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 h_eff=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 h_gr identified as h_eff 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 ℏ_gr 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.

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.

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 Z_n,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 h_eff 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 h_eff=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 h_eff= 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 (h_eff), 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 h_eff 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.

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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.

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 h_eff=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 B_end=.2 Gauss identifiable as the monopole flux part of the Earth's magnetic field B_E= .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 h_eff=n× h₀. The cyclotron frequency of K ion is f_c(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 f_c(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.

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 h_eff=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 h_eff 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 B_end= .2 Gauss identifiable as monopole flux part of Earth's magnetic field about .5 Gauss. B_end 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 B_end 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 h_eff=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 h_eff 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.

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 r_i,k of P_i(r) and defining "special moments in the life of self having t_i=r_i,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∘ .. Q_n. 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 X⁴_c 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 r_n 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.

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
perception 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.

Helium problem and CNO problem: two anomalies explained by dark fusion

Helium problem means that there are stars with very low Helium content in the very early Universe. The predicted content is 3 times higher. This suggests that the view about Big Bang Nucleosynthesis (BBN) is not quite correct. If the BBN abundance is one third from the accepted, there must be an additional mechanism producing He and it cannot be stellar fusion.

The popular article"Astronomers detect very unusual chemical composition in ancient star's atmosphere" tells about unexpectedly high C, N, and O contents in the atmosphere of one of the oldest and most elementally depleted stars known - a "primitive star" scientists call J0815+4729 representing. For a more technical representation see the original article. This finding obviously challenges the views about stellar nuclear fusion since the star in question is very young star and the element abundances should be near to those produced in BBN. Note however that the elemental abundances are associated with atmosphere of the star. Could there be a variant of fusion process taking place outside the stellar cores?

TGD predicts new nuclear physics, which could explain these anomalies. I have already earlier considered explanation of various anomalies (see this and this ). These two anomalies are only additional items in a long list.

1. "Cold fusion" researchers, originally labelled as swindlers and crackpots, are nowadays regarded respectable scientists. Genuine cold fusion not allowed by standard nuclear physics is not in question and "low energy nuclear reactions" (LENR) is a politically more correct expression. "Nuclear transmutation" is also a term used.
   

   In TGD framework "cold fusion" is replaced by dark fusion involving generation of dark proton strings (some protons can transform to neutrons) having interpretation as dark nuclei (see this and this). They would have non-standard value h_eff =n×h₀ of effective Planck constant and would be formed of protons directly because of thei large Compton length. Dark nuclei can transform to ordinary nuclei. This would give rise to "cold fusion".
   
   

2. Dark fusion would precede ordinary nuclear fusion occurring in the cores of stars and contribute to the nuclear abundances and modify the predictions of bigbang fusion and stellar fusion and explain a long list of astrophysics anomalies. Also the theory of ordinary hot fusion would be changed. The fusion reactions could occur via a creation of dark nuclei - rather than via tunnelling - and the dark nuclei would read and reaction products would tranform back to ordinary nuclei.
   
   
3. The model change the view about the prestellar period of stars. "Cold" fusion in TGD sense would serve as a "warm-up band" and the energy liberated as dark nuclei generated from protons transform to ordinary nuclei would transform to ordinary nuclei and gradually heat the matter so that ordinary nuclear physics enters in the game and stellar core is born. The dark fusion generates nuclei with all nuclear weights.
   
   

How could understand the two anomalies in terms of dark fusion? Consider first the Helium content of the early Universe.

1. Light elements D, T, He, Be would have been produced during by Big Bang Nucleosynthesis (BBN) during first few minutes (see this and this). The production ceased as the temperature became too low for nuclear reactions to occur. Nuclear reactions started again in the stellar cores and according to the prevailing wisdom produced the heavier elements.
   

   The relative abundance of Helium (which cannot be produced in stellar interiors), estimated to be about 25 per cent, would be determined by BBN. He abundance depends on the density protons and the exact value of Hubble constant determining the expansion rate. It is possible to vary these parameters so that the observed value of He abundance (difficult to observe, for instance for Sun it is not known) is taken as the input.
   
   

2. Giving up entire Big Bang theory (BB) is not a plausible idea. One can modify the parameters of BB to obtain a lower amount of Helium. This however requires an additional fusion mechanism, which must have been at work outside stellar cores and produced higher He content outside stars after BB.
   

   The contribution of dark fusion tends to increase the abundances determined by BBN. The amount of Helium produced in BBN should be considerably lower than believed and Helium poor stars would provide a better upper bound for He produced in BB. The amount of He would increase at least by a factor 3 by the production during pre-stellar periods by dark fusion. This implies that the density fraction of baryonic matter - few per cent in standard picture - would have been even lower. This does not seem to be a problem.
   
