Tuesday, June 28, 2022

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. 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 Ih 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 Λgr= GME/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 heff meaning scaled up sizes for the basic structures. For heff=hgr the minimum size would naturally be Λgr! 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 H1.5O 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 H1.5O.

    Dark protons with heff=hgr 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.

  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 Λgr≈ .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

Thursday, June 23, 2022

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 2m3n, 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,...,pn) of primes and even integers defines a group with respect to multiplication as the group B(m1,m2,...,mn) 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 MG,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 2m/2nf0 and avoids this problem. This means replacement of rationals by its algebraic extension generated by 21/12.

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 21/20 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 Eb and E. The microintervals between this note and either Eb 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

Wednesday, June 22, 2022

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 νe+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 νe on dark weakly interacting matter. Also the neutrino must be dark and the values of heff 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 heff=nh0: this proposal has a number theoretic origin in the TGD framework. Darkness implies that the particles with the same value of heff 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 heff>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 νe+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 heff, 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 heff>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

Tuesday, June 21, 2022

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 heff=nh0 includes also gravitational Planck constant hgr= 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 Λgr= 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

Sunday, June 12, 2022

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

Sunday, June 05, 2022

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 -tLΨn+1- -tRΨn-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.

Tuesday, May 31, 2022

Can the initial stellar mass distribution of galaxy really depend on its distance from Earth?

Initial mass function (IMF) is used in the modelling of the galaxies. IMF would be the initial distribution of stellar masses as a given galaxy started to evolve about 10-13.6 billion years ago. It would be very natural to assume that the IMF is universal and the same for all galaxies, and this has indeed been done. The candidate for a universal IMF has been determined from the data related to the Milky Way and its satellites. There are however several candidates for the galactic IMF. It has been however found that the IMF depends on the distance of the galaxy from Earth and that the IMFs tend to concentrate on larger stellar masses. The dependence of MF on this distance is in conflict with the standard view about time assuming that the geometric past is fixed.

Zero energy ontology (ZEO) of TGD suggests a solution to the paradox.TGD Universe is quantum coherent also in astrophysical scales and "big" state function reductions (BSFRs) reversing the arrow of time occur for stars making them blackholes. This is the case also for Kerr-Newman rotating blackholes. Also quasars as white holes become galactic blackholes with an arrow of time opposite to that for a distant environment. ZEO implies that the geometric past and thus the IMF of the galaxy changes in the sequence of BSFRs. A simple argument based on the fact that massive stars have shorter age shows that the IMF for large distances from Earth indeed is concentrated on larger stellar masses.

See the article TGD based explanation of the satellite plane anomaly of the cold dark matter model or the chapter Cosmic string model for the formation of galaxies and stars.

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

Articles and other material related to TGD.

Monday, May 30, 2022

How can the perception of quale have a finite duration?

There is a philosophical problem related to the fact that the experience of, say, color has a duration. One could argue that the idea that color sensations correspond to SFRs, that is, a single moment of consciousness, is not consistent with this. One can imagine two ways to overcome this objection.

First option

One could argue as follows.

  1. It is not possible to experience that one is not conscious so that the illusion of finite duration of sensory quale is created.
  2. The "small" SFR as the TGD counterpart of a weak measurement in quantum measurement theory based on zero energy ontology (ZEO) begins as a cognitive measurement cascade in a Galois group of extension of rationals associated with a rational polynomial defining a given space-time region (see this andthis ). This cascade corresponds to a decomposition of the representation of Galois group for a functional composite polynomial P1○ ... ○ Pn for which Galois group of the algebraic extension has decomposition to a semidirect product of relative Galois groups Gi associated with pairs Pi,Pi+1. This yields a product of irreps of Gi.
  3. The cognitive cascade as a quantum correlate of analysis, is followed by measurements in quark spin and momentum degrees of freedom for the quark states defining the irreps of Gi. One can argue that the duration of the qualia mental image corresponds to the geometric lifetime of this sequence since eventually a BSFR, which means the death of the qualia mental image occurs. By the above argument, the steps in this sequence would not be experienced separately.
  4. There is an objection against this view. ZEO (see this, this and this) motivates the proposal is that we are during sleep living in an opposite direction of time and classically it is impossible to receive signals from that period since the signals travel in an opposite time direction (TGD predicts that also signals with "wrong" time direction can be received and sent but are rare and the process involves BSFR at the level of system representing mental images as subself). However, when we wake up in the morning, we remember that we were conscious yesterday and realize that we do not remember anything about the period of sleep. Could the same argument apply to mental images related to qualia?

Second option

One could also argue as follows.

  1. State function reductions (SFRs) (actually "small" SFRs responsible for the "flow of consciousness"") initiate a conscious experience of say some quale realized as subself, mental image. The next "small" SFR would end this experience and initiate a new one. If SFR is "big", the mental image dies and reincarnates with the opposite arrow of time and experience disappears from the consciousness of self.

    Mathematicians would say that a delta function is replaced with a step function as far as interpretation is considered. Nothing at the level of mathematical formalism has changed.

    The structure of conscious experiences reflects the structure of the physical states. In this spirit, one could argue that SFRs serve as a holographic data at the ends of the duration of the conscious experience, which determine the conscious experience associated with the duration itself. One would have have holography of consciousness.

