number theoretic origin in the TGD framework. Darkness implies that the particles with the same value of h_eff appear in the vertices of scattering diagrams. Dark and ordinary particles can however transform to each other in 2-vertex and this corresponds to mixing. The identification of what this weakly interaction dark matter might be, was not considered.

The anomaly associated with the neutron life-time is another anomaly, which the dark proton hypothesis explains (see this). The two methods used to determine the lifetime of neutrons give different results. The first method measures the number of protons emerging to the beam in neutron decays. Second method measures the number of neutrons. The TGD explanation of the anomaly is that a fraction of neutrons decay to a dark proton, which remains unobserved in the first method. Second method detects the reduction of the intensity of the neutron beam and is insensitive to what happens to the proton so that the measurements give slightly different results.

These findings inspire the question whether the inert neutrinos are dark neutrinos in the TGD sense and therefore have h_eff>h? The mixing of the incoming neutrinos with their dark variants would take place in the ⁷¹Ga experiment. Dark neutrinos would not interact with ⁷¹Ga target since neutrons inside the ⁷¹Ga nuclei are expected to be ordinary so that the ν_e+n\rightarrow p+e^- scattering rate would be lower as observed.

The identification of sterile neutrinos as dark neutrinos can be consistent with the Micro-Boone anomaly if one can identify the weakly interacting dark matter.

1. Dark neutrons should not be present in the liquid Argon. Could the weakly interacting dark matter be meson-like states consisting of dark d quarks or anti-u quarks? Since the scattering from them cannot contribute to the nuclear weak interaction, these flux tubes must be outside Argon nuclei. By the large value of h_eff, they would connect Argon nuclei.
2. The TGD inspired model of nuclei describes them as nuclear strings consisting of nucleons connected by meson-like strings with quark and antiquark at its ends. The model of "cold fusion" (see this, this and this) inspired the proposal that dark nuclei consisting of dark protons connected by dark meson-like strings are formed in a water environment and give rise to what might be called dark nuclei.

   The nuclear binding energy of the dark nuclei is scaled down by the ratio of the length scale defined by the distance between dark protons to nuclear length scale. The decay of dark nuclei to ordinary nuclei liberates more nuclear energy than ordinary nuclear reactions. Also strings of nuclei connected by dark meson-like flux tubes can be imagined. One can also consider flux tube bonded clusters of nuclei.

3. The TGD based model for living matter involves in an essential way the formation of dark proton sequences at flux tubes when water is irradiated in presence of gel, by say infrared light.

   Could these dark flux tube bonds between nuclei relate to hydrogen bonds and hydrogen bonded clusters of water molecules? Could the "Y...H" of the hydrogen bond Y...H-X actually correspond to a dark meson-like flux tube bond between nuclei of Y and H? Could the attractive nuclear interaction between Y and X generated in this way increase the density of the liquid phase and explain the strange finding that the density of water above freezing point is higher than the density of the solid state?

   Interestingly, according to the Wikipedia article (see this), Ga has some strange thermodynamic properties. The density of Ga above freezing point is higher than that of solid state. This property is shared also by water, silicon, germanium, bismuth, and plutonium. Ga has a strong tendency to supercool down to temperatures below 90 K.

4. This suggests that liquid phases could in some situations form structures connected by dark meson-like flux tubes. If h_eff>h phases are generated as long range quantum fluctuations at quantum criticality and if quantum criticality is behind the thermodynamic criticality, this could happen near or above criticality for solid-liquid phase transition and even solid-gas phase transition.

   If this kind of flux tubes connecting Argon nuclei (Argon does not have anomalous thermodynamics) are present in a liquid Argon detector, they explain the observed anomalous contribution to neutrino-Argon scattering.

   Also in Gallium this could be the case as suggested by the higher density above freezing point. Could one detect the anomalous scattering of neutrinos from the proposed flux tube bonds connecting Ga atoms and study the anomalous scattering as a function of the temperature?

See the article Neutrinos and TGD or the chapter TGD as it is towards end of 2021.

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

Articles related to TGD

Comparison of Orch-OR hypothesis with the TGD point of view

Penrose-Hameroff (P-H) model and its variants such as Diosi-Penrose (D-P) model have been leading candidates for a quantum theory of consciousness. In light of recent experiments and theoretical arguments, the D-P model looks highly implausible. The key problem is energy conservation, which is actually the central problem of general relativity and caused by loss of Poincare invariance. The basic idea of Penrose about quantum gravitational superposition is almost a must but in the framework of general relativity its mathematical realization is not possible.