   

Dark fusion outside stellar interiors could also explain the anomalously high CNO content in the atmospheres of stars as being due to the prestellar period and have nothing to do with the physics in the stellar cores. Exceptionally high C, N, and O abundances would be produced by dark fusion outside stellar interiors - such as stellar atmospheres - and relate to the warmup period.

What is intriguing C, N, and O playing a central role in biology are involved. There is evidence for bio-fusion - not taken seriously by the mainstream - and since Pollack effect (see this) generating dark nuclei at room temperature in presence of say solar radiation, is central in TGD based quantum biology, dark fusion producing ordinary nuclei in living matter is predicted (see this).

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

Articles and other material related to TGD.

About detection of gravitation radiation from TGD cosmic strings

Thanks to Wes Johnson for the link about detection of cosmic strings by gravitational waves (see this and also this).

First a technical note to avoid mis-understandings.

1. Cosmic strings discussed in the article are very different from those of TGD. They are defects in gauge theories at which something - say the phase of Higgs like field becomes ill-defined. Vortex core is analogous to this kind of string: the direction of velocity becomes ill-defined. They carry a very high density of energy.
   
   
2. In TGD framework cosmic strings are string like objects and correspond to 4-D space-time surfaces which having 2-D string world sheet as projection to M⁴ factor of H=M⁴xCP₂. Flux tubes are obtained by thickening the 2-D M⁴ projection to 4-D.
   

   String tension is determined by the value of length scale dependent cosmological constant and by the value of Kähler coupling strength and is for the cosmic strings of the same order of magnitude as for GUT cosmic strings. String tension is roughly proportional to length scale dependent dependent cosmological constant for the flux tubes and behaves like 1/L²(k), where L(k) &protpo; 2^k/2 is p-adic length scale. String tension approaches to zero in long length scales.
   
   

3. In TGD there are also genuine 2-D string world sheets and partonic 2-surfaces identifiable as 2-D singularities of space-time surfaces as minimal surfaces and accompany flux tubes. At number theoretical level they correspond to the singularities of the tangent space for the M⁸ counterpart of space-time surface at which 4-D quaternionic tangent space reduces to 2-D. They are mapped to singularities of H counterpart of space-time surface by M⁸-H duality. I will say later something about the nature of these singularities at the level of H.
   
   

The article mentions two interesting effects making making perhaps possible detection of gravitational waves emitted by cosmic strings - which by their huge mass density are ideal for generating gravitational waves. I have not considered these since the cosmic strings in TGD sense or flux tubes make themselves visible directly via the formation of galaxies, stars, and even planets and they are visible also in other scales. Magnetic anomalies is one examples of the anomalies.

Could one detect the gravitational waves created by cosmic strings - either GUT strings or cosmic strings in TGD sense?

1. Reconnections of cosmic strings are possible both in GUTs and TGD. In GUTs the closed loops decay by emitting gravitational radiation. In TGD framework the monopole flux prevents dissipation of the energy but graviton bursts can be emitted from cusps and kinks of string.
   
   
2. In TGD framework the periods of thickening for cosmic strings and flux loops transform part of the energy to ordinary matter and also gravitational radiation is generated. Generation of quasars or their predecessors during TGD analog of inflationary period leading from cosmic string dominance to radiation dominated cosmology would give rise to the most intense emission.
   
   
3. The crucial question whether cosmic strings are still there and if not, what is the radius of the flux tubes determined the p-adic length scale L(k) &propto 2^1/2. If the radius is too large, there are hopes for the detection of gravitational radiation. The radiation power must be proportional to the square of string tension that is 1/L²(k)&propto 2^-2k approaching zero with exponential rate. k=2 could correspond to order of magnitude not far from that for GUT cosmic strings. If ordinary blackhole like entities correspond to k=107 charactering proton and proton Compton length, the power of detecting gravitational radiation from the corresponding flux tubes is exremely low.
   
   
4. The writhing of cosmic string is the first effect discussed in the popular article. Bullwhip makes a crack-like sound. I understand that the direction of whip must change by almost 180 degrees in writhing - total turning back (I hope I am correct here). Same could happen for cosmic strings but now the motion of string approaching light velocity would replace sound velocity. A signal propagating in single direction would be generated. During the period 2005-2010 LIGO detected no signal. The reason could be that the signal comes only in single direction: they did not have luck.
   

   The TGD counterparts cracks might be very rare if the dynamics allows them at all. In TGD preferred extremal property poses infinite number of additional constraints on the minimal surface solution as a generalization of constraints expressing conformal invariance in string models besides minimal surface property - in fact, the additional condition is that an extremal of 4-D Kaehler action is also in question. All known extremals have this property.
   

   What makes this interesting that for fermionic string world sheets as singularities of 4-D minimal surfaces are proposed to be discontinuities in the direction of tangent space of space-time surface - kind of 2-D fold in 4-D cloth in H=M⁴xCP₂. Also this fold represents total turning back. Writhing would represent a discontinuous tangent for string - a 1-D fold in this 2-D fold: fold inside fold? Can one allows this kind of singularities?
   
   

5. Second very elegant method relies on the change in the timing of pulsars. The gravitational wave, which can have very low frequency as in case of cosmic strings causes variation of the period of pulsar: gravitational waves cause variation of lengths and this is variation of the period as length of time interval. Hitherto nothing has been observed.
   
   

See the article 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.

Magnetars as additional support for monopole flux tubes

There is an interesting popular article about magnetars in Quanta Magazine (see this). The article tells about the latest findings of Zhou and Vink and colleagues (see this) giving hints about the mechanism generating the huge magnetic fields of magnetars.

Neutron stars have surface magnetic field of order 10⁸ Tesla. Magnetars have surface magnetic field stronger by a factor 1000 - of order 10¹¹ Tesla. The mechanism giving rise to so strong magnetic fields at the surface of neutron star is poorly understood. Dynamo mechanism is the first option. The rapidly rotating currents at the surface of neutron star would generate the magnetic field. Second model assumes that some stars simply have strong magnetic fields and the strength of these magnetic fields can vary even by factor of order 1000. Magnetars and neutron stars would inherit these magnetic fields. The model should also explain why some stars should have so strong magnetic fields - what is the mechanism generating them. In Maxwellian world currents would be needed in any case and some kind of dynamo model suggests itself.

Dynamo model requires very rapid rotation with rotation frequency measured using millisecond as a natural unit. The fast rotation rate predicts that magnetars are produced in more energetic explosions than neutron stars. The empirical findings however support the view that there is no difference between supernovas producing magnetars and neutron stars. Therefore it would seem that the model assuming inherited magnetic fields is favored.

What says TGD? TGD view about magnetic fields differs from Maxwellian view and this allows to understand the huge magnetic without dynamo mechanism and could give a justification for the inheritance model.

1. TGD predicts that magnetic field decomposes to topological field quanta - flux tubes and sheets - magnetic flux tubes carry quantized magnetic flux. Flux tubes can have as cross section either open disk (or disk with holes) or closed surface not possible in Minkowskian space-time. The cross section can be sphere or sphere with handles.
   
   
2. If the cross section is disk a current at its boundaries is needed to create the flux. If the cross section is closed surface, no current is needed and magnetic flux is stable against dissipation and flux tube itself is stable against pinching by flux conservation. These monopole fluxes could explain the fact that there are magnetic fields in cosmological scales not possible in Maxwellian theory since the currents should be random in cosmological scales.
   

   This also solves the maintenance problem of the Earth's magnetic field. Its monopole part would stable and 2/5 of the entire magnetic field B_E=.5 Gauss from TGD based model of quantum biology involving endogenous magnetic field B_end=.2 Gauss identifiable in terms of monopole flux.
   
   

The model for the formation of astrophysical objects in various scales such as galaxies and stars and even planets and also for quantum biology relies crucially on monopole fluxes.

1. The proposal (see this) is that stars correspond tangles formed to long monopole flux tube. Reconnection could of course give rise to closed short flux tubes and one would have kind of spaghetti.
   

   The interior of Sun would contain flux tubes containing dark nuclei as nucleon sequences and one ends up to a modification of the model of nuclear fusion based on the excitation of dark nuclei (see darkcore). The model solvs a 10 year old anomaly of nuclear physics of solar core discovered by Asplund et al. From the TGD based model of "cold fusion" one obtains the estimate that the flux tube radius is of order electron Compton length, and thus about h_eff/h₀≈ m_p/m_e∼ 2000 times longer than proton Compton length. This has been assumed also in the TGD based model of stars (see this).
   
   

2. The final states of stars could correspond to a volume filling spaghettis of flux tube analogous to blackhole. They would be characterized by the radius of the flux tube, which would naturally correspond to a p-adic length scale L(k)∝ 2^k/2: one could speak of various kinds of blackhole like entities (BHEs). There radius of the flux tube would be scaled up by the value of effective Planck constant h_eff=n× h₀ so that one would have n∝ 2^k/2 in good approximation.
   
   
3. The p-adic length scales L(k), with k prime are good candidates for p-adic lengths scales. Most interesting candidates correspond to Mersenne primes and Gaussian Mersennes M_G,k= (1+i)^k-1. Ordinary blackhole could correspond to a flux tube with radius of order Compton of proton corresponding to the p-adic length scale L(107).
   

   For neutron star the first guess would be as the p-adic length scale L(127) of electron from the model of Sun.
   L(113) assignable to nuclei and corresponding to Gaussian Mersenne is also a good candidate for magnetar's p-adic length scale. L(109) assigned to deuteron would correspond to an object very near to blackhole corresponding to L(107) (see this). Also the surface and interior of BHE would carry enormous monopole fluxes 32 times stronger than for magnetars.
   

   The are just guesses but bringing in quantized monopole fluxes together with p-adic length scale hypothesis allows to develop a quantitative picture.
   
   

Consider first the flux quantization hypothesis more precisely.

1. The observation that to the vision about monopole magnetic fields and hierarchy of Planck constants now derivable from adelic physics was that the irradiation of vertebrate brain by ELF frequencies induces physiological and behavioral effects which look like quantal. As if cyclotron transitions in endogenous magnetic field B_end= 2B_E/5≈ 0.2 Gauss would have been in question. The energies of photons involved are however ridiculously small and cannot have any effects. The proposal was that the effective value of Planck constant is quantized: h_eff=nh₀ and can have very large values in living matter. The energies E=h_efff of photons could thus be over thermal threshold and have effects. The matter with non-standard value of h_eff would correspond to dark matter.
   
   
2. One can make the picture more quantitative by considering the quantization of flux. The radius r of a flux tube carrying unit magnetic flux is known as magnetic length r²= Φ₀/eπ B , where Φ₀ corresponds to minimal quantized flux Φ₀ =BS= Bπ r²= n× hbar/eB for flux tube having disk D² as cross section. If B_end is ordinary Maxwellian flux one obtains for B_end=0.2 Gauss r= 5.8 μm which is rather near to L(169)= 5× 10^-6 μm Cell membrane length scale L(151)= 10 nm corresponds to the scaling B_end→ 2¹⁸B_end≈ 5 Tesla and 1 Tesla corresponds to the magnetic length r=2.23 × L(151).
   

   One can argue that one must have quantization of flux as multiples of h_eff. The geometric interpretation is that ℏ_eff=nℏ₀ corresponds to n-sheeted structure (Galois covering) and the above quantization gives flux for a single sheet. The total flux as sum of these fluxes is indeed proportional to ℏ_eff.
   
   

3. For monopole flux tubes disk D² is replaced with sphere S² and the area S=π× r² in magnetic flux is replaced with S=4π r². This means scaling r→ r/2 for the magnetic length. The p-adic length scale becomes L(167), which corresponds to Gaussian Mersenne is indeed the scale that might have hoped whereas the ordinary flux quantization giving L(169) was a disappointment. This gives a solution to a longstanding puzzle why L(169) instead of L(167) and additional support for monopole flux tubes in living matter. As a matter of fact, there are four Gaussian Mersennes corresponding to k∈ {151,157,163,167} giving rise to 4 p-adic length scales in the range [10 nm, 2.5 μm] in the biologically most important length scale range. This is a number theoretic miracle.
   
   

It is useful to list some numbers for monopole flux by using the scaling ∝ 1/L²(k)∝ 2^-k/2 to get a quantitative grasp about the situation for magnetars and other final states of stars.

1. For monopole flux L(151) corresponds to 2¹⁶B_end(k=167) ≈ 1.28 Tesla. For ordinary flux it corresponds to 2.56 Tesla. A good mnemonic is that Tesla corresponds to r= 1.13× L(151).
   
   
2. For neutron star one has B∼ 10⁸ Tesla. For monopole flux this would correspond for ordinary flux magnetic length r≈ 1.13 pm roughly 2.8L_e, where L_e= .4 pm is electron Compton length. Note that the corresponding p-adic length scales is L(127)=2.5 pm ≈ 2.2r so that also interpretation in terms of L(125) can be considered. For non-monopole flux one would have roughly r=2.26 pm. Neutron star would be formed when all flux tubes become dark flux tubes and perhaps form single connected volume filling structure.
   
   
3. For magnetar one has magnetic field about B=10¹¹ Tesla roughly 1000 times stronger than for neutron star. For monopole flux this would give r= 30 fm to be compared with the nuclear p-adic length scale L(113)= 20 fm. Could the p-adic length scale L(109)= 2L(107)= 5 fm correspond to a state rather near to blackhole? L(109) would would have 16 times stronger surface magnetic field B≈ .45 × 10¹² Tesla than magnetar. For the TGD counterpart of ordinary blackhole having k=107 the surface magnetic field B≈ 1.8 × 10¹² Tesla would be 32 times stronger than for magnetar.
   
   

All these estimates are order of magnitude estimates and p-adic lengths scale hypothesis only says something about scales.

See the article Magnetars as a support for the notion of monopole flux tube, the longer article Cosmic string model for the formation of galaxies and stars 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.

Too heavy too early

I got a link to a rather thought provoking article telling about particular quasars identified as a super-massive blackhole (780 million solar masses). Quite generally quasar masses vary in the range 10⁸-10⁹ solar masses. Galactic blackholes have mass in the range 10⁵-10⁹ solar masses. Milky Way blackhole has much smaller mass about 4× 10⁶ solar masses.

Remark: I prefer to talk about blackhole like entities (BHEs): for TGD view about BHEs see this .

1. The first question considered by the researches is what burned away the neutral fog around the BHE: it is known that re-ionization must have burned away the fog ending the "dark ages" during which the Universe was transparent but there were no sources of light, which we could see (cosmic redhsift). Dark ages ended when re-ionization took place by light burning away the fog - perhaps light coming from dwarf galaxies and high energy photons from quasars did this. Despite re-onization the light could propagate since the density of matter absorbing it was so low.
   
   
   
2. There is also second deep problem: quasar - if indeed BHE - is too massive quite too early. This problem is met for all quasars - the age of the universe is measures using 1 billion years as a natural time unit for the observed quasars. If the galactic blackholes were former quasars, their masses should be larger than for quasars. The mass of Milky Way BHE is however of order 10⁶ solar masses and much smaller than for quasars.
   

   From the list of blackholes one gets an idea about the masses of galactic BHEs. Typically masses are considerably lower than quasar masses. There is however lenticular (between elliptic and spiral galaxy having disk but not spiral structure) galaxy NGC 1277 with galactic blackhole with mass about 1.7×10¹⁰M(Sun).
   

   The smaller mass scale makes it is difficult to believe that galactic blackholes could be former quasars. One can also ask whether very old lenticular galaxies, which posses neither spiral structure but have galactic plane could be formed from quasars and whether the central object could be quasar.
   
   

These problems challenge the interpretation of quasars as BHEs and TGD suggests an interpretation of all quasars as time reversals of BHEs - whitehole like entities (WHEs). Zero energy ontology (ZEO) of TGD indeed allows time reversed states and the arrow of time changes in ordinary, "big" state function reductions (BSFRs), which in TGD Universe can occur even in astrophysical scales so that even BHEs could be time reversals of WHEs. BSFRs would occur routinely in living matter, and self-organization as a process in apparent conflict with second law could be based on time reversal at magnetic body (MB) carrying dark matter as h_eff =n×h₀ phases. Self-organization would be based on dissipation with reversed arrow of time at MB and violate standard arrow of time. In accordance with experimental facts, it would require energy feed since the creation of states with non-standard value of h_eff requires energy feed.

ZEO allows to imagine two solutions to the problem of "too-young-to- be-so-heavy" problem.

1. Quasars could be WHEs (see this) and they would feed matter to environment rather that eating it (there was not much to eat yet!). The dark energy and matter of a tangled of cosmic string would transform to ordinary matter eventually creating the visible galaxy as the tangle thickens to magnetic flux tube and loses its energy. The predecessors of quasars would be generated during inflationary period as tangles of cosmic strings of primordial cosmology started to thicken and Einsteinian space-time with 4-D M⁴ projection in M⁴×CP₂ was created. Before this it was 2-D string world sheet. The fog, presumably hydrogen around the quasar formed from cosmic string energy, was formed from the energy of cosmic string.
   

   The huge energy emission by quasars could accompany a reduction of length scale dependent cosmological constant leading to the emission of volume energy whose density is proportional to cosmological constant.
   
   
   

2. One can also imagine that quasars were indeed BHEs which got their mass from the material produced by the decaying cosmic strings before stars were even formed. This would be less radical option than a) and require that BHEs of galactic nuclei started to form much later than quasars and have therefore much smaller masses. They are however present in all elliptic galaxies except dwarfs. Elliptic galaxies are rather old and could have perhaps formed as self-intersections of the flux tube tangle giving rise to the elliptic galaxy.
   
   

Remark: An interesting but unrelated question is whether the energy of cosmic string was liberated as leptons and quarks later and transformed to baryonic matter outside the strings. Or whether the annihilation and generation of baryons and leptons occurred already inside cosmic strings thickened to flux tubes. Flux tubes are not thick: their radius correlates with the value of length scale dependent cosmological constant. For the "cosmological" cosmological constant the radius is only of the order of size of large neuron. In solar interior it corresponds to electron Compton length for dark matter and to proton Compton length for ordinary baryonic matter.

See the article TGD View about Quasars or the article 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.

Cosmic strings and angular momentum problem of general relativity

Some comments about Vladimir Nechitailo's World-Universe model (thanks to Vladimir for asking comments). In particular a reaction to the claim

"The angular momentum problem is one of the most critical problems in BBM. Standard Cosmology cannot explain how Galaxies and Extra Solar systems obtained their substantial orbital and rotational angular momenta, and why the orbital momentum of Jupiter is considerably larger than the rotational momentum of the Sun. WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. ".

I cannot quite agree with this statement.

I have not explicitly considered the problem of large angular momenta in TGD. I do not think that the problem is non-conservation - note however that general relativity has problem with classical conservation laws which led to the idea about space-times as surfaces in M⁴×S.

The challenge is to explain naturally the large angular momenta which - as I remember - obey the analog of stringy mass formula: mass squared proportional to angular momentum. In TGD framework monopole flux tubes made possible by the homology of CP₂ lead to a picture in which cosmic strings with huge string tension carrying magnetic and volume energy thicken to flux tubes, and in this process lose magnetic energy transform to ordinary matter.

Cosmic strings explain dark matter and energy: galaxies are associated as tangles to long cosmic strings and the gravitational field of long cosmic string explains the flat velocity spectrum of distant stars. I recently constructed a detailed model for the spiral galaxies and the rotation of the galactic matter around the long cosmic string explains the large angular momenta. For halo models one does not obtain this prediction. Large angular momenta are of course associated also to distant stars with constant velocity.

WUM is in TGD replaced with cosmic strings as non-Einsteinian 4-D space-times surfaces with with 2-D M⁴ projection and complex manifold of CP₂ as CP₂ projection would dominate the primordial cosmology transforming to radiation dominated cosmology by the thickening of M⁴ projection of cosmic string to 4-D. This period would be analog of inflation. Dark matter corresponds h_eff=n×h₀ phases at flux tubes present in all scales - even biological and also hadronic as remnants of primordial period.

See for instance the articles Cosmic string model for the formation of galaxies and stars and A model for the formation of galaxies .

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

Articles and other material related to TGD.

Still about quantum measurement theory in ZEO

The relation between zero energy ontology (ZEO) based quantum measurement theory and adelic vision could be much clearer. The following considerations suggest a more precise picture about cognitive representations and formulation of quantum measurement theory for them.

In the sequel ZEO based theory of consciousness (see this) as quantum measurement theory is discussed first by starting with a criticism of physicalism and after that introducing ZEO based view about consciousness as quantum measurement theory as a solution to the problems of physicalism.

After this the relation between zero energy ontology (ZEO) based quantum measurement theory and adelic vision (see this) is discussed. The considerations suggest a more precise picture about cognitive representations and formulation of quantum measurement theory for them. One can generalize classical cognitive representations as number theoretical discretizations of space-time surfaces in the extension of rationals considered to their quantum counterparts as wave functions in the Galois group of the extension and introduce also fermions as spinors in the group algebra of Galois group. The strongest option is purely number theoretical representations of spinors as spinors in this group algebra. Presumably however M⁸ spinors are required and have interpretation in terms of octonion structure.

An attractive vision is that number theoretical quantum measurements reduce to measurement cascades involving a sequence of state function reductions reducing the entanglement between wave functions in sub-Galois group H and group G/H and ends up to a prime Galois group for group algebra has prime dimension and represents Hilbert space prime not decomposable to tensor product.

Also time measurement is considered from the number theoretic perspective assuming M⁸-H duality (see this). Clock readings are realized as roots of the rational polynomial determining the space-time surface in M⁸. Time measurement would involve a localization to a definite extension of rationals, whose dimension n must be proportional to the temporal distance T between the tips of causal diamond (CD) to guarantee fixed time and energy resolution.

See the article Still about quantum measurement theory in ZEO.

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

Articles and other material related to TGD.

Still about the topology of elementary particles and hadrons

In its recent form TGD allows several options for the model of elementary particles (see this). I wrote this piece of text because I got worried about details of the definition of wormhole contact appearing as basic building brick of elementary particle.

1. Wormhole contacts in 4-D sense (having Euclidian signature of induced metric) modellable as deformed pieces of CP₂ type extremals connecting Minkowskian space-time sheets (representable as graphs of a map M⁴→ CP₂) are identified basic building bricks of elementary particles. 3-D light-like orbits of 2-D wormhole throats- partonic 2-surfaces - at which the signature of induced metric changes from Euclidian to Minkowskian - partonic orbits - are assumed to be carriers of elementary particle quantum numbers.
   
   
2. One can identify simplest wormhole contact as topological sum: two surfaces touch each other. Remove 3-D regions from both space-time sheets and connecting the topologically identical boundaries with a cylinder X²× D¹, where X² has the topology of the boundary characterized by genus. The assumption that X² is boundary requires that its projection to CP₂ is homologically trivial. This is not consistent with the assumption that the flux tube carries monopole flux. These wormhole contacts are unstable and must be distinguished from wormhole contacts mediating monopole flux. I have not however defined the notion precisely enough.
   
   
3. One can consider several situations in which homologically non-trivial wormhole contact appears.
   

   Option I: Assume that the 3-D time=constant sections of 2 Minkowskian space-time sheets are glued together along their boundaries to form a closed 2-sheeted surface and the throats of wormhole contact - partonic 2-surfaces - serve as magnetic charges creating opposite fluxes. One can say that the two throats have opposite homology charges and therefore form a homologically trivial 2-surface to which one can glue the wormhole contact along its boundaries. The flux at sheet B could be seen as return flux from sheet A and the throat could be seen as very short monopole flux tube.
   

   Option II: Assume no gluing along boundaries for the 3-D time=constant sections of 2 Minkowskian space-time sheets. In this case one must assume at least two wormhole contacts to get vanishing homology charges at both sheets. At both space-time sheets the throats of the contacts with opposite homology charges would be connected by monopole fluxes flowing through the wormhole contacts identifiable as a very short monopole flux tube. This makes sese also for the Option I and might be required since is not clear whether space-time having boundaries carrying monopole flux can be glued together.
   

   Remark: One can also consider the light-like orbit of partonic 2-surface connecting its ends (the minimal distance between partonic 2-surfaces vanishes). The homology charges of ends are opposite in ZEO.
   
   

The proper identification of the model of elementary particles remains still open (see this and this). What relevance do these two options this picture have to the model of elementary particles?

1. For Option I leptons and gauge bosons could be identified as single wormhole contact carrying non-trivial homology flux. The size scale of the closed space-time sheet would correspond to the Compton wavelength of the particle. This model is the simplest one at the level of scattering diagrams and was re-considered in the article SUSY in TGD framework.
   

   Even Euclidian regions of single space-time sheet with vanishing homology charge can be considered as a model for leptons and gauge bosons. In this case it is however not clear how to understand how the size scale of the particle as Compton length could be understood at space-time level. This model was one of the first models. I have also considered the identification of the particle as boundary component of Minkowskian space-time surface.
   
   

2. Option II was assumed in the model following the original model for leptons and gauge bosons. It was also proposed that electroweak confinement as dual description of massivation takes place in the sense that the weak charges associated with the two wormhole contacts cancel each other. The size scale of flux tube at given sheet would correspond to the Compton length assignable to the particle. In this case scattering amplitudes are more complex topologically.
   
   

What about baryons?

1. The simplest model assumes that quarks do not differ from leptons and gauge bosons in any manner. The contribution of the quarks to masses of hadrons is very small fraction of total mass, which suggests that color flux tubes carrying also homology charge are present and give the dominating contribution.
   

   One can also consider a structure formed by color magnetic monopole flux tubes carrying most of the hadron mass with Minkowskian signature carrying flux of 2 units branching to two flux tubes carrying 1 unit each. The flux tubes would have length given by hadronic p-adic length scale. The ends of flux tubes would be wormhole throats connected by wormhole contacts to the mirror image of this structure. One can say that homology charges 2,-1,-1 assignable to the throats of single space-time sheet sum up to zero. This brings in mind color hypercharge. Could color confinement have vanishing of homology charge as classical space-time correlate?
   
   

2. In the proposal for the TGD based realization of space-time supersymmetry and the notion of super-space I considered two alternative identification of leptons. Leptons and quarks could correspond to the different chiralities of M⁴× CP₂ spinors and lepton and baryon numbers would be separately conserved. For second option leptons would b local 3-quark composites and therefore analogous to spartners of quarks: this option is possible only in TGD framework and the reason is that color is not spin-like quantum number in TGD framework. Baryon and lepton numbers would not be separately conserved.
   

   One can ask what could be the simplest mechanism inducing the decay of baryon as 3-quark composite involving only 3 wormhole contacts and giving lepton as a local 3-quark composite plus something. Wormhole throats of 3 quarks carrying the quark quantum numbers should fuse together to form a leptonic wormhole throat, and the 3 quark lines representing boundaries of string world sheets should fuse to single line. If the sum of quark homology charges is vanishing, lepton must have a vanishing homology charge unless the reaction involves also a step taking care of the conservation of homology charge as a decay of the resulting wormhole contact with vanishing monopole flux to two wormhole contacts with opposite monopole fluxes. Already the first step of the decay process is quite complex, and one can hope that the rate for the reaction is slow enough.
   
   

See the article SUSY in TGD framework 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.

Evidence for 3 different temperatures at Milky Way halo

The TGD based model for Milky Way suggests the presence of 3 cosmic strings thickened to flux tubes. Galactic disk has indeed 3 components with different thickness. There is support for the presence of 3 components also in the Milky Way halo (see this), thanks to Wes Johnson for the link) as gas at different temperatures, and perhaps assignable to 3 different cosmic strings.

The information was gained by studying X rays from a blazar, very active energetic core of a distant galaxy emitting intense beams of light. The blazar was at distance of 5 billion light years. The light passed through the galactic halo and the temperature of the halo was determined from the properties of light received at Earth.

The halo was expected to have single temperature in the range between 10⁴-10⁶ K. It was however found to contain 3 components at different temperatures, and the hottest component had temperature about 10⁷ K. The unexpectedly high temperature is proposed to be due to the winds emanating from the disc of stars of MW. It was also found that the halo contains besides hydrogen also significant amounts of heavier elements suggesting that the halo has received material created by certain stars during their lifetime and final stages.

In TGD framework "cold fusion" (see this) outside stellar interiors could have generated at least part of the heavier elements. "Cold fusion" proceeds by a formation of dark nuclei identifiable as dark nucleon sequences at magnetic flux tubes with h_eff/h≈ m_p/m_e∼ 2000 and having radius of electron Compton length. Nuclear binding energy is scaled down by a factor of about 1/2000 to keV range. Dark nuclei would have transformed to ordinary nuclei liberating practically all nuclear binding energy outside stellar nuclei. This process would serve as a kind of warm-up band in the pre-stellar evolution leading eventually to the ordinary fusion (see this).

See the article A model for galaxy formation 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.

Direct astrophysical evidence for monopole flux tubes

Monopole flux is the key property of flux tubes proposed to be behind various astrophysical structures. Is there any direct evidence for this? Evidence has emerged for the existence of giant clouds with size about 100 AU in the vicinity of the supermassive GBHE of Milky Way (see this and this). These objects - called G objects - look like gas clouds but behave like stars. G objects stretch longer when nearer to GBHE but get their original shape when farther away. One would expect that they are torn apart by the enormous tidal forces created by GBHE.

The identification could be as visible matter assignable to a spaghetti like structure formed by monopole like flux tube, which could have also produced the visible matter in the thickening of the flux tube. By flux conservation the monopole flux prevents the flux tubes from splitting even in the huge gravitational field of supermassive GBHE. Without monopole flux tubes to which visible matter is gravitationally bound the structure would be torn to pieces. In Maxwellian world monopole flux tubes are not possible. In biology the behavior of gels (the contents of an egg is the basic example) could be based on monopole flux tubes connecting the cells together.

See the article A model for galaxy formation
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.

A model for the formation of galaxies

I have proposed a general vision about galaxy formation as formation of tangles on cosmic strings carrying monopole flux. The strings can be long and also short. In the case of long string the model explains flat velocity spectrum of distant stars automatically. For closed short strings the velocity spectrum is not flat. There is however no detailed model for the galaxy formation. In particular, the complex structure of spiral galaxies is poorly understood. Even the question whether there is single long cosmic string orthogonal to the galactic plane or cosmic string parallel to the spiral structure in galactic plane - as proposed decades ago in the original model - or both has remained open. In the sequel I make an attempt to collect the essential facts about elliptic and spiral galaxies and consider a qualitative model for the galaxy formation consistent with these facts. The goal is rather modest: just to develop an internally consistent view about the evolution of galaxies.

1. The simplest model for elliptic galaxy is as a closed string possibly reconnected as a loop from long string or as a tangle of a cosmic string having topology analogous to that of field lines of dipole magnetic field. Quasar would have preceded the formation of the tangle in which string would have thickened to flux tube and dark energy would have transformed to ordinary matter. Quasars would be time reversal of galactic blackhole like entity (GBHE).
   
   
2. In the case of spiral galaxies the existence of vast polar structures (VPOS) in the plane orthogonal to the galactic plane of spiral galaxy (see this) strongly suggest that two cosmic strings are involved and that the spiral structure believed to correspond to a standing wave analogous to traffic jam is associated with dark matter of a long cosmic string. This model conforms with the fact that the stars of spiral galaxies are older than those of elliptic galaxies except inside the bulge.
   

   The asymmetry between the two planes suggests that the spiral arms are formed when an elliptic galaxy identified as a tangle of a long string S_|| formed via a quasar stage in the galactic plane has collided with a cosmic string S_⊥ orthogonal to the galactic plane. These collisions are unavoidable for non-parallel strings and gravitational attraction causes the needed relative motion.
   

   The differential rotation of portion of S_|| around S_⊥ would have deformed S_|| to a spiral shape. S_|| would have also generated the visible spiral arm pair in the transformation of dark energy to ordinary matter. Galactic bulge would correspond to the elliptic galaxy and galactic blackhole like entity (GBHE) would have formed from the matter in bulge: this conforms with the fact that elliptic galaxies have always galactic blackhole. The galactic bar could be analogous to the dipole of dipole magnetic field. In principle also the string orthogonal to the galactic plane could produce ordinary matter by thickening.
   
   

One open question relates to the fact that TGD predicts two kinds of cosmic strings with closed transverse cross section and having vanishing induced Kähler field or non-vanishing induced Kähler form carrying monopole flux. The latter are stable against splitting by the conservation of the monopole flux and have no counterpart in Maxwellian electrodynamics. The monopole flux tubes could correspond to the cosmic strings giving rise to galaxies, stars, and even planets as tangles. Non-monopole flux tubes might serve as gravitational flux tubes mediating gravitational interactions. Presumably both kinds of flux tubes are involved but their precise roles are not well-understood.

See the article A model for the formation of galaxies 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.