  2. Is this interpretation consistent with the fact that change is necessary for qualia as already basic physiological facts show? For instance, if the saccadic motion of the eye is prevented, the perceptive field becomes dark first and after that the visual consciousness disappears. This finding can be consistent with the new view since the lifetimes of the qualia mental images as subselves are certainly finite.
Critical reader could ask whether the two options are only slightly different verbalizations of the same basic intuition and perhaps regard the latter verbalization as mathematically clearer. The latter option looks clearer than the first one although it does not literally conform with what I have been telling for three decades about SFRs as basic building bricks of conscious experience! It can take decades to express really clearly what you have understood!

See the article Some objections against TGD inspired view of qualia or the chapter General Theory of Qualia.

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

Articles and other material related to TGD. 


Tuesday, May 24, 2022

p-Adic particle massivation and entanglement: are all physical states massless?!

Unlike Higgs mechanism, p-adic thermodynamics provides a universal description of massivation involving no other assumptions about dynamics except super-conformal symmetry which guarantees by the existence of p-adic Boltzmann weights.

The number theoretic picture leads to a deeper understanding of a long standing objection against p-adic thermodynamics (see this) as a thermodynamics for the scaling generator L0 of Super Virasoro algebra.

If one requires super-Virasoro symmetry and identifies mass squared with a scaling generator L0, one can argue that only massless states are possible since L0 must annihilate these states! All states of the theory would be massless, not only those of fundamental particles as in conformally invariant theories to which twistor approach applies! This looks extremely beautiful mathematically but seems to be in conflict with reality already at single particle level!

The resolution of the objection is that thermodynamics is indeed in question.

  1. Thermodynamics replaces the state of entire system with the density matrix for the subsystem and describes approximately the interaction with the environment inducing the entanglement of the particle with it. To be precise, actually a "square root" of p-adic thermodynamics could be in question, with probabilities being replaced with their square roots having also phase factors. The excited states of the entire system indeed are massless (see this).
  2. The entangling interaction gives rise to a superposition of products of single particle massive states with the states of environment and the entire mass squared would remain vanishing. The massless ground state configuration dominates and the probabilities of the thermal excitations are of order O(1/p) and extremely small. For instance, for the electron one has p= M127=2127-1≈ 1038.
  3. In the p-adic mass calculations (see this and this), the effective environment for quarks and leptons would in a good approximation consist of a wormhole contact (wormhole contacts for gauge bosons and Higgs and hadrons). The many-quark state many-quark state associated with the wormhole throat (single quark state for quarks and 3-quark-state for leptons (see this).
  4. In M8 picture (see this and this) tachyonicity is unavoidable since the real part of the mass squared as a root of a polynomial P can be negative. Also tachyonic real but algebraic mass squared values are possible. At the H level, tachyonicity corresponds to the Euclidean signature of the induced metric for a wormhole contact.

    Tachyonicity is also necessary: otherwise one does not obtain massless states. The super-symplectic states of quarks would entangle with the tachyonic states of the wormhole contacts by Galois confinement.

  5. The massless ground state for a particle corresponds to a state constructed from a massive single state of a single particle super-symplectic representation (CP2 mass characterizes the mass scale) obtained by adding tachyons to guarantee masslessness. Galois confinement is satisfied. The tachyonic mass squared is assigned with wormhole contacts with the Euclidean signature of the induced metric, whose throats in turn carry the fermions so that the wormhole contact would form the nearby environment.

    The entangled state is in a good approximation a superposition of pairs of massive single-particle states with the wormhole contact(s). The lowest state remains massless and massive single particle states receive a compensating negative mass squared from the wormhole contact. Thermal mass squared corresponds to a single particle mass squared and does not take into account the contribution of wormhole contacts except for the ground state.

  6. There is a further delicate number theoretic element involved (see this and this). The choice of M4⊂ M8 for the system is not unique. Since M4 momentum is an M4 projection of a massless M8 momentum, it is massless by a suitable choice of M4⊂ M8. This choice must be made for the environment so that both the state of the environment and the single particle ground state are massless. For the excited states, the choice of M4 must remain the same, which forces the massivation of the single particle excitations and p-adic massivation.
These arguments strongly suggest that pure states, in particular the state of the entire Universe, are massless. Mass would reflect the statistical description of entanglement using density matrix. The proportionality between p-adic thermal mass squared (mappable to real mass squared by canonical identification) and the entropy for the entanglement of the subsystem-environment pair is therefore natural. This proportionality conforms with the formula for the blackhole entropy, which states that the blackhole entropy is proportional to mass squared. Also p-adic mass calculations inspired the notion of blackhole-elementary particle analogy (see this) but without a deeper understanding of its origin.

One can regard the breaking of conformal invariance induced by the thermodynamical description of entanglement as a TGD counterpart for the breaking of gauge symmetry.

Polynomials P define two kinds of space-time surfaces depending on whether their roots determine either mass or energy shells. For the energy option a space-time region corresponds by M8-H duality (see this and this) to a solution spectrum in which the roots correspond to energies rather than mass squared values and light-cone proper time is replaced with linear Minkoski time. The physical interpretation of this solution spectrum has remained unclear.

The energy option gives rise to a p-adic variant of the ordinary thermodynamics and requires integer quantization of energy. This option is natural for massless states since scalings leave the mass shell invariant in this case. Scaling invariance and conformal invariance are not violated.

One can wonder what the role of these massless virtual quark states in TQC could be. A good guess is that the two options correspond to phases with broken resp. unbroken conformal symmetry. In gauge theories to phases with broken and unbroken gauge symmetries. The breaking of gauge symmetry indeed induces breaking of conformal symmetry and its breaking is more fundamental.

  1. Particle massivation corresponds in gauge theories to symmetry breaking caused by the generation of the Higgs vacuum expectation value. Gauge symmetry breaking induces a breaking of conformal symmetry and particle massivation. In the TGD framework, the generation of entanglement between members of state pairs such that members having opposite values of mass squared determined as roots of polynomial P in the most general case, leads to a breaking of conformal symmetry for each tensor factor and the description in terms of p-adic thermodynamics gives thermal mass squared.
  2. > What about the situation when energy, instead of mass squared, comes as a root of P. Also now one can construct physical states from massless virtual quarks with energies coming as algebraic integers. Total energies would be ordinary integers. This gives massless entangled states, if the rational integer parts of 4-momenta are parallel. This brings in mind a standard twistor approach with parallel light-like momenta for on-mass shell states. Now however the virtual states can have transversal momentum components which are algebraic numbers (possibly complex) but sum up to zero.

    Quantum entangled states would be superpositions over state pairs with parallel massless momenta. Massless extremals (topological light rays, see this) are natural classical space-time correlates for them. This phase would correspond to the phase with unbroken conformal symmetry.

  3. One can also assign a symmetry breaking to the thermodynamic massivation. For the energy option, the entire Galois group appears as symmetry of the mass shell whereas for the mass squared option only the isotropy group does so. Therefore there is a symmetry breaking of the full Galois symmetry to the symmetry defined by the isotropy group. In a loose sense, the real valued argument of P serves as a counterpart of Higgs field.

    If the symmetry breaking in the model of electroweak interaction corresponds to this kind of symmetry breaking, the isotropy group, which involves also a subgroup of quaternionic automorphisms as analog of Galois group, could act as a discrete subgroup of SU(2)L× U(1). The hierarchy of discrete subgroups associated with the hierarchy of Jones inclusions assigned with measurement resolution suggests itself. It has the isometry groups of Platonic solids as the groups with genuinely 3-D action. In the QCD picture about strong interactions there is no gauge symmetry breaking so that a description based on the energy option is natural. Hadronic picture would correspond to mass squared option and symmetry breaking to the isotropy group of the root.

To sum up, in the maximally symmetric scenario, conformal symmetry breaking would be only apparent, and due to the necessity to restrict to non-tachyonic subsystems using p-adic thermodynamics. Gauge symmetry breaking would be replaced with the replacement of the Galois group with the isotropy group of the root representing mass squared value. The argument of the polynomial defining space-time region would be the analog of the Higgs field.

See the article Two objections against p-adic thermodynamics and their resolution, the chapter TGD as it is towards the end of 2021, or the chapter About TGD counterparts of twistor amplitudes.

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

Articles and other material related to TGD. theory.fi/tgdmaterial.html">Articles and other material related to TGD.

Monday, May 23, 2022

Dark meiosis and the mystery of why different cells express the chromosomes of father and mother in different manner

Condensed matter physicists are discovering that the world of electrons at atomic level is govering by knotting and linking (this). This picture is just what TGD predicts but applies to all systems, not only electrons, and in all scales from hadron physics to cosmology. Besides particles there are magnetic flux tubes connecting them to a network. This is completely new from the perspective of quantum field theory based description.

Since 3-space is a surface in M4×CP2 is 3-D, flux tubes and string world sheets accompanying them are necessarily linked and knotted: this distinguishes TGD from string models. This implies braiding and makes possible topological quantum computation (TQC) like activities at fundamental level, in particular in living matter and especially at the DNA level.

Since spacetime is 4-D, string world sheets and flux tubes can reconnect. This is a new element to TQC like activity. Reconnection is a fundamental aspect of the TGD inspired quantum biology.

Meiosis serves as a good example demonstrating how powerful predictions this vision leads to. Meiosis as a recombination of DNAs would be induced by a reconnection of the magnetic flux tubes. The reconnecting flux tubes, which accompany mother' and father's chromosomes, which control the ordinary DNA strands, carry "dark" genes with codons realized as dark proton triplets. Darkness means large effective Planck constant h_eff and high "IQ" therefore ability to control ordinary biomatter.

This leads to a solution of the mystery of why the gene expression, which selects either the allele for mother and father, does this differently in different cells (see this). The explanation is that dark meiosis, which yields a pair of different dark gametes for dark DNA, occurs already in cell replication for daughter cells and differently in each cell replication. Ordinary meiosis occurs only later and dark gamete serves as a controller and template for it. Since the dark gametes select whether the allele of mother or father is selected by resonance mechanism, dark meiosis effectively creates new descendants at cell level as far as transcription and replication are considered. 50 replications would mean 250 ≈ 1015 descendants living in the same body and expressing themselves genetically!

Natural selection would therefore occur already at the cell level and only those dark gametes, for which the cells controlled by them survive and have produced ordinary gametes as their images, have a change to participate in sexual production, which is like the finals in Olympics.

Second implication is that the two gametes produced in dark meiosis in cell replication and going to different cells are related by father ↔ mother symmetry and since XX chromosome pair characterizes female and XY chromosome pair male, sister and brother which are mirror images of each other emerge. Therefore cells have a well-defined sex!

This raises questions. Could same cellular sex dominate in organelles and even organs so that also these could be said to have a well-defined sex? Could the battle between sexes start already at the cell level and possibly lead to extinction of the other sex? Do cells have sexual relationships like us and tend to pair? Could possible multi-cellular structures with a well-defined sex have this kind of relationships? What comes into mind are epithelial layers consisting of two cell layers and various binary structures in the body and brain.

See the article Mysteries related to gene expression and meiosis or the chapter ZEO, adelic physics, and genes.

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

Articles and other material related to TGD.

About the number theoretic aspects of zero energy ontology

The interaction between number theoretic vision, ZEO, and the TGD view DNA enriches all of them. In this article the recent view about quantum measurements is discussed in light of the recent progress in the understanding of the number theoretic aspects of TGD.

By M8-H duality space-time regions would be determined by polynomials whose roots define in M>4⊂ M8 3-D mass shells providing the data for holography fixing the space-time surfaces. Whether product polynomials besides irreducible polynomials should be allowed has been an open question. The product polynomials could naturally correspond to free states unable to entangle. The functional composition was earlier interpreted as formation of many-particle states but perhaps a more natural interpretation is as a generation of sheets of the many-sheeted space-time with interactions having wormhole contacts as geometric correlates.

This modified picture leads to a re-analysis of state function reduction (SFR), in particular the notions of "big" SFR and "small" SFR from a number theoretic perspective. This leads to a more precise view about the notion of time and time evolution. The emerging picture can be applied to TGD inspired theory of consciousness, in particular various aspects related to the notion of time and memory.

See the article About the number theoretic aspects of ZEO or the chapter with the same title.

Sunday, May 15, 2022

Mysteries associated with lightnings, ball lightnings and the electrosphere of Earth

Lightning and ball lightning are electrospheric phenomena involving several poorly understood aspects. Also the origin of the electrosphere of Earth is still a mystery. In the TGD framework it is possible to deduce information about magnetic and electric bodies of Earth (briefly MB and EB) by using empirical inputs and these phenomena.
  1. Ball lightings are known to be real are not understood. Ball lightning-like phenomena can be created also artificially in microwave ovens using match. Matches contain organic material and this serves as a good hint.
  2. There is a New Scientist article, which gives a popular representation of ball lightings (see this). The theory of Cameron (see this) is mentioned in the article. The theory assumes that lightnings are essentially phenomena associated with the electromagnetic radiation field alone and neglects the fact that plasma is very probably involved. The theory relies on exact solutions of Maxwell's equations and proposes that ball lightnings involve monochromatic electromagnetic fields which are knotted and linked making the field configurations topologically nontrivial. Both magnetic and electric field lines can be knotted. This does not however imply topological stability since the linearity of Maxwell's equations implies that these field configurations are unstable. The finding that lifetime is long enough for microwave lengths does not conform with the fact that visible light is involved. Another theory mentioned in the article is by Boerner and proposes that lightning comes from another dimension. What this could actually mean, is of course a highly non-trivial question.
  3. The basic mystery is how ball lightning can survive for so long a time. An ordinary plasma ball is not expected to do so. This suggests that ball lightning obeys non-linear dynamics and is some kind of topological entity robust by their topological non-triviality.
  4. A very natural expectation is that ball lightning is a self-organizing system consisting of plasma which radiates. Self-organization requires energy feed. It could come as a Coulombic energy from the electric field of Earth through which part of the plasma of ball lightning has arrived. Here one encounters a problem. The electric resistance of the atmosphere causes a dissipation of the energy so that the charged particles cannot accelerate to high energies. How could lightning avoid this?
  5. Two problems are always better than one. The second puzzle is that ordinary lightnings involve relativistic electrons and gamma rays. This is impossible in standard physics due to the already mentioned electric resistance of the atmosphere. Could ball lightning involve a new phase of matter, for which the dissipation is very small. Perhaps because it interacts very weakly with the ordinary matter of the atmosphere?
  6. The third mystery is that the surface of Earth carries a negative charge, which creates an electric field. This field is essential for the generation of lightning. The origin of this field is however not understood.
  7. There is also a fourth problem. Dark matter exists but there is no generally accepted theory of dark matter. All experiments trying to detect proposed candidates for dark matter particles (the particle physicist's way to solve a problem is to propose a new particle) have failed. There is of course also the mystery of life but it is better to stop here.
In the sequel a TGD based model for electrosphere is deduced by using various empirical inputs and the TGD based view about dark matter and the model of quantum biology inspired by it. A model, which allows us to understand these phenomena in the TGD framework, is developed. The model relies on the TGD based model of dark matter residing at the flux tubes of the magnetic body. The gravitational magnetic bodies of both Earth and Sun are important.The notion of the electric body of Earth as an analog of the cell membrane acting as a generalized Josephson junction is developed. Lightning and ball lightning would be associated with the analog of action potential.

See the article Mysteries associated with lightnings, ball lightnings and the electrosphere of Earth or the chapter About Concrete Realization of Remote Metabolism.

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

Articles and other material related to TGD.

Thursday, May 12, 2022

Quantum Gravitation and Topological Quantum Computation

The progress in the understanding of the role of quantum gravitation in quantum biology (see this), as it is understood in the TGD framework, leads to the questions about the role of quantum gravivation in topological quantum computation (TQC). I sketched the first TGD based vision about DNA as a TQCer for about 13 years ago. In particular, a model of the system consisting of DNA and nuclear/cell membrane system acting as a TQCer was discussed.

TGD has evolved a lot after this and there are several motivations for seeing what comes out from combining the recent view about quantum TGD and TGD inspired quantum biology with this model.

  1. There is a rather detailed view about the role of dark matter as phases of ordinary matter with the effective Planck constant heff=nh0. Large values of heff allow to overcome the problems due to the loss of quantum coherence.

    This leads to the notion of the dark DNA (DDNA), whose codons are realized as dark proton triplets and proposed to accompany the ordinary DNA. Also dark photon triplets are predicted and one ends up to a model of communications and control based on dark cyclotron resonance in which codons serve as addresses and modulation of the signal frequency scale codes the signal to a sequence of pulses. Nerve pulses could be one application.

  2. Quite recently, also the understanding of the possible role of quantum gravitation in biochemistry, metabolism, bio-catalysis, and in the function of DNA has considerably increased. The gravitational variants of hydrogen bonds and valence bonds between metal ions having very large value of heff= hgr, where hgr=GMm/v0 is the gravitational Planck constant originally introduced by Nottale, are in a key role in the model and explain metabolic energy quantum as gravitational energy liberated when dark protons "drops" from a very long gravitational flux tube in the transition hgr → h. Also electronic metabolic energy quantum is predicted and there is empirical support for this.
  3. A further motivation comes from the number theoretic vision of quantum TGD. Galois groups as symmetry groups represent new physics and the natural questions are whether Galois groups could give rise to number theoretic variants of anyons and what could the TGD counterparts of the condensed matter (effective) Majorana electrons proposed by Kitaev as anyon like states?

    The answer is that quantum superpositions of symmetric hydrogen bonded structures of form X..H-H+X-H...X are excellent candidates for the seats of dark (heff>nh0>h) bi-localized electrons defining TGD analogs of condensed matter Majorana electrons.

    The Galois groups permute the roots of a polynomial, which determines a space-time region by M8-H duality. The roots correspond to mass squared values, in general algebraic numbers, and thus to mass hyperboloids in M4c⊂ M8c. The H images correspond to 3-hyperboloids with a constant value a=an of light-cone proper time. Therefore the Galois group can permute points with time-like separation. Note however that the real or rational parts of two values of a can be same.

    This looks very strange at first but actually confirms with the fact that time-like braidings defining TQC correspond in TGD time-like braidings (involving also reconnections) of string like objects defining string world sheets, which are not now time evolutions of space-like entities as physical state but correspond to time-like entities defining boundary data necessary for fixing holography completely. Their presence is forced by the small failure of the determinism of the action principle involved and is completely analogous to the non-determinism for soap films with frames serving as seats for the failure of determinism.

  4. Braidings appear therefore at the level of fundamental TGD and correspond to string world sheets. They are possible only in 4-D space-time but not in string models.

    Also TQC-like processes appear automatically at the level of fundamental physics. In particular, the number theoretical state function reduction cascade for the Galois group following the time evolution induced by braiding can be regarded as a generalization of a decomposition of integers to primes: now primes are replaced by simple groups defining primes for finite groups. Nature is doing number theory!

  5. Also zero energy ontology (ZEO) brings in new elements. The change of the arrow of time in "big" state function reductions (BSFRs) implies that dissipation with a reversed arrow of time provides an automatic error correction procedure. Also TQC in which the arrow of time varies for sub-modules, can be considered.
See the article Quantum Gravitation and Topological Quantum Computation or the chapter with the same title.

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

Articles and other material related to TGD. 


Wednesday, May 11, 2022

TGD based solution of the satellite plane anomaly

The satellite galaxies of larger galaxies tend to move in a plane around the host as described in the review article of Pawlovski whereas the ΛCDM predicts that the orbits are more or less random. The article gives illustrations showing the concentration around the planes for the Milky Way, Andromeda, and Centaurian. The plane of satellites is approximately orthogonal to the plane of the host galaxy in all cases.

Quite generally, ΛCDM fails on short scales. The success in long scales is understandable in the TGD framework since the approximation of the mass density of cosmic strings by a continuous mass density is good in long scales.

Why planar orbits are preferred?

TGD predicts (see this , this , and this) a fractal network of very massive long cosmic strings which can locally thicken to flux tubes: this thickening involves transformation of dark energy and possible dark matter of cosmic string to ordinary matter giving rise to galaxies and other structures. Also stars would have thickened flux tube tangles inside themselves. The model finds support from the observation that galaxies form long strings as found decades ago (Zeldowich was one of the discoverers).

The TGD based model predicts the formation of planes in which objects in various scales move. The prediction is fractal: this applies to planets around stars, stars around galaxies, satellite galaxies around larger galaxies,....

This model explains the satellite plane anomaly and also the earlier anomalies if the galaxies are associated with the long "cosmic strings" predicted by TGD (see this). They create a strong gravitational potential giving rise to a radial force in the plane orthogonal to the cosmic string. The motion along the string is free whereas the planar motion is rotation. The velocity spectrum is flat as required by the flatness of the galactic velocity spectrum. In the simplest model cosmic string is the carrier of galactic dark matter and dark energy. No dark matter halo and no exotic dark matter particles are needed.

Helical orbits are the most general orbits. If a concentration of matter occurs to a plane, it tends to catch objects moving freely in the direction of string to its vertical gravitational field and planar sheets such planetary systems, spiral galaxies, and the planar systems formed by satellite galaxies can form.

The first guess is that the satellite galaxies move in the plane of the host galaxy. The plane is however approximately orthogonal to the plane of the host in the 3 cases illustrated in the review article of Pavlowski.

  1. I have proposed that the intersections of nearly orthogonal cosmic strings could induce the thickening to flux tubes and transformation of the dark energy of flux tubes to ordinary matter starting to rotate in the planes defined by the intersecting cosmic string.
  2. These intersections are unavoidable for strings like objects in 4-D space-time and would occur at discrete points. In the collision of cosmic strings, these points would define the nucleus of the host galaxy, say the Milky Way. The satellite galaxies would be assignable to the plane defined by the second colliding cosmic string, which would take the role of stars in the plane of the host galaxy.

    The colling cosmic strings would be in a very asymmetric position. Why this asymmetry? Could the satellites correspond to circular pieces of cosmic string generated in the collision by reconnections (note the analogy with reconnections of magnetic flux tubes of solar wind occurring during auroras) and generating the matter of the satellite.

    Why only the second cosmic string would have satellites around it? For two separate cosmic strings it is difficult to understand why reconnection would form loops. This process is natural for the two antiparallel strands of a closed U-shaped loop. Cosmic strings indeed form loops.

This model involves two strings. One can also consider a single cosmic string.
  1. Cosmic strings are closed in a large enough scale, and the model for quantum biology encourages to consider U-shaped cosmic strings for which the parallel string portions carry opposite magnetic fluxes and can naturally reconnect. The flux tube could self-reconnect and generate loops, possibly assignable to the satellite galaxies. The reconnection process would be fundamental in TGD inspired quantum biology (see for instance \cite{btart/alleledominance}).
  2. In the reconnection of the strands carrying opposite magnetic flux would form a section S orthogonal to the long part L of the U-shaped string. Could one assign the host galaxy with L and the satellite galaxies to S? L and S would define nearly orthogonal planes and the satellite galaxies could form around loops created from L by a repeated reconnection and they would rotate around the host in the plane defined by S.

Is there something that could define galactic planes?

One can wonder whether there is something, which serves as a seed for the concentration of stars around a selected plane, perhaps associated with the boundary of a cell of the honeycomb structure. The collision of two cosmic strings would naturally define two planes of this kind. In the case of a single U-shaped closed string, which looks a more promising option, there is no obvious identification of the plane orthogonal to this object.

  1. In the TGD Universe, space-time is a 4-surface in H=M4× CP2 and also membrane like entities are predicted as 4-D minimal surfaces of H having lower-D singularities analogous to the frames of a soap film minimal surface property (and simultaneous extermality with respect to Kähler action) fail but the field equations for the entire action involving volume term and Kähler action are satisfied at the singularities.
  2. One can also consider 3-D singularities, which form a tessellation of H3 at a given moment of cosmic time a and assign it with the honeycomb of large voids. The frame would be a tessellation. The quantization of cosmic redshifts in a given direction, discussed from the TGD viewpoint n here, could be seen as evidence for cosmic tessellations having astrophysical objects at their nodes.

    The boundaries of the large cosmic voids form a honeycomb structure and could correspond to a tessellation of H3. The long U-shaped cosmic strings would be associated with the boundaries of the cells of the honeycomb and perhaps even form a 2-D lattice like structure.

  3. The objects M1× X2× S1, where M1 is time axis, X2 is a piece of plane of E2, and S1 is a geodesic sphere of CP2, define very simple minimal surfaces carrying no induced Kähler field. The objects X2× S1 could accompany the boundaries of the honeycomb cells. Universe could be populated by these membrane-like objects. Cell membrane is one important example.
  4. Planar or approximately planar objects orthogonal to the cosmic string could tend to gather the matter flowing along helical orbits along the cosmic string. These planes would accompany planetary, galactic, etc... planes and the honeycomb structure could be also seen as a fractal analog of a multicellular structure.
  5. Warped planes represent slightly more complex minimal surfaces with 3-D M4 projection (a thin metal foil or sheet of paper gets warped) for which the plane is deformed but still flat minimal surface. I am not sure whether the "warping" \cite{bcast{warping (see this) of the outer regions of galactic planes, which has received attention recently (see this" and this") but has been detected already 1956, is really really warping that is vertical deformation, which depends only single coordinate varying along a straight line (a 2-D plane wave of membrane).
See the article A solution of two galactic anomalies in the TGD framework or the chapter Cosmic string model for the formation of galaxies and stars.

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

Articles and other material related to TGD.

Tuesday, May 10, 2022

10 times too high amount of He-4 in atmosphere as evidence for cold fusion

I learned an interesting piece of fact related to nuclear physics anomalies. It has been found that the amount of 3He in the Earths' atmosphere is ten times higher than expected.

The result is not deduced by measuring the amount 3He but that of 4He. The amount of the latter is too high and since 4He produces 3He, the amount of 3He must be higher than normal if we believe in standard nuclear physics.

The first report by Fleischmann and Pons about "cold fusion" was the claim that 4He is produced by fusion of two deuterium nuclei. "Cold fusion" was labelled as pseudoscience first but now it has been accepted as a real science and cold fusion researchers are not regarded as science criminals anymore.

Could this extra 4He be produced by "cold fusion"? No extra 3He, not produced in "cold fusion", would be needed.

The TGD based model for cold fusion (see this, this, and this) relies on the notion of dark nuclei and one of the basic predictions is that heavier nuclei can be produced outside stellar cores at much lower temperatures than in the Sun. In the TGD framework, prestellar evolution would start by "cold fusion" and would lead eventually to such a high temperature that ordinary fusion would start.

"Cold fusion" solves many problems of the standard nuclear physics based view. For instance, the production of nuclei heavier and iron is poorly understood: the hypothesis that Supernovae might have produced them remains unproven. Also the abundances of many light nuclei, such as Lithium, are poorly understood. Also the model for solar fusion has an anomaly discovered a few years ago. There is also evidence that living matter produces nuclei such as Calcium by some unknown mechanism.

See the article Cold fusion again or the chapter with the same title.

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

Articles and other material related to TGD.

Thursday, May 05, 2022

DMT experiences and hyperbolic geometry

I received a link to a highly inspiring talk about a modelling of DMT induced experiences in terms of 2-D and more generally 3-D hyperbolic geometry. The title of the talk was "DMT and Hyperbolic Geometry". The talk was by a person using the name "Algekalipso" and I understand that the person in question is Andres Gomez Emilsson. The organization in question is a non-profit organization known as Qualia Research Institute. There is also article with essentially the same content.

1. Can one characterize DMT experiences by using temperature like parameters?

The question posed in the beginning of the talk was whether there could exist parameters analogous to temperature allowing a general qualitative understanding of the nature of the DMT and more general psychedelic experiences. The proposal was that the DMT experience could be characterized by two parameters.

  1. The first parameter characterizes how "hyperbolic" the visual field is and is identifiable as the curvature of the hyperbolic space. The idea is that during a DMT trip the experienced 3-space is not Euclidean but hyperbolic. This kind of geometry has been proposed as an effective statistical geometry of the brain in which functionally similar neurons distant from each other are close to each other.

    In the TGD framework, this effective geometry could correspond to a real hyperbolic geometry of 3-D hyperbolic space playing a key role in TGD and assignable naturally to the magnetic body (MB) (see this). What would be experienced would be the projection of objects of H3 to the usual Euclidean space E3.

    In the TGD framework, space-times are minimal surfaces apart from singularities analogous to frames of soap films and their basic aspect is local saddle point property possessed also by hyperbolic spaces (see this). Maybe DMT experiences make it possible to visually perceive 3-surfaces as objects in H3. Also the usual vision also corresponds to hyperbolic vision but with a small value of the H3 curvature.

  2. The second parameter would characterize the complexity of the experience and could in the TGD framework correspond to algebraic complexity associated with the extension of rationals assignable to a given space-time region (see this and this).

    The value heff=nh0 of the effective Planck constant, which can be larger than h, would correspond to the dimension n of the extension of rationals and serve as a universal IQ. Dark matter would correspond to phases of ordinary matter with heff ≠ h.

    As the IQ increases, the experience transforms from simple to complex and eventually chaotic since the experiencer is not able to make sense of it. Under some assumptions this would relate to the formation of Julia set type fractals (see this).

2. About hyperbolic spaces

First some mathematical background.

  1. Hyperbolic 3-space H3 is a generalization of 1-D hyperbola of 2-D space-time as a curve defined by condition t2-x2= a2 but with its metric being induced from the 2-D Minkowski metric ds2= dt2-dx2 . By performing all possible rotations of this 1-D hyperbola one obtains H3.
  2. In particle physics H3 corresponds to mass shell E2-p2= m2 and in cosmology to cosmic time identifiable as a2=tr-r2 in M4 ⊂ M4× CP2. a defines Lorentz invariant cosmic time and is therefore analogous to absolute time invariant under Lorentz boosts which do not affect the tip of the light-cone. It is not invariant under translations however.

    In the TGD framework H3 has a central role and plays a key role also in the model of the brain involving the notion of magnetic body (MB). One could say that cognitive and sensory representations are realized at the intersection of MB with H3.

  3. The value of cosmic time a characterizes the curvature of H3. The curvature is proportional to 1/a2 and the smaller the value of a, the larger the curvature and "hyperbolicity". As a decreases, one approaches the analog of the Big Bang with infinite curvature. As a increases, one approaches flat E3 in an infinite future. Cosmic evolution proceeds from the Big Bang to the future whereas DMT trip would be a travel towards the moment of Big Bang. One can of course ask whether trips could also be in the opposite time direction.
  4. The lecture (see also the written version) contains a nice description of hyperbolic geometry. In particular, the volume of a ball in H3 increases exponentially as a function of its radius and this means that H3 has a lot of volume. This might be very relevant for memory storage. This can be easily understood from the visualization in terms of real hyperboloid.
  5. The counterpart of plane E2 of E3 in H3 is 2-D hyperbolic space H2 and Poincare sphere gives a good view about what the projections of the tesselations of H2 look like when projected to E2. The radial size for the basic unit of tessellations decreases with the distance from the origin whereas the region around the origin looks like E2.
  6. The hyperbolic geometry H2 embedded locally in E3 has the saddle property meaning that in one direction the observer is at the bottom of the valley and in another direction at the top of the hill. This property has analog also at the level of abstract geometry: geodesic lines diverge very rapidly since the curvature scalar is negative: for spheres they converge.
  7. By their negative curvature, H3 and H2 allow tessellations (analogs of lattices in E3 and E2) which are not possible in E3. For instance. 7-polygons are possible. The number of tessellations is infinite whereas in E2 only 17 wall papers are possible.
  8. Hyperbolic analogs of plants are mentioned as fractals.
3. A possible interpretation of DMT experiences

DMT experiences could reflect both the relationship between the geometries of hyperbolic 3-space and Euclidian 3-space represented as 3-surfaces of Minkowski space and the algebraic complexity assignable to the tesselations of H3.

3.1 DMT trip as travel backwards in cosmic time

It was already mentioned that the proper time parameter a and algebraic complexity characterized by extension of rationals could characterize DMT experience. The increased complexity in turn means approach to apparent chaos since it is not possible to comprehend too high complexity. The following description is what I understood from the representation of Emilsson. I have not personally made DMT trips except spontaneously decades ago. This experience was so impressive that I got a passion to understand conscious experience from a quantum physics point of view.

  1. For small DMT does, the visual experiences correspond to patterns in plane E2 ⊂ E3, which can be regarded as plane H2⊂ H3 for large value of a and thus small curvature.

    The 17 lattices of E2, called wallpapers, serve as a background for the visual field. As if one would be perceiving two different worlds simultaneously. The lattices can be dynamical and pulsate. This kind of experience was part of the "Great Experience" decades ago.

  2. As the DMT dose increases, the value of a decreases and one moves towards the Big Bang, so to say. In TGD and TGD inspired theory of consciousness, causal diamonds (CDs), identified as intersections of future and past directed light-cones, could be called correlates of perceptive fields. CD is analogous to a Big Bang followed by a Big crunch. The CDs form a fractal hierarchy.

    The visual field becomes more and more hyperbolic. What we would see is the projection of the patterns of H2a⊂ H3a⊂ M4+ to E2t⊂ E3t⊂ M4+, where a is cosmic time and t is the linear Minkowski time.

  3. At the next step the 2-D patterns in H3 are replaced by patterns in H3 as hyperbolic analogous of curved surfaces in E3 and one can say that the dimension of the visual field becomes 3.
  4. In TGD Universe space-time surfaces are minimal surfaces (see this) and analogous to 4-D soap films spanned by frames appearing as singularities where minimal surface property and also the determinism of field equations fail so that the frames are space-time correlates as seats of non-determinism. The saddle property of minimal surface could explain the appearance of the "hyperbolic plants" which Emilsson lists as part of DMT experience.
Do we really see a hyperbolic world or does the visual perception reflect only the statistical geometry of the brain? The TGD proposal is that these two views reflect real space-time surfaces. One can of course argue that since conscious experience itself is associated with quantum jumps in the TGD framework so that the experience is about becoming rather than about being in the physical sense.

3.2. Algebraic complexity of the experience as a second parameter

The second parameter discussed in the talk was meant to characterize what was called valence as a measure for the degree of "bliss" of the experience. TGD counterpart would be algebraic complexity associated with the extension of rationals defined by the polynomial defining the space-time region. The value of heff/h0=n as dimension of extension would serve as the parameter . For large values of n the situation becomes too complex to comprehend or remember and the bliss is lost.

In the TGD framework more complex systems can be engineered as functional composites of polynomials and this leads to the increase of heff. One can interpret this also as a construction of many-particle states with each polynomial, which represents a particle-like entity (see this and this). When a fixed polynomial is iterated functionally, one obtains a fractal known as Julia set so that the connection with fractals is quite concrete (see this).

To sum up, the reports of Emilsson suggest a very concrete connection between DMT experience and TGD based views of space-time and number theoretical vision about quantum theory explaining dark matter as heff=nh0 phases. DMT perception would be perceptions of both ordinary and dark matter simultaneously.

4. Possible implications for the interpretation of TGD

The proposed picture involving in an essential manner both H3 and E3 suggests some quite non-trivial implications concerning the physical interpretation of TGD.

4.1 H3 is ideal for information storage and holography

The hyperbolic radial distance rH in H3 from origin is given by rH= a arsinh(rE/a) ≈ a log(rE/a), where rE is the Euclidean distance in E3. rH depends logarithmically of rE slowly. The area S=4π a2r2 of the hyperbolic sphere of radius u projected to Euclidean sphere with r increases as function of u as S≈ 4π a2exp(2u/a). One can imbed a tree graph (say) m ranches in the node much more effectively than in the Euclidean case. One can think of the tree grapas a simple model for a neural network consisting of layers such that n:th layer has mn nodes for

If a given node requires fixed area Δ S, the solid angle Δ Ω required by a node decreases as 1/r2 whereas in E3 it remains constant, the number of these areas at sphere increases as S/Δ S= 4π exp(2u/a)/Δ S. In the Euclidean case it increases as S/ΔS= 4π r2/Δ S. This means that the geometric information storage capacity ofH3 is exponentially larger. Therefore the idea that the 3 surfaces associated with H3a could serve as information storage is very attractive.

4.2 H3 and the origin of p-adic length scale hypothesis

p-Adic prime assignable to a region of the space-time surface is identified as the largests ramified prime associated with the polynomial defining the region of the space-time surface. p-Adic length scale hypothesis states that the physical preferred p-adic primes correspond to p-adic primes p≈ mk, where m is a small integer: m=2 is the most important case.

I have proposed that there are two scales involved. The small p-adic length scale associated with m and the exponentially larger p-adic length scale proportional to p1/2. The origin of these scales has remained a mystery.

Could the small scales correspond to the radial scales rH and large scales to radial scales rE?

  1. H3 allows tessellations playing a key role in TGD framework and the size scale of the cell of the tesselation defines a natural length scale unit Δ rH= aX, which could define the small scale and scales would be expressible in terms of this unit.
  2. In E3 the natural scale would correspond to Euclidean lattices with constant cell size Δ rE. For rH= Δ rH, rE = a sinh(rH/a) ≈ aexp(rH/a) would give rE ≈ aexp(nX= a mΔ X/log(m).
  3. rE=Lp= p1/2R would give p1/2R = amΔ Xlog(a)/log(m). p-Adic length scale hypothesis p≈ mk requires X= klog(m)/2log(a/R).

    Note that there would be a logarithmic dependence of the p-adic length scale on the a, which would have an interpretation as a renormalization of the p-adic length- and mass scales.

See the article DMT experience and hyperbolic geometry or the chapter Magnetic Sensory Canvas Hypothesis.

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

Articles and other material related to TGD.