Thursday, May 30, 2019

TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors

There are two mysterious looking correspondences involving ADE groups. McKay correspondence between McKay graphs characterizing tensor products for finite subgroups of SU(2) and Dynkin diagrams of affine ADE groups is the first one. The correspondence between principal diagrams characterizing inclusions of hyper-finite factors of type II1 (HFFs) with Dynkin diagrams for a subset of ADE groups and Dynkin diagrams for affine ADE groups is the second one.

I have considered the interpretation of McKay correspondence in TGD framework already earlier
but the decision to look it again led to a discovery of a bundle of new ideas allowing to answer several key questions
of TGD.

  1. Asking questions about M8-H duality at the level of 8-D momentum space led to a realization that the notion of mass is relative as already the existence of alternative QFT descriptions in terms of massless and massive fields suggests (electric-magnetic duality). Depending on choice M4⊂ M8, one can describe particles as massless states in M4× CP2 picture (the choice is M4L depending on state) and as massive states (the choice is fixed M4T) in M8 picture. p-Adic thermal massivation of massless states in M4L picture can be seen as a universal dynamics independent mechanism implied by ZEO. Also a revised view about zero energy ontology (ZEO) based quantum measurement theory as theory of consciousness suggests itself.

  2. Hyperfinite factors of type II1 (HFFs) and number theoretic discretization in terms of what I call cognitive representations provide two alternative approaches to the notion of finite measurement resolution in TGD framework. One obtains rather concrete view about how these descriptions relate to each other at the level of 8-D space of light-like momenta. Also ADE hierarchy can be understood concretely.

  3. The description of 8-D twistors at momentum space-level is also a challenge of TGD. 8-D twistorializations
    in terms of octo-twistors (M4T description) and M4× CP2 twistors (M4L description) emerge at imbedding space level. Quantum twistors could serve as a twistor description at the level of space-time surfaces.

McKay correspondence in TGD framework

Consider first McKay correspondence in more detail.

  1. McKay correspondence states that the McKay graphs characterizing the tensor product decomposition rules for representations of discrete and finite sub-groups of SU(2) are Dynkin diagrams for the affine ADE groups obtained by adding one node to the Dynkin diagram of ADE group. Could this correspondence make sense for any finite group G rather than only discrete subgroups of SU(2)? In TGD Galois group of extensions K of rationals can be any finite group G. Could Galois group take the role of G?

  2. Why the subgroups of SU(2) should be in so special role? In TGD framework quaternions and octonions play a fundamental role at M8 side of M8-H duality. Complexified M8 represents complexified octonions and space-time surfaces X4 have quaternionic tangent or normal spaces. SO(3) is the automorphism group of quaternions and for number theoretical discretizations induced by extension K of rationals it reduces to its discrete subgroup SO(3)K having SU(2)K as a covering. In certain special cases corresponding to McKay correspondence this group is finite discrete group acting as symmetries of Platonic solids. Could this make the Platonic groups so special? Could the semi-direct products Gal(K)×L SU(2)K take the role of discrete subgroups of SU(2)?

HFFs and TGD

The notion of measurement resolution is definable in terms of inclusions of HFFs and using number theoretic discretization of X4. These definitions should be closely related.

  1. The inclusions N M of HFFs with index M: N<4 are characterized by Dynkin diagrams for a subset of ADE groups. The TGD inspired conjecture is that the inclusion hierarchies of extensions of rationals and of corresponding Galois groups could correspond to the hierarchies for the inclusions of HFFs. The natural realization would be in terms of HFFs with coefficient field of Hilbert space in extension K of rationals involved.

    Could the physical triviality of the action of unitary operators N define measurement resolution? If so, quantum groups assignable to the inclusion would act in quantum spaces associated with the coset spaces M/ N of operators with quantum dimension d= M: N. The degrees of freedom below measurement resolution would correspond to gauge symmetries assignable to N.

