Thursday, February 27, 2020

Could solar system be modelled as a miniature version of spiral galaxy?

The fractality of the TGD Universe motivates a model for planetary systems as miniature version of the model of spiral galaxy discussed in (see this). The first two key elements are many-sheeted space-time, the notion of magnetic flux tubes - both monopole flux tubes and gravitational flux tubes without monopole flux - and the identification of dark matter as phases of ordinary matter labelled by effective Planck constant heff=n× h0 (h=6h0 is a good guess (see this, this and this). Also the TGD generalization of Nottale's model for planetary system as analog of Bohr atom characterized by large gravitational Planck constant hgr identified as heff is in a key role (see this) and this).

A further key aspect is the prediction of twistor lift of TGD (see this) and this) that cosmological constant is length scale dependent and characterizes various systems in all scales. The phase transitions reducing the cosmological constant lead to expansion of space-time sheet and define a sequence of jerks replacing smooth cosmic expansion for astrophysical objects expected in standard cosmology but not observed.

TGD provides a model for "cold fusion" based on dark fusion (see this) and suggests the possibility of fusion outside stellar cores perhaps serving as "warm-up band" for hot fusion during pre-stellar evolution. Also a new view about nuclear fusion in stellar interiors is suggestive (see this).

I did not originally end up with the model to be discussed from general theoretical considerations.

  1. The first empirical input were the problems related to the collision - and accretion models for the formation of planets - TGD allows to consider the replacement of these models with quantal model involving the dark nuclear fusion in planetary cores.

  2. The discovery of "too" heavy blackholes and neutron stars by LIGO (see this) suggesting that TGD view about the formation of also planets could provide understanding about the role of angular momentum.

  3. There are also problems related to the understanding of the entire planetary system: the dramatic difference between terrestrial and giant planets is not really understood.

The problematic aspects of the Bohr orbit model together with the poorly understood differences between terrestrial and giant planets lead to a proposal that phase transition increasing the ℏgr by factor 5 and accompanying a transition reducing the length scale dependent cosmological constant Λ could have scaled up the orbital radii of former inner planets. The transition could have also scaled up the radii of the former inner planets so that they became giant planet.

See the article Could solar system be modelled as a miniature version of spiral galaxy? 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.

Friday, February 21, 2020

Do we really understand neutron star pairs or even neutron stars?

The observation of gravitational radiation by LIGO allowing interpretation as fusion of two neutron stars has challenged the views about neutrons stars and star formation: see the popular article in Quanta Magazine about the work of Enrico Ramirez-Ruiz and colleagues. Single neutron star collision with exceptional characteristics as such is not enough for revolution. One can however ask what it could mean if this event is not a rare statistical fluctuation but business as usual.

  1. The pair has too high total mass: only 10 per cent of stars are estimated to be massive enough to make so massive neutron stars. Something in the models for star formation might be badly wrong.

  2. Also the models for the formation of neutron star pairs are unable to explain why the abundance of so massive pairs would be so high as LIGO would predict. There could be something wrong also in the models for the collisions of stellar objects.

TGD provides several new physics elements to the possible model.
  1. Galaxies, stars, even planets are tangles in cosmic strings carrying dark energy and (also galactic) dark matter and thickened to monopole flux tubes not possible in standard gauge theories. This leads to a general model of stars and of final states of stars as flux tube tangles as spaghettis filling the volume and thus maximally dense. One obtains nice quantitative predictions plus a generalization of the notion of blackhole like entity (BHE) so that all final states of stars are BHEs: BHEs would be characterizized by the quantized thickness of the flux tube in question.

    Also a TGD based modification of the view about nuclear fusion required by a 10 year old nuclear physics anomaly and "cold fusion" is involved solving a long list of nuclear physics related anomalies (see this).

  2. Collision of stellar objects producing blackholes can occur much more often than expected. Suppose one has two long flux tube portions going very near to each other: they could be portions of the same closed flux tube or of two separate flux tubes. The situation would be this for instance in galactic nuclei of spiral galaxies (see this.

    The colliding stellar objects correspond to flux tube tangles moving along them. Since the stellar objects are forced to move along these cosmic highways, their collisions as cosmic traffic accidents become much more frequent than for randomly moving objects in ordinary cosmology. The cosmic highways force them to come near to each other at crossings and gravitational attraction strengthens this tendency.

    Situation would be analogous in bio-chemistry: bio-catalysis would involve flux tubes connecting reactants and the reduction of effective Planck constants would reduce flux tube length and bring the reactants together and liberating the energy to overcome the potential wall making reaction extremely slow in ordinary chemistry.

    Already the high rate of collisions might allow to understand why the first collision of neutron stars observed by LIGO was that for unexpectedly high total mass.

This model does not yet answer the question why so heavy neutron stars are possible at all. Also the fusion of "too heavy" blackholes has been observed by LIGO (for TGD inspired comments see this). Thus the blackhole formation of a neutron star pair with unexpectedly high combined mass supports the expecation that "too" heavy stars are a rule rather than exception.
  1. The problem is that during the formation of blackhole or neutron the radius of the star decreases and the star should throw out a lot of angular momentum to avoid too high spinning velocity in the collapse. This can be achieved by throwing out mass but this makes heavy blackholes and neutron stars impossible.

  2. Can TGD provide a solution of this problem? Suppose that both galaxies and stars are tangles along long cosmic strings locally thickened to monopole flux tubes carrying dark matter and energy in TGD sense Long flux tube would provide new degrees of freedom. Could the angular momentum of collapsing star consisting of ordinary matter be transferred from the star to the cosmic string/flux tube without large loss of stellar mass.

    Suppose that one has single monopole flux tube or a pair of monopole flux tubes as analog of DNA double strand (flux tubes would combine to form a closed flux tube) forming a rotating helical structure. This structure could store the angular momentum to its rotation. Also the radiation and particles travelling around these helical flux tubes could take away part of the angular momentum but flux tubes themselves as TGD counterparts of galactic dark matter could do the main job. Heavy blackholes would be a direct signature for energy and angular mmentum transfer between ordinary matter and galactic dark matter in TGD sense.

See the article LIGO and TGD 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, February 20, 2020

Three variants of dark genetic code and an objection against bio-harmony

The experiments of Montagnier et al give support for DNA remote replication. Re-consideration of the TGD based model for remote replication lead to a the model for DNA replication leads to an identification of a third exotic realization of DNA codons based for which dark codons and nucleotides defining the letters of codons are paired. The nucleotides have no valence bonds and are effectively free but actually correlated and realize genetic codon.

Three variants of dark genetic code

Consider first the three exotic variants of the genetic code.

  1. The notion of MB suggests that dark proton sequences assumed to explain Pollack effect (see this) realize dark genetic code. Dark DNA (DDNA) codon would correspond to 3-proton triplet assignable to closed flux tubes attached to a a long flux tube by U-shaped flux tube appendix giving rise to dark gene (see this). Attaching means formation of U-shaped appendices from long flux tube and DDNA codon which reconnect to a pair of flux tubes. 3-proton states define dark analogs of DNA, RNA, tRNA, and amino-acids ( DDNA, DRNA, DtRNA, DAA) (see this). The numbers of DDNAs coding for given DAA are same as for vertebrate genetic code.

  2. Second dark code is needed for communications and realizes genetic codons as dark 3-photon states - 3-chords of bio-harmony (see this). The model emerged from a model of musical harmony based on icosahedron and tetrahedron. 12-note scale is identified as a Hamiltonian cycle - a path going through all 12 vertices of icosahedron - such that going from vertex to neighbor corresponds to quint. Hamiltonian cycles have cyclic group Zn,where n=0,2,4,6 is the order of the group, as symmetries. n=0 corresponds to chaotic orbit and disharmony. Each of the 20 faces - triangles - corresponds to a chord of given harmony.

    One identifies the orbit of given face as DAA coded by faces (DDNAs) at the orbit. By combining 3 harmonies with n=6, n=4 and n=2 one obtains 20+20+20 chords and the numbers of DNA coding given AA are essentially those in vertebrate code. By gluing tetrahedron to one face one obtains 4 additional chords (DDNAs) and 1 additional note very near to one of the notes of Pythagorean scale, whose problem is that it does not quite close. The numbers for analogs of DNA codons coding for for given DAA are same as for vertebrate code.

    The chords would be represented as "music of light" as states of 3 dark photons. Music expresses and creates emotions and bio-harmony would provide a physical correlate for emotional states at molecular level (see this).

  3. Dark codes would be fundamental and chemical code would be their mimicry. One expects DDNA-DNA pairing with DDNA codons represented as dark proton triplets. DDNA codons and dark photon chords have no decomposition to letters (chinese and western languages provide an analog). This suggests that DNA replication and transcription cannot take letter-wise but but codon-wise. Amazingly, there is evidence that DNA replicates in codon-wise manner during RNA era (see this).

    Nucleotides/letters in the water environment of DNA double strand should appear as loosely bound but correlated triplets of nucleotides associated with closed flux tubes containing dark DNA codon. They would represent exotic DNA codons. This would force fixed order of nucleotides essential for the code. By absence of valence bonds between nucleotides they would be effectively free but strongly correlated. This representation of the code would be crucial for replication and transcription.

These 3 codes allow to understand replication and transcription of DNA replaced in TGD with DDNA-DNA pair. The prediction is that the replication takes place codon by codon and might kill the model.

A model of replication based on this picture generalizes to remote replication suggested by the findings of Montagnier (see this). The DDNA codons of ordinary DNA strand would be attached with a long side of closed flux tube as dark gene. In remote replication heff of dark gene would change and dark gene would be transferred to chamber B from A. After that the replication would proceed as usual.

An objection against bio-harmony

There is a serious objection against the realization of dark genetic code in terms of bio-harmony. The emission of 3 dark photons simultaneously looks extremely non-probable process.

Number theoretical physics suggests a solution of the problem. Number theoretical physics (this) is a central part of quantum TGD and quantum biology and provides physical correlates for cognition. It explains dark matter as heff=nh0 phases of ordinary matter with n identified as order of Galois group of extension of rationals and as dimension of extension. This picture predicts automatically evolution as increase of n in quantum jumps.

  1. There is analogy with color confinement. Baryons consist of 3 quarks. Color symmetry is a symmetry of strong interactions and quarks form color triplets. Free quarks do not appear in the final states, which givs rise to color confinement: only color singlets, in particular baryons consisting of 3 quarks and mesons consisting of quark and antiquark are possible.

    This suggests that also now there must be a symmetry such that dark photons have new quantum numbers, which vanish for physical states such as dark photon triplets.

  2. What these quantum numbers could be? The only candidate, which comes in mind are discrete quantum numbers related to the Galois group of extension of rationals defining number theoretic symmetry. For ordinary h= 6h0 Galois group has n=6 elements and equals to Z6=Z2× Z3 (see (see this and (see this).

    It appears as subgroup of higher Galois groups for which heff= n× h=6nh0 one would have extension of extension. Z3 confinement would require 3-photon states, which are Z3 singlets with number theoretic colors summing up to zero. One would obtain only 3-chords. Ordinary photons would be Z3 singlets.

  3. Also the 3 protons of DDNA codon could form Z3 triplet. Number theoretic color confinement would allow only 3-proton triplets. Genetic code is predicted correctly and the number letters in the codons is predicted to be 3.

This raises two interesting questions.
  1. Quantum-classical correspondence (QCC) is a exact part of TGD. Therefore I have considered the possibility that all physical symmetries could have number theoretical space-time correlates. However, at space-time level one cannot have representations of color group with non-vanishing triality t=0,+/- 1. Same applies to spin half-odd integer representations of rotation group. Could SU(2)× SU(3) representations with triality t=+/- 1 and spin half-odd integer have triplet representation of Z3 and double representation of Z2 as space-time correlates? Z6 would be the minimal Galois group allowing to realize spin and color for quarks.

  2. Number theoretical physics predicts that Galois group for any extension of rationals acts as new hidden discrete symmetry. Could number theoretical confinement implying new selection rules be true quite generally? The larger the degree n of extension (heff), the larger the scale in which confinement holds true, is. For instance, genes could be analogs of color singlet many particle states for a larger subgroup.

This is not the only option. I have already earlier considered with Peter Gariaev (see this) a proposal in which dark photons would communicate the genetic information from A to B. The problem is how the massless extremals (MEs) (see this). associated with them can be parallel and of same length: this would require that they form a quantum coherent entity. Could one consider a modification of the above proposal assuming that gene is an entity of N codons confined number theoretically? Could one can speak about dark photon genes as composites of N dark photon 3-chords? The information would be sent by dark photon gene representing entire music piece, as one might say. In chamber B energy-frequency resonance would generate a linear configuration of exotic codons, which would reduce to DDNA-DNA pair when heff is reduced.

See the article New results about dark DNA inspired by the model for remote DNA replication or the chapter Quantum Mind, Magnetic Body, and Biological Body.

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

Articles and other material related to TGD.

The dynamics of SSFRs as quantum measurement cascades in the group algebra of Galois group

Adelic physics, M8-H duality, and zero energy ontology lead to a proposal that the dynamics involved with "small" state function reductions (SSFRs) as counterparts of weak measurements could be basically number theoretical dynamics with SSFRs identified as reduction cascades leading to completely un-entangled state in the space of wave functions in Galois group identifiable as wave functions in the space of cognitive representations. As a side product a prime factorization of the order of Galois group is obtained.

The result looks even more fascinating if the cognitive dynamics is a representation for the dynamics in real degrees of freedom in finite resolution characterized by the extension of rationals. If cognitive representations represent reality approximately, this indeed looks very natural and would provide an analog for adele formula expressing the norm of a rational as the inverse of the product of is p-adic norms. The application at the level of genes is especially interesting.

See the article The dynamics of SSFRs as quantum measurement cascades in the group algebra of Galois group or the chapter Zero Energy Ontology and Matrices.

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

Articles and other material related to TGD.

Monday, February 17, 2020

New results about dark DNA inspired by the model for remote DNA replication

In TGD inspired vision about quantum biology relying on the notion of magnetic body (MB) carrying dark matter as phases of ordinary matter with effective Planck constant heff=n× h0 one ends up with the notion of dark DNA realized as sequences of dark protons and to the surprising finding that dark proton triplets realize vertebrate genetic code and basic biomolecules DNA,RNA,tRNA, and amino-acids.

The objection against dark photon 3-chords (3-photon states) is that the simultaneous emission of 3 dark photons used in communications as 6-bit unit is extremely non-probable. A possible solution of the problem is that dark photons carry number theoretic color associated with Z3 sub-group of Galois group. Number theoretic color confinement would imply that only 3-chords can appear as asymptotic states analogous to baryons. If dark protons are also number theoretic color triplet, dark codons must consists of 3 protons and therefore also ordinary codons have 3 letters.

The findings of Montagnier et al (see this) raise the possibility of remote replication of DNA. Montangier's experiment involves two chambers A and B. A contained water and genes and B water and DNA nucleotides. There were channels between the chambers but so thin that DNA could not get through. Besides this there was present em field with 7 Hz frequency. Same genes as in A appeared also in B. As if remote replication of genes in A had happened in B. I have written an articles about Montagnier's findings. Gariaev has reported similar phenomenon already before Montagnier et al: we wrote together an article discussing TGD based model for the finding.

How did the genetic information pass to B and how the remote replication took place? Somehow the radiation made the remote metabolism possible or at least more probable. Clearly the information about gene - not only about codons but also about their order and relative positions - should have been communicated from A to B. I have already earlier considered this problem but found no satisfactory solution to it.

Concerning the role of the 7 Hz frequency, there are two hints.

  1. The nominal value of the lowest Schumann frequency is 7.8 Hz, not far from 7 Hz. Could one think that macroscopic quantum coherence in the scale of Earth was involved. 7.8 Hz correspond to wavelength equal to circumference of Earth.

  2. "Endogenous" magnetic field Bend=.2 Gauss identifiable as the monopole flux part of the Earth's magnetic field BE= .5 Gauss explains the findings of Blackmanand others about quantal looking effects of radiation at frequencies seem to be multiples of cyclotron frequencies of biologically important ions.

    The problem is that the energies of cyclotron photons are ridiculously small for ordinary value of Planck constant. This was one of the motivations for the hypothesis that dark matter corresponds to phases of ordinary matter with effective Planck constant heff=n× h0. The cyclotron frequency of K ion is fc(K+) =7.1 Hz. The flux tubes with length of corresponding cyclotron frequency are also of the order of Earth circumference.

This raises several questions.
  1. Did water generate flux tubes with magnetic field with frequency equal to fc(K+) =7.1 Hz and strengthening coupling to a radiation with Schumann frequency or K cyclotron frequency or both so that the communications with the MB of Earth or/and layer of MB corresponding to K cyclotron was strengthened? The TGD based mechanism of water memory would be involved.

  2. Did this make the remote replication more probable? How?

  3. What DNA actually looks like in TGD Universe? What actually happens in DNA replication? What could happen in remote DNA replication?

In the sequel the questions whether cyclotron frequency or Schumann frequency or both were involved and how their presence made possible remote replication remain without detailed answer although it is clear that the presence of dark photons with this frequency should make possible the control by MB generating coherence of ordinary matter in the scale determined by the sizes of the chambers. These questions however led to a considerable increase in the understanding of dark variants of genetic code predicted by TGD.
  1. To understand remote replication one must understand replication. Dark codons do not decompose into letters like chemical codons: this poses strong constraints on the replication and transcription if one assumes DDNA-DNA-pairing. These constraints strongly suggests that the nucleotides in the water environment of DNA are not actually free but form loosely bound triplets representing codons and bound with DDNAs. This means a new variant of genetic code realizing codons as loose triplets of nucleotides in the water environment.

  2. This proposal brings in mind TGD based model for viruses, which can decompose into pieces shared between several host cells and re-combine later as also the observation that the dense states of bacteria population have resemblance to multi-cellular embryos. The common TGD inspired explanation would be that the pieces of virus and cells of bacterial population are connected by magnetic flux tubes and form a single loosely bound unit at the level of MB. The prediction is that replication occurs in codon-wise manner: this has been observed to be possible for RNA. It might be that the loose nature of exotic DNA codons allows this to occur quite generally.

  3. Remote replication in this framework reduces to ordinary replication in TGD sense if also dark genes are formed by attaching flux tubes characterizing dark codons to a long flux tube associated with gene. Remote replication requires that the portion of dark gene accompanying ordinary gene is transferred from chamber A to chamber B in the experiment of Montagnier.

See the article New results about dark DNA inspired by the model for remote DNA replication or the chapter Quantum Mind, Magnetic Body, and Biological Body.

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

Articles and other material related to TGD.

Sunday, February 16, 2020

50 Hz electric stimulation of central lateral thalamus can wake up from anaesthesia

Thanks for Ashton Martin for very interesting link related to neuroscience. The popular article tells about the work of Michelle Redinbaugh et al (see this).The researchers have conducted experiment on monkeys in anaesthesia and conclude that the activation of central lateral thalamus by 50 Hz electric oscillations may enable consciousness. Activation of the central lateral thalamus and deep layers of the cerebral cortex drives pathways in the brain that carry information between the parietal and frontal lobe in the brain, the study suggests.

From TGD point view the conclusion is too far fetched and reflects the naive "consciousness-module" thinking. The fining is however very interesting from the view point of TGD inspired theory of consciousness and quantum biology.

  1. The wakeup from anaesthesia happened using 50 Hz electric stimulation of cetral lateral thalamus.

  2. In TGD framework magnetic body (MB) carries dark matter as phases of ordinary matter with effective Planck constant heff=n×h0, which can be very large. n serves as a kind of IQ and MB serves as a master using biological body (BB) - in particular brain - as slave. EEG and it scale variants serve as a tool for communication to and control by MB. EEG photons are dark with large heff and can transform to bio-photons in visible and UV energy range and thus affect molecular transitions.

  3. MB has layered structure with cyclotron frequencies of biologically important ions associated with the control by MB in "endogenous" magnetic field Bend= .2 Gauss identifiable as monopole flux part of Earth's magnetic field about .5 Gauss. Bend explains the findings of Blackman and others about the effects of ELF radiation on brain and also why EEG correlates with consciousness and brain state. Without MB sending of EEG radiation to outer space would be horrible waste of energy resources.

  4. For 7Li the cyclotron frequency for Bend is 50 Hz. Litium is known to have healing effect on depression and heal axonal infection. Depression and other problems could be due to the lack of communications to MB or control by MB. This would be due to a lack of magnetic flux tubes containing cyclotron B-E condensate of biologically important ions. MB could not take care of BB.

  5. Interestingly, the rate of lightnings in Earth's atmosphere is 50 Hz (see this) and corresponds to a very strong peak in the em resonance spectrum of Earth including also Schumann resonances at 7.8, 14, 20, 26, 33, 39, 45 and 59 Hertz (see this). TGD inspired theory of consciousness predicting self hierarchy and that the MB of Earth - Magnetic Mother Gaia - is also a conscious entity, suggests a connection.

  6. The finding suggests that some layer of MB of thalamus region producing dark cyclotron radiation at cyclotron frequency of Li manages to wake up this brain region in presence of irradiation. How?

    1. The model of water memory based on MB and water as a poly-phase involving dark magnetic flux tubes with heff=n×h0 suggests that 50 Hz frequency generates in water flux tubes with cyclotron frequency of 50 Hz which act as receiving and sending antennas.

    2. Water would detect this frequency by tuning the thickness of the flux tubes to tune cyclotron frequency to 50 Hz: this is possible for monopole flux tubes not allowed by Maxwellian ED: flux is conserved and changing the thickness changes the cyclotron frequency. The antennas can send and receive 50 Hz radiation. The 50 Hz antennae generated by oscillation em field would be able to receive the cyclotron radiation from MB and wake up.

    3. The flux tubes can also tune to the cyclotron frequencies associated with the MBs of invader molecules and this would make possible to generate "fake" molecules as MBs of water clusters. This would explain water memory, and give rise to basic recognition mechanism of immune system. Also homeopathy would be real effect and be based on the build-up of "fake" variants of molecules as flux tube antennae tuned to cyclotron frequency spectrum of MB of molecule. This requires metabolic energy feed to increase the value of heff at magnetic flux tubes and the agitation of water would provide this energy.

See the article Lithium and Brain 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.

Tuesday, February 04, 2020

Could quantum randomness have something to do with classical chaos?

There was an interesting guest post by Tim Palmer in the blog of Sabine Hosssenfelder (see this).

Balmer's idea

Consider first what was said in the post "Undecidability, Uncomputability and the Unity of Physics. Part 1"
by Tim Palmer.

  1. I understood (perhaps mis-) that the idea is to reduce quantum randomness to classical chaos. If this is taken to mean that quantum theory reduces to chaos theory, I will not follow. The precise rules of quantum measurement having interpretation as measurements performed for the observables - typically generators of symmetries - are very restrictive and it is extremely difficult to image that classical physics could explain them. Quantum theory is much more than probability theory. Probabilities are essentially moduli squared for probability amplitudes and this gives rise to interference and entanglement. Therefore the idea of reducing state function reduction (SFR) and quantum randomness to classical chaos does not look promising. One could however consider the possibility classical chaos is in some sense as a correlate for quantum randomness or associated with state function reductions.

  2. The difficulty to combine general relativity (GRT) to quantum gravity was mentioned. The difficulty is basically due to the loss of Poincare symmetries in curved space-time. Already string models solve the problem by assuming that strings live in M10 or its spontaneous compactification. Strings are however 2-D, not 4-D, and this leads to a catastrophe. In TGD H= M4× CP2 allows to have Poincare invariance and conservation laws are not lost. In QFT picture this means that the existence of energy guarantees existence of Hamiltonian defining time evolution operator and S-matrix.

  3. It was noticed that chaos in quantum theory cannot be assigned to Schrödinger equation. This is true and applies quite generally to unitary time evolution generated by unitary S-matrix acting linearly. It as also noticed that in statistical mechanism Liouville operator defines a linear equation for phase space probability distribution analogous to Schrödinger equation. Liouville equation allows the classical system to be non-linear and chaotic. Could Schrödinger equation in some sense replace Liouville equation in in quantum theory since phase space ceases to make sense by Uncertainty Principle.

    Could Schrödinger equation allow in some sense non-linear chaotic classical systems? In Copenhagen interpretation no classical system exists except at macroscopic limit as an approximation. One has only wave function coding for the knowledge about physical system changing in quantum measurement. There is no classical reality and there are no classical orbits of particle since one gives up the notion of Bohr orbit. Could Bohr orbit be more than approximation?

The authors consider also the question about definition of chaos.
  1. Chaos is difficult to define in GRT. The replacement time coordinate with its logarithm exponentially growing difference becomes linearly growing and one does not have chaos. By general coordinate invariance this definition of chaos does not therefore make sense.

  2. Strange attractors are typical asymptotic situations in chaotic systems and can make sense also in general relativity (GRT). They represent lower dimensional manifolds to which the dynamics of the system is restricted asymptotically. It is not possible to predict to which strange attractor the chaotic dynamical system ends up. This definition of chaos makes sense also in GRT.

Remark: One must remember that the notion of chaos is often used in misleading sense. The increase of complexity looks like chaos for external observer but need not have anything to do with genuine chaos.

Could TGD allow realization of Palmer's idea in some form?

It came as a surprise to me that these to notions could a have deep relationship in TGD framework.

  1. Strong form of Palmer's idea stating that quantum randomness reduces to classical chaos certainly fails but one can consider weaker forms of the idea. Even these variants fail in Copenhagen interpretation since strictly speaking there is no classical reality, only wave function coding for the knowledge about the system. Bohr orbits should be more than approximation and in TGD framework space-time surface as preferred extremal of action is analogous to Bohr orbit and classical physics defined by Bohr orbits is an exact part of quantum theory.

  2. In the zero energy ontology (ZEO) of TGD the idea works in weaker form and has very strong implications for the more detailed understanding of ZEO and M8-M4× CP2 duality. Ordinary ("big") state functions (BSFRs) meaning the death of the system in a universal sense and re-incarnation with opposite arrow of time would involve quantum criticality accompanied by classical chaos assignable to the correspondence between geometric time and subjective time identified as sequence of "small" state function reductions (SSFRs) as analogs of weak measurements. The findings of Minev et al give strong support for this view and Libet's findings about active aspects of consciousness can be understood if the act of free will corresponds to BSFR.

M8 picture identifies 4-D space-time surfaces X4 as roots for "imaginary" or "real" part of octonionic polynomial P2P1 obtained as a continuation of real polynomial P2(L-r)P1(r), whose arguments have origin at the the tips of B and A and roots a the light-cone boundaries associated with tips. Causal diamond (CD) is identified intersection of future and past directed light-cones light-cones A and B. In the sequences of SSFRs P2(L-r) assigned to B varies and P1(r) assigned to A is unaffected. L defines the size of CD as distance τ=2L between its tips.

Besides 4-D space-time surfaces there are also brane-like 6-surfaces corresponding to roots ri,k of Pi(r) and defining "special moments in the life of self having ti=ri,k ball as M4+ projection. The number of roots and their density increases rapidly in the sequence of SSFRs. The condition that the largest root belongs to CD gives a lower bound to it size L as largest root. Note that L increases.

Concerning the approach to chaos, one can consider three options.

Option I: The sequence of steps consisting of unitary evolutions followed by SSFR corresponds to a functional factorization at the level of polynomials as sequence P2=Q1∘ Q2∘ .. Qn. The size L of CD increases if it corresponds to the largest root, also the tip of active boundary of CD must shift so that the argument of P2 L-r is replaced in each iteration step to with updated argument with larger value of L identifiable as the largest root of P2.

Option II: A completely unexpected connection with the iteration of analytic functions and Julia sets, which are fractals assigned also with chaos interpreted as complexity emerges. In a reasonable approximation quantum time evolution by SSFRs could be induced by an iteration of a polynomial or even an analytic function: P2 =P2→ P2 2 →.... For P2(0)=0, the roots of P2° N consist of inverse images of roots of P2 by P2° -k for k=0,...,N-1.

Suppose that M8 and X4 are complexified and thus also t=r and "real" X4 is the projection of X4c to real M8. Complexify also the coefficients of polynomials P. If so, the Mandelbrot and Julia sets (see this and this) characterizing fractals would have a physical interpretation in ZEO.

Chaos is approached in the sense that the inverse images of the roots of P2 assumed to belong to filled Julia set approaching to points of Julia set of P2 as the number N of iterations increases in statistical sense. The size L as largest root of P2° N would increase with N if CD is assumed to contain all roots. The density of the roots in Julia set increases near L since the size of CD is bounded by the size Julia set. One could perhaps say that near the t= L in the middle of CD the life of self when the size of CD has become almost stationary, is the most intensive.

Option III: A conservative option is to consider only real polynomials P2(r) with real argument r. Only non-negative real roots rn are of interest whereas in the general case one considers all values of r. For a large N the inverse iterates of the roots of P2 would approach to the real Julia set obtained as a real projection of Julia set for complex iteration.

How the size L of CD is determined and when can BSFR occur?

Option I: If L is minimal and thus given by the largest root of P2° N in Julia set, it is bound to increase in the iteration (this option is perhaps too deterministic). Should L be smaller than the sizes of Julia sets of both A and B if the iteration gives no roots outside Julia set.

Could BSFR become probable when L as the largest allowed root for P2° N is larger than the size of Julia set of A? There would be no more new "special moments in the life of self and this would make death and re-incarnation with opposite arrow of time probable. The size of CD could decrease dramatically in the first iteration for P1 if it is determined as the largest allowed root of P1: the re-incarnated self would have childhood.

Option II: The size of CD could be determined in SSFR statistically as an allowed root of P2. Since the density of roots increases, one would have a lot of choices and quantum criticality and fluctuations of the order of clock time τ=2L: the order of subjective time would not anymore correspond to that for clock time. BSFR would occur for the same reason as for the first option.

The fact that fractals quite generally assignable to iteration (see this) appear everywhere gives direct support for the ZEO based view about consciousness and self-organization and would give a completely new meaning for "self" in "self-organization". Fractals, quantum measurement theory, theory of self-organization, and theory of consciousness would be closely related.

See the article Could quantum randomness have something to do with classical chaos? 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.

Sunday, February 02, 2020

Why AI pattern recognition can differ dramatically from human pattern recognition?

I heard an interesting lecture "On Adversial Attacks" by Anna-Mari Rusanen in Mind and Mater Workshop Friday 2020. There is a popular article in finnish about the adversial attacks by Anna-Mari Rusanen.
I did not not find in the web any article in english by Anna-Mari Rusanen but one can find an article "Towards Deep Learning Models Resistant to Adversarial Attack" about the topic in english.

The problem of pattern recognition is that using a rather small perturbation of the input the recognized pattern can differ radically from the real pattern. For instance, small modifications of the traffic sign chan change the recognized sign dramatically. This makes possible adversial attacks, which are obviously a safety threat. Consider for instance self-driving cars.

It is clear that pattern recognition does not work like human brain. The origin of the problem is poorly understood. Some-one in the audience noticed, that in pattern recognition the difference between input and the recognized standard pattern is minimized. One has variational principle. This principle can be however selected in several manners. Could the variational principles used in pattern recognition (PR) differ for artificial PR and PR by human brain?

I know next to nothing about pattern recognition in practice but dare to ask whether the variational principle for artificial PR is completely local. One compares the proposal of PR program to a set of standard patterns, say photos about faces, as such. The function considered for black-white picture has value 1 or 0 for given pixel depending on whether the pixel is black or white. The sum over the differences of this function for input and standard picture is minimized.

Human brain however functions also holistically. Should the variational principle be (more) non-local. For instance, could one use Fourier transform for the standard patterns and for the input and do the his local minimization for the difference of functions defined in the space of wave vectors. The function would not be anymore simple since Fourier transform would have continuous values and this would require more memory resources.

Very probably this method is used in the recognition of speech, where frequency space is more natural. Human brain could of course use both methods as suggested by left/right -- reductionistic/holistic dichotomy. In music "right" would correspond to harmony and melody and "left" to rhythm and note durations. Could this principle could apply also to vision, perhaps all perception?

See the articles DMT, pineal gland, and the new view about sensory
and Emotions as sensory percepts about the state of magnetic body? .

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

Articles and other material related to TGD.