TGD provides an alternative view based on the identification of space-times as 4-surfaces in M⁴× CP₂ related by M⁸-H duality to 4-surfaces in M⁸. In this approach Poincare invariance is exact. In the TGD framework the hierarchy of Planck constants h_eff=nh₀ includes also gravitational Planck constant h_gr= GMm/v₀ introduced first by Nottale. This makes it possible to realize quantum coherence (in particular, gravitational one ) in arbitrarily long spatial and temporal scales.

In this article P-H and P-P models are compared with the TGD point of view. In TGD, the generation of quantum gravitational binding energy liberates energy and provides the basic mechanism of metabolism and a direct connection with quantum biochemistry emerges. The gravitational magnetic bodies (MBs) of Earth and Sun are in an essential role. Could one invent a mechanism involving only self-gravitational interaction energies of the living body itself? The large gravitational Compton length Λ_gr= GM/v₀ requires the presence of a large mass, say star, which would serve as basic metabolic energy source but the presence of a planet is not necessary in the prebiotic stage.

There are strong indications that water is a quantum critical system at the physiological temperature range. This suggests that scaled variants of magnetic bodies of water blobs as candidates for proto cells appear in quantum superposition with values of the parameter v₀. This would induce large density fluctuations at the level of the ordinary biomatter. State function reduction would induce a phase transition to a scaled-up state in the presence of energy feed. The return to the original state would liberate the gravitational energy as metabolic energy. Note that there are also indications for the quantum (gravitational) criticality of microtubules so that they would be very special from the point of view of life and neuron level consciousness.

The gravitational self-interaction energy for water blobs with Planck mass corresponds to an energy scale of 3.5 meV identifiable as the energy difference between two opposite membrane potentials. Could gravitational metabolic energy make possible the action potential of proto cells observed even for monocellulars?

See the article Comparison of Orch-OR hypothesis with the TGD point of view or the chapter Quantum gravitation and quantum biology in TGD Universe.

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

Articles related to TGD

The Possible Role of Spin Glass Phase and P-Adic Thermodynamics in Topological Quantum Computation: the TGD View

Topological quantum computation (TQC) or more generally, a TQC-like process (to be referred as TQC), is one possible application of TGD. The latest article summarizes the recent number theoretic view about TQC in TGD inspired biology. There are several new physics elements involved. Mention only the notion of many-sheeted space-time involving the notions of electric and magnetic body; the new view about quantum theory relying on the M⁸-H duality relating number theoretic and geometric views about physics and predicting the hierarchy of effective Planck constants assignable to a hierarchy of extensions of rationals; cognitive representations as unique discretization of space-time surface realizing generalized quantum computationalism; and zero energy ontology (ZEO) suggesting a new vision about quantum error correction. Quantum gravitation plays a key role in the proposal.

The engineering aspects of TQC were not discussed. The question that inspired this article was whether classical computation which relies strongly on non-equilibrium thermodynamics, could provide guidelines to end up with a more detailed view.

This led to a proposal in which p-adic thermodynamics assigned with the TGD based description of spin glasses would play a key role. TQC would involve quantum annealing in the spin glass energy landscape for the fermion states associated with flux tube structures. Anyons would be replaced with representations of the Galois group.

Physical states are however Galois singlets and many fermion states would involve entanglement between irreps of (relative) Galois group associated with spin resp. momentum degrees of freedom and give rise to a superposition of Galois singlets. The state function reduction ending TQC would project a tensor product of a given irrep from this superposition.

The entanglement between representations should be engineered in such a manner that the desired outcome of TQC would have the largest entanglement probability. p-Adic thermodynamics could give the entanglement probabilities. A connection with the travelling salesman problem emerges besides the connection with the factorization of the Galois group to prime factors appearing as relative Galois groups, which are simple (prime).

See the article The Possible Role of Spin Glass Phase and P-Adic Thermodynamics in Topological Quantum Computation: the TGD View or the chapter with the same title.

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

Articles related to TGD

Self-organized quantum criticality and 1/f noise as a possible signature for the reversal of the arrow of time

Reza Rastmanesh sent a paper by Dmitri Zhukov with title "How the theory of self-organized criticality explains punctuated equilibrium in social systems" (see this)

Self-organized criticality (SOC) is a very interesting phenomenon. Systems with SOC are able to stay near criticality. This is difficult, maybe even impossible, to understand in standard ontology since critical states are repellors of the dynamics and the system is expected to approach a stable state rather than remaining near criticality.

One can understand SOC as a manifestation of zero energy ontology (ZEO),which forms the cornerstone of TGD-based quantum measurement theory and TGD inspired theory of conscious experience. "Big" and "small" state function reductions (SFRs), BSFR and SSFR are the basic notions. BSRR is the TGD counterpart of ordinary state function reduction but reverses the arrow of time. SSFR is the counterpart of "weak" measurement and much like classical measurement: in particular, the arrow of change is preserved.

1. In TGD the magnetic body of a SOC system would be quantum critical and involve BSFRs in arbitrarily long scales at the level of MB. Since BSFR changes the arrow of time, the repellor becomes an attractor and the system would return to the vicinity of what was a repeller earlier. Homeostasis, which means an ability to stay near criticality, would be made possible by BSFRs: no complex biological control programs would be needed.
2. The period of time reversed time evolution for BSFR would correspond from the viewpoint of an outsider with an opposite arrow of time to an apparently stable state. The time reversed evolution to the geometric past would send classical signals to the direction of the geometric past of the observer and they would not be received by an outsider in the geometric future. Hence time reversed states are difficult to observe if the time reversed system is totally in the geometric past of the receiver.

   In the case of MB this need not be the case and the receiver could be in the geometric past with respect to the signal source at MB and receive the "negative energy" signal of MB just as would happen in memory recall. This could correspond to anticipation. This was discussed in one of our articles.

3. It would seem that BSFR corresponds to the "avalanche" from the point of view of an observer. Earthquakes (see this) represent one example of this kind of BSFR.
4. 1/f noise is one basic characteristic of SOC and ZEO provides an explanation for it so that 1/f noise could be seen as evidence for ZEO. If the states of time reversed MB are near quantum criticality for BSFR, there are quantum fluctuations and by the scale invariance of the quantum dynamics of TGD they have 1/f spectrum.

   [Supersymplectic symmetry involves super-conformal symmetry and scaling invariance justifying 1/f, I just wrote an article about this related to p-adic mass calculations (see this) ]

There are two ways in which 1/f noise could be interpreted as signals sent by the time reversed SOC MB. There are two options.

1. Suppose that the time reversed SOC MB is in the geometric past of the observer.

   Could the 1/f noise be induced by signals sent by the MB with a reversed arrow of time from the geometric past? These signals would be impossible in the standard classical world since they would propagate in the "wrong" time direction (which would now be the "right" time direction for their receiver!).

   "Negative energy signals" are assumed in the model of memory based on time reflection, which involves a BSFR for the system receiving or sending the signal. Could a subsystem of time reversed MB make BSFRs reversing their arrow of time so that they would send signals to the geometric future?

2. Suppose that the observer is in the geometric past of the time reversed SOC MB. In this case the observer would receive the signal sent by MB propagating into geometric past and the receival would involve BSFR for some subsystem of the receiver.

   If this picture makes sense, 1/f signals could be seen as communications of time reversed systems with signals propagating in the observer's direction of time.

   So: if the time reversed systems exist and if they are also able to send signals also in the time direction of the receiver with some probability, the 1/f noise could be understood as a support for ZEO and TGD based model of memory recall as time reflection.

There is an amusing correspondence with everyday life. A period of sleep would be a counterpart for the silent period predicted by ZEO (sleep as a "small death") and near the wake-up the 1/f fluctuations would become stronger. EEG indeed shows 1/f noise. During aging the noise level increases: old people have problems with sleep as I know so well!

See the article Homeostasis as self-organized quantum criticality? the chapter with the same title.

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

Articles and other material related to TGD.

A duality between certain non-hermitian systems in flat space with unitary systems in curved space

I learned about an interesting new  duality (see  the  popular article). The claim of the article "Curving the space by non-Hermicity" of Zhou et al (see this") is that dissipative dynamics, which allows a phenomenological description using non-hermitian  Hamiltonian, can in some cases be transformed to a non-dissipative dynamics by introducing non-flat Hilbert space Kähler metric.

The claim that this solves a physics mystery  could  be seen as a hype.

1.  Non-hermitian  quantum mechanics is a trick used to model  dissipative dynamics. However, in some cases this phenomenological model yields a system,  which is unitary and conserves probabilities. Authors show that in   these cases  the resulting system can be dual to a  unitary system defined in a curved space.
2.  The finding is that a    non-hermitian quantum dynamics in the  1-D  lattice considered allowing probability conservation with a modified inner product, can  be formulated as a hermitian and thus unitary dynamics in a 2-D lattice  of  a 2-D hyperbolic space with a  curved metric. Dimensional reduction is involved.    

   Non-hermitian Hamiltonians can  indeed allow also real energy eigenstates and probability conserving time evolution (see this).  By replacing complex conjugation representing T with a PT transformation in the inner product, the Hamiltonian becomes hermitian and defines unitary time evolution  and has a real energy spectrum. This is the case now.  

3. In the general case,   non-hermitian Hamiltonians give rise to non-conserved probabilities and can be used to describe dissipative systems phenomenologically without taking into account  the environment.

This is shown concretely for  what is known as the Hatano-Nelson model.

1. In this  1-D lattice model Schrödinger equation for an energy eigenstate of a non-Hermitian  Hamilton is discretized in such a manner that second partial derivative  associated with kinetic energy is replaced with a sum -t_LΨ_n+1- -t_RΨ_n-1  in which hopping amplitudes appear.  For L=-R, the equation reduces  to the analog of ordinary Schödinger equation.
2. At continuum limit this equation reduces to a dimensionally reduced Schrödinger equation at the 1-D boundary of a  hyperbolic upper plane if   the momentum component vertical to the boundary vanishes. For a non-vanishing vertical momentum one obtains additional potential term. The 2-D Schrödinger equation is probability conserving so that one can say that a 1-D system in  which non-hermitian Hamiltonian allows real energy eigenstates and the absence of dissipation is equivalent to a 2-D system with a hyperbolic metric.

 Authors interpret the 2-D hyperbolic  lattice as a curved lattice in 3-D  ordinary space so that Schrödinger equation is written in the induced metric, which is hyperbolic.  This is true for the considered  very special kind dissipative interaction with environment.  

One could perhaps see the situation   differently. The points of this lattice represent state basis for a discretized space of localized quantum state so that one can also  talk about  state basic of Hilbert space for which one has introduced metric,  which is non-Hermitian in 1-D case but  becomes hermitian  if the inner product is defined by a Käher metric of the  discretized 2-D hyperbolic plane. Hilbert space basis, with states labelled by   a lattice of ordinary Hilbert space, would be  in question and its points label elements of the state basis of a Hilbert space.  The hopping amplitudes in 1-D lattice would be non-hermitian inner product for the neighboring basis elements  and   would be non-symmetric  but for the  2-D extension of Hilbert space basis  Hilbert state basis would have Kähler metric. The reason why  I made this point  is that I have worked   with a different idea involving fermionic Fock space with a Kähler metric which would replace the unitary S-matrix as a description of quantum dynamics    (see this, this, and this)

1. TGD generalizes the Einstein' geometrization program from gravitation by including also the  standard model gauge interactions by replacing space-time with a 4-surface in H=M⁴×CP₂. Quantum TGD generalizes the problem to the level of the entire quantum theory by introducing the "world of classical worlds" (WCW) as the space of space-time surface in H satisfying holography required to general coordinate invariance in 4-D sense.
2. One can ask whether Einstein's geometrization of physics program could be extended also to Hilbert space level in the sense that a curved Hilbert space with a Kähler metric would replace unitary S-matrix: its identification and construction has been a long standing problem.   Kähler metric would characterize fermionic interactions at Hilbert space level. The  motivation is that in the infinite-D case the Kähler metric is highly unique and could in the TGD framework  completely fix the fermionic physics. In  fact, Kähler metric for the WCW   would do  the same for the bosonic physic).  For instance, the Kähler metric of WCW is expected to be essentially unique if it exists at all: already for loop spaces this is the case. Constant curvature metric for which all points of space are metrically equivalent is in question.    
3. The Kähler metric satisfies  orthogonality conditions guaranteeing probability conservation are  very similar to those associated with a unitary S-matrix and this is possible under rather weak additional conditions.  This  would work in the fermionic Fock space.  This would mean giving up the dogma of the unitary S-matrix proposed first by Wheeler. The problem of S-matrix is that any unitary transformation of Hilbert space can define S-matrix. The replacement of the S-matrix with Kähler metric could in infinite-D context fix the physics completely.  

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

Articles and other material related to TGD.