  2. Adelic approach provides an alternative approach to the notion of finite measurement resolution. The cognitive representation identified as a discretization of X4 defined by the set of points with points having H (or at least M8 coordinates) in K would be common to all number fields (reals and extensions of various p-adic number fields induced by K). This approach should be equivalent with that based on inclusions. Therefore the Galois groups of extensions should play a key role in the understanding of the inclusions.

How HFFs could emerge from TGD?
  1. The huge symmetries of "world of classical words" (WCW) could explain why the ADE diagrams appearing as McKay graphs and principal diagrams of inclusions correspond to affine ADE algebras or quantum groups. WCW consists of space-time surfaces X4, which are preferred extremals of the action principle of the theory defining classical TGD connecting the 3-surfaces at the opposite light-like boundaries of causal diamond CD= cd× CP2, where cd is the intersection of future and past directed light-cones of M4 and contain part of δ M4+/-× CP2. The symplectic transformations of δ M4+× CP2 are assumed to act as isometries of WCW. A natural guess is that physical states correspond to the representations of the super-symplectic algebra SSA.

  2. The sub-algebras SSAn of SSA isomorphic to SSA form a fractal hierarchy with conformal weights in sub-algebra being n-multiples of those in SSA. SSAn and the commutator [SSAn,SSA] would act as gauge transformations. Therefore the classical Noether charges for these sub-algebras would vanish. Also the action of these two sub-algebras would annihilate the quantum states. Could the inclusion hierarchies labelled by integers ..<n1<n2<n3.... with ni+1 divisible by ni would correspond hierarchies of HFFs and to the hierarchies of extensions of rationals and corresponding Galois groups? Could n correspond to the dimension of Galois group of K.

  3. Finite measurement resolution defined in terms of cognitive representations suggests a reduction of the symplectic group SG to a discrete subgroup SGK, whose linear action is characterized by matrix elements in the extension K of rationals defining the extension. The representations of discrete subgroup are infinite-D and the infinite value of the trace of unit operator is problematic concerning the definition of characters in terms of traces. One can however replace normal trace with quantum trace equal to one for unit operator. This implies HFFs and the hierarchies of inclusions of HFFs. Could inclusion hierarchies for extensions of rationals correspond to inclusion hierarchies of HFFs and of isomorphic sub-algebras of SSA?

New aspects of M8-H duality

M8-H duality (H=M4× CP2) has become one of central elements of TGD. M8-H duality implies two descriptons for the states.

  1. M8-H duality assumes that space-time surfaces in M8 have associative tangent- or normal space M4 and that these spaces share a common sub-space M2⊂ M4, which corresponds to complex subspace of octonions (also integrable distribution of M2(x) can be considered). This makes possible the mapping of space-time surfaces X4⊂ M8 to X4⊂ H=M4× CP2) giving rise to M8-H duality.

  2. M8-H duality makes sense also at the level of 8-D momentum space in one-one correspondence with light-like octonions. In M8=M4× E4 picture light-like 8-momenta are projected to a fixed quaternionic M4T⊂ M8. The projections to M4T⊃ M2 momenta are in general massive. The group of symmetries is for E4 parts of momenta is Spin(SO(4))= SU(2)L× SU(2)R and identified as the symmetries of low energy hadron physics.

    M4⊃ M2 can be also chosen so that the light-like 8-momentum is parallel to M4L⊂ M8. Now CP2 codes for the E4 parts of 8-momenta and the choice of M4L and color group SU(3) as a subgroup of automorphism group of octonions acts as symmetries. This correspond to the usual description of quarks and other elementary particles. This leads to an improved understanding of SO(4)-SU(3) duality. A weaker form of this duality S3-CP2 duality: the 3-spheres S3 with various
    radii parameterizing the E4 parts of 8-momenta with various lengths correspond to discrete set of 3-spheres S3 of CP2 having discrete subgroup of U(2) isometries.

  3. The key challenge is to understand why the MacKay graphs in McKay correspondence and principal diagrams for the inclusions of HFFs correspond to ADE Lie groups or their affine variants. It turns out that a possible concrete interpretation for the hierarchy of finite subgroups of SU(2) appears as discretizations of 3-sphere S3 appearing naturally at M8 side of M8-H duality. Second interpretation is as covering of quaternionic Galois group. Also the coordinate patches of CP2 can be regarded as piles of 3-spheres and finite measurement resolution. The discrete groups of SU(2) define in a natural manner a hierarchy of measurement resolutions realized as the set of light-like M8 momenta. Also a concrete interpretation for Jones inclusions as inclusions for these discretizations emerges.

  4. A radically new view is that descriptions in terms of massive and massless states are alternative options leads to the interpretation of p-adic thermodynamics as a completely universal massivation mechanism having nothing to do with dynamics. The problem is the paradoxical looking fact that particles are massive in H picture although they should be massless by definition. The massivation is unavoidable if zero energy states are superposition of massive states with varying masses. The M4L in this case most naturally corresponds to that associated with the dominating part of the state so that higher mass contributions can be described by using p-adic thermodynamics and mass squared can be regarded as thermal mass squared calculable by p-adic thermodynamics.

  5. As a side product emerges a deeper understanding of ZEO based quantum measurement theory and consciousness theory. 4-D space-time surfaces correspond to roots of octonionic polynomials P(o) with real coefficients corresponding to the vanishing of the real or imaginary part of P(o).

    These polynomials however allow universal roots, which are not 4-D but analogs of 6-D branes and having topology of S6. Their M4 projections are time =constant snapshots t= rn,rM≤ rn 3-balls of M4 light-cone (rn is root of P(x)). At each point the ball there is a sphere S3 shrinking to a point about boundaries of the 3-ball.

    What suggests itself is following "braney" picture. 4-D space-time surfaces intersect the 6-spheres at 2-D surfaces identifiable as partonic 2-surfaces serving as generalized vertices at which 4-D space-time surfaces representing particle orbits meet along their ends. Partonic 2-surfacew would define the space-time regions at which one can pose analogs of boundary values fixing the space-time surface by preferred extremal property. This would realize strong form of holography (SH): 3-D holography is implied already by ZEO.

    This picture forces to consider a modification of the recent view about ZEO based theory of consciousness. Should one replace causal diamond (CD) with light-cone, which can be however either future or past directed. "Big" state function reductions (BSR) meaning the death and re-incarnation of self with opposite arrow of time could be still present. An attractive interpretation for the moments t=rn would be as moments assignable to "small" state function reductions (SSR) identifiable as "weak" measurements giving rise to to sensory input of conscious entity in ZEO based theory of consciousness. One might say that conscious entity becomes gradually conscious about its roots in increasing order. The famous question "What it feels to be a bat?" would reduce to "What it feels to be a polynomial?"! One must be however very cautious here.

What twistors are in TGD framework?

The basic problem of the ordinary twistor approach is that the states must be massless in 4-D sense. In TGD framework particles would be massless in 8-D sense. The meaning of 8-D twistorialization at space-time level is relatively well understood but at the level of momentum space the situation is not at all so clear.

  1. In TGD particles are massless in 8-D sense. For M4L description particles are massless in 4-D sense and the description at momentum space level would be in terms of products of ordinary M4 twistors and CP2 twistors. For M4T description particles are massive in 4-D sense. How to generalize the twistor description to 8-D case?

    The incidence relation for twistors and the need to have index raising and lowering operation in 8-D situation suggest the replacement of the ordinary l twistors with eitherwith octo-twistors or non-commutative quantum twistors.

  2. Octotwistors can be expressed as pairs of quaternionic twistors. Octotwistor approach suggests a generalization of twistor Grassmannian approach obtained by replacing the bi-spinors with complexified quaternions and complex Grassmannians with their quaternionic counterparts. Although TGD is not a quantum field theory, this proposal makes sense for cognitive representations identified as discrete sets of spacetime points with coordinates in the extension of rationals defining the adele implying effective reduction of particles to point-like particles.

  3. The notion of super-twistor can be geometrized in TGD framework at M8 level but at H level local many-fermion states become non-local but still having collinear light-like momenta. One would have a proposal for a quite concrete formula for scattering amplitudes!

    Even the existence of sparticles have been far from obvious hitherto but now it becomes clear that spartners indeed exist and SUSY breaking would be caused by the same universal mechanism as ordinary massivation of massless states. The mass formulas would be supersymmetric but the choice of p-adic prime identifiable as ramified prime of extension of rationals would depend on the state of super-multiplet. ZEO would make possible symmetry breaking without symmetry breaking as Wheeler might put it.

  4. What about the interpretation of quantum twistors? They could make sense as 4-D space-time description analogous to description at space-time level. Now one can consider generalization of the twistor Grassmannian approach in terms of quantum Grassmannians.

A possible alternative interpretation of quantum spinors is in terms of quantum measurement theory with finite measurement resolution in which precise eigenstates as measurement outcomes are replaced with universal probability distributions defined by quantum group. This has also application in TGD inspired theory of consciousness: the idea is that the truth value of Boolean statement is fuzzy. At the level of quantum measurement theory this would mean that the outcome of quantum measurement is not anymore precise eigenstate but that one obtains only probabilities for the appearance of different eigenstate. One might say that probability of eigenstates becomes a fundamental observable and measures the strength of belief.

See the article TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors or the chapter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy" with the same title.

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

Articles and other material related to TGD.

Tuesday, May 21, 2019

McKay correspondence, ADE hierarchy, and inclusions of hyperfinite factors in number theoretical vision

There are two mysterious looking correspondences involving ADE groups. McKay correspondence between McKay graphs characterizing tensor products for finite subgroups of SU(2) and Dynkin diagrams of affine ADE groups is the first one. The correspondence between principal diagrams characterizing inclusions of hyper-finite factors of type II1 (HFFs) with Dynkin diagrams for a subset of ADE groups and Dynkin diagrams for affine ADE groups is the second one.

These correspondences are discussed from number theoretic point of view suggested by TGD and based on the interpretation of discrete subgroups of SU(2) as subgroups of the covering group of quaternionic automorphisms SO(3) (analog of Galois group) and generalization of these groups to semi-direct products Gal(K)×L SU(2)K of Galois group for extension K of rationals with the discrete subgroup SU(2)K of SU(2) with representation matrix elements in K. The identification of the inclusion hierarchy of HFFs with the hierarchy of extensions of rationals and their Galois groups is proposed.

A further mystery whether Gal(K)×L SU(2)K could give rise to quantum groups or affine algebras. In TGD framework the infinite-D group of isometries of "world of classical worlds" (WCW) is identified as an infinite-D symplectic group for which the discrete subgroups characterized by K have infinite-D representations so that hyper-finite factors are natural for their representations. Symplectic algebra SSA allows hierarchy of isomorphic sub-algebras SSAn. The gauge conditions for SSAn and [SSAn,SSA] would define measurement resolution giving rise to hierarchies of inclusions and ADE type Kac-Moody type algebras or quantum algebras representing symmetries modulo measurement resolution.

A concrete realization of ADE type Kac-Moody algebras is proposed. It relies on the group algebra of Gal(K)×L SU(2)K and free field representation of ADE type Kac-Moody algebra identifying the free scalar fields in Kac-Moody Cartan algebra as group algebra elements defined by the traces of representation matrices (characters).

What could be the interpretation of quantum spinors? In TGD particles are massless in 8-D sense and in general massive in 4-D sense but 4-D twistors are needed also now so that a modification of twistor approach is needed. The incidence relation for twistors suggests the replacement of the usual twistors with either non-commutative quantum twistors or with octo-twistors. Quantum twistors could be associated with the space-time level description of massive particles and octo-twistors with the description at imbedding space level. A possible alternative interpretation of quantum spinors is in terms of quantum measurement theory with finite measurement resolution in which precise eigenstates as measurement outcomes are replaced with universal probability distributions defined by quantum group. This has also application in TGD inspired theory of consciousness.

The outcome of octo-twistor approach together with M8-H duality leads to a nice picture view about twistorial description of massive states based on quaternionic generalization of twistor (super-)Grassmannian approach. A radically new view is that descriptions in terms of massive and massless states are alternative options, and correspond to two different alternative twistorial descriptions and leads to the interpretation of p-adic thermodynamics as completely universal massivation mechanism having nothing to do with dynamics. As a side product emerges a deeper understanding of ZEO based quantum measurement theory and consciousness theory relying on the universal roots of octonionic polynomials of M8, which are not 4-D but analogs of 6-D branes. This part of article is not a mere side track since by M8-H duality the finite sub-groups of SU(2) of McKay correspondence appear quite concretely in the description of the measurement resolution of 8-momentum.

See the article TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors or the chapter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy" with the same title.

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

Articles and other material related to TGD.

Friday, May 17, 2019

An overall view about models of genetic code and bio-harmony

During last years kind of brain storming period has occurred in the TGD inspired models of bio-harmony and genetic code. A lot of ideas, some of them doomed to be short lived, have emerged, and it seems that now it its time for a thorough cleanup and integration with the general ideas of TGD inspired quantum biology.

TGD leads to 3 basic realizations of the genetic code. One can also consider 3 realization also for bio-harmony. The question is which of them is the realistic one or whether several options can be considered. In this article these ideas are discussed critically and open problems are summarized.

The three genetic codes correspond to a fundamental realization in terms of dark proton sequences (dark nuclei) with 3-proton representing codon. Second realization is the chemical realization and the third realization is in terms of dark photon 3-chords mediating the interaction between various realizations. Frequency resonance is very natural interaction between dark levels and energy resonance between dark level and chemical level. The possibility to modify the value of heff for flux tube makes possible to have for given codon single resonance energy.

The homonymy of the genetic codes at various levels is discussed. At the dark level the fact that icosahedral harmonies can have common 3-chords implies the first homonymy. The basic difficulty of Pythagorean scale realized in terms of quint cycle realized already by Pythagoras becomes the solution of this problem. The well-known homonymies in RNA-tRNA correspondence and even in RNA-AA correspondence can be understood in the model in which dark photon 3-chords mediate the interactions.

See the article An overall view about models of genetic code and bio-harmony or the chapter of "Genes and Memes: Part II" with the same title.

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

Articles and other material related to TGD.

Saturday, May 11, 2019

The problems leading to inflation and those created by inflation and TGD solution to them

The Wikipedia article about inflationary cosmology gives a good summary of inflation theory and its problems. What is nice that inflation theory is a solution to real problems. What is not nice is that it leads to new problems.

  1. Horizon problem: temperature constant in extreme accuracy. No time to equilibrate.

  2. Flatness problem: 3-space is unexpectedly flat suggesting critical 3-space so that 3-curvature vanishes. Here inflation theorists should have though a second though. Criticality suggests criticality in thermodynamical and even in quantum sense.

  3. Monopole problem of GUTs. Monopoles are not observed. This is a problem of GUTs and thus all theories that are based on GUTs as QFT limit.

This is a nice starting point. The inflationary solution of the problems would be a rapid expansion.

Inflation theory relies on GUT paradigm and proposes exponentially fast expansion due to a decay of false vacuumwith non-vanishing energy density decaying to particles. Horizon size becomes large. The fluctuations of the curvature of 3-space get extremely small and 3-space flattens. Monopole density goes to zero. Observed universe would correspond to the content of single horizon.

It has however turned out that there are problems - Steinhardt is one of the critical voices. In particular, one cannot avoid fine tuning after all. Inflation theory remains qualitative. There is no empirical evidence for inflaton fields, and Russian doll cosmology is strongly suggestive leading to multiverse.

TGD provides an alternative solution. First TGD very briefly.

  1. TGD emerges as a solution of energy problem of GRT and also as generalization of string models replacing string world sheets with space-time surfaces. TGD provides a new view about space-time. Space-times are 4-D surfaces in M4×CP2 . M4 and CP2 are fixed uniquely by the existence of twistor lift of TGD requiring that the twistor spaces involved have Kähler structure.

    6-D Kähler action dimensionally reduces to a sum of a volume term - cosmological constant having a spectrum- and the analog of Maxwell action action. Preferred extremals are minimal surfaces - geometric analogs for massless fields - and extremals of also Maxwell action simultaneously but having 2-D string world sheets as singularities at which there is charge transfer between the two action terms. String like objects thicken to magnetic fluxes as their M4 projection thickens. The action is essentially generalization of the action of point like charge in Maxwell field obtained by replacing point like particle with 3-D surface.

  2. New view about quantum theory based on what I call zero energy ontology (ZEO) and number theoretical vision involving extension of physics to adelic physics with p-adic sectors of the theory describing cognition. Effective Planck constant is predicted to have hierarchy with values heff= n×h0, n dimension of algebraic extension of rationals to which parameters of extremals belong. This hierarchy of phases has interpretation as dark matter. Quantum coherence in even astrophysical and cosmic scales becomes possible. In biology the implications are dramatic.

Consider now the TGD solution to problems motivating inflation and also many other problems.
  1. The problem of cosmological constant. Twistor lift replaces space-time surface with the analog of its twistor space - an S2 bundle with twistor structure induced from the product of twistor spaces of M4 and CP2. Length scale dependent cosmological constant is the outcome of dimensional reduction of 6-D surfaces to S2 bundle with space-time surface as base-space.

    Cosmological constant decreases in stepwise during cosmological evolution in phase transitions. During the expansion periods following the reduction of cosmological constant the Kähler magnetic energy of expanding flux tube transforms to particles but eventually the expansion halts since volume term increases and one reaches energy minimum. This process produces matter.

  2. The solution to the problem of dark energy. The interpretation of the energy of monopole flux tubes having flux and return flux at different space-time sheets connected by tiny wormhole contacs is as dark energy: the reason is that test particle between the sheets experiences no classical forces. Long range gravitational fields are however created. Also the recent accelerating phase in the recent cosmology might correspond to such a transition. What is amazing that there is direct connection with biological scales.

  3. What before possible rapidly expanding period leading to radiation dominated phase? There was no space-time in the usual sense - that is as 4-surfaces with 4-D M4 projection - but cosmic strings with 2-D M4 projections. String like objects dominated.

  4. Was there a period of rapid inflationary expansion? The stepwise variation of cosmological constant in phase transitions means increase of the thickness of the flux tubes assignable naturally to cosmological expansion at QFT limit. The transition from string dominated to radiation dominated phase creating space-time in GRT sense would be one example. There would be entire series of this kind of fast expansions during which cosmological constant would be reduced. The recent accelerated expansion of the Universe would be also example of this kind of phase transition.

    Quantum criticality provides second perspective. The phase transition from cosmic string dominated phase to radiation dominated phase is the first transition of this kind and one expects approximate flatness of 3-space at QFT limit since criticality does not allow dimensional parameters. Vanishing 3 curvature is highly plausible at the quantum field theory limit in which space-time sheets are replaced with a slightly curved deformation of M4 and fields are identified as sums of purely geometrically determined induced fields at various space-time sheets. This requires very fast expansion and at the limit of vanishing cosmological constant -infinitely large space-time sheets - one theory allows vacuum extremals representing very fast expansion

  5. Why the constancy of the cosmic temperature? The cosmic string phase would have been quantum coherent in long scales or at least scales corresponding to the recent horizon size. The general prediction of quantum coherence even in astrophysical scales in the recent Universe and this revolutionizes the vision about astrophysics. The network formed by cosmic strings/flux tubes is like a nervous system and long range correlations between astrophysics of distant objects are predicted. The "Axis-of-Evil" -one of the problems of inflation - is an excellent example of this. Flux tubes replace wormholes in ER-EPR correspondence and make possible long range quantum entanglement.

  6. Solution of the initial singularity problem. The energy density in cosmic string dominated phase behaved like 1/a2 (a the proper time coordinate of M4 light-cone). Energy per co-moving volume went to zero. No initial singularity: silent whisper amplified to relatively big bang.

  7. Solution of the monopole problem. Cosmic strings can carry monopole flux but there are no magnetic charges. This is due to geometry of CP2- Kähler form is monopole field in homological sense.

  8. Magnetic field problem: how there can be magnetic fields in all scales in the recent cosmology?- currents creating them are not possible in early cosmology. Monopole magnetic fields require no currents to create them. Monopole flux tubes are in central role in the model for the formation of galaxies, stars, even planets, even magnetic fields of Sun and Earth. Even in biology, and down to elementary particles physics. String like objects are accompanied by genuine fermionic strings associated with singularities of minimal surfaces seem to populate the entire physics in sharp contrast to superstrings.

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

Articles and other material related to TGD.

Friday, May 10, 2019

Heavy element surprise

Again a surprise in astrophysics (see the popular articles here and here and the slides here. It is really amazing how little we actually know about the mechanism producing heaver elements.

  1. Big bang produces H, He, and also Be but in trace amounts. Heavier elements are absent and are believed to be produced in stars. How the heavier elements are formed? This is the problem. One proposal is that during super-nova explosions so called r-process produces heavier elements outside supernova but SN1987A did not provide support for this.

    One proposal is that the heavier elements are produced in the collisions of neutron stars. A further proposal is that they are produced in collapsing accretin disk when neutron star collapses to blackhole.

  2. Standard hypothesis is that so called population III stars produce elements heavier than Be. These stars would be very large and very short lived - age would have been around 105-106 years. Not a single population III star has been however observed but one could blame their short ages as a reason for this. So called population II stars would be their successors and have been observed. The amount of heavier elements in them is still much lower than in Sun.

  3. Astrophysicists Frebel and Ezzeddine have studied the spectral signatures of a population II star HE 1327-2326 and discovered it to contain unusually large amount of Zinc which is heavier that iron. This looks very strange since elements heavier than Fe should be produced much later.

It has been proposed that the first stars did not explode in a spherically symmetric manner but generated jets in opposite directions, and Frebel and Ezzeddine suggests that this might explain the strange findings. Jets would have distributed heavier elements from population III stars stars to surroundings in a very undemocratic manner. Although the total amount of heavier elements would have been small, the density of heavier elements in the birthplaces of population II stars along the jets would have been much higher than spherically symmetric model predicts.This could explain the high amount of Zinc.

While reading the article, I realized that the jetty picture is very natural in TGD framework.

  1. Asymmetric jets are very natural in TGD vision about the formation of galaxies as tangles associated with long cosmic string known to form linear structuress. This picture solves the galactic dark matter problem: dark matter and energy reside at cosmic strings thickened to flux tubes and create just the desired gravitational potential to explain flat velocity spectrum of distant stars. That there would be no dark matter halo conforms with the various findings strongly suggesting that this halo does not exist.

    Flux tubes of long cosmic strings are what I call wormhole magnetic fields that is have same M4 projection except in the regions where there are galaxies and stars. Wormhole magnetic field portions outside galaxies would be essentially dark energy since test particles do not experience the associated magnetic and electric fields. However, long range gravitational fields are created and make themselves visible as flat velocity spectrum around spiral galaxies.

    The cosmic strings would have thickened and liberated energy in the process and given rise to ordinary visible matter: this would be analogous to the decay of inflaton field except that the magnetic energy and volume energy characterized by length scale dependent cosmological constant would replace energy of inflaton field.

    The topology of tangles consisting of a looped monopole flux tube carrying monopole flux resembled the field line topology of dipole magnetic field. Stars and eventually even planets would have ormed as sub-tangles around the flux tubes. Universe would be like highly neural network with quantum coherence even in cosmic scales instead of uncorrelated galaxies and stars.

  2. The explosion of very earlier star like entity would have automatically created jets propagating along the flux tubes emanating from so that instead of being distributed in a spherically symmetric manner the elements in the earlier star would have propagated directly to the birth places of new stars along the flux tube having the exploded star as tangle. This would changes completely the view about star formation.

But what these very earlier stars might have been?
  1. TGD based view about dark suggests a new mechanism for the production of heavier elements (see this). What I call dark nuclei (having non-standard value heff=n× h0 of Planck constant) would be dark protons sequences along flux tubes and have nuclear binding energy much smaller than ordinary nuclei.

    Pollack effect (see this) would give rise to these dark nuclei and they would be present in living matter and give a fundamental realization of genetic code: ordinary matter with ordinary value of Planck constant would mimic the dynamics of magnetic body having higher "IQ" (higher evolutionary level in number theoretical evolutionary hierarchy defined by extensions of rationals see
    this) definable as heff/h0=n and identifiable as dimension of extension of rationals.

    The connection between biology and astrophysics looks of course strange but this is what the fractality of TGD Universe predicts. Same cosmic strings thickened to flux tubes are in all length scales and basic mechanisms are the same.

  2. Dark nuclei would have been formed first and caused pre-heating during the pre-stellar phase. As the temperature became high enough, ordinary fusion reactions started and stars were born. The spontaneous transformation to ordinary nuclei liberating almost all nuclear binding energy would have also occurred and is proposed as a model for "cold fusion" reported to produce heavy elements.

  3. One can ask why so much Zinc in HE 1327-2326? Was "cold fusion" involved already at that time as TGD based model indeed proposes? Could the postulated but unseen population III stars be pre-stellar objects generating heavy elements by "cold fusion" and spraying them along flux tubes directly to the new stars rather than dispersing them to all possible directions? The Universe would have been a network analogous to neural system rather than soup and the formation of stars would have been a collective process with correlations in super-astrophysical length scales.

    This is the also the picture about living mater provided by TGD, where flux tube network makes possible for reacting molecules to find each other and also provides a mechanism of catalysis based on the reduction of heff liberating energy allowing to overcome the potential walls preventing the chemical reactions.

See the short article Heavy element surprise , the article Cold Fusion Again , or the chapter with the same title.

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

Articles and other material related to TGD.

Sunday, May 05, 2019

Solar surprise

Sabine Hossenfelder gave a link to a popular article about totally shocking new findings about Sun. There are 5 times more gamma rays than expected and the spectrum has a deep and narrow dip around 40 GeV. Spectrum continues to much higher energies than expected, at least up to 100 GeV. One proposal is that there could be dark matter in the interior of Sun yielding the gamma rays but is unclear how they could get to the surface without experiencing the same fate as ordinary gammas from nuclear reactions.

There is also a correlation with sunspot cycle. Basic data and observations related to correlations with the solar cycle are discussed in two articles (see this and this).

  1. Power law spectrum is harder than for cosmic rays: spectral indices are n=-2.2 and n=-2.7 respectively (one has power law behavior En for the flux). The spectral intensity at 100 GeV is very nearly the maximum flux predicted by the model assuming that reflection of cosmic gamma rays gives to the gammas.

  2. The spectrum has two components: poloidal component farther from equator and equatorial component largest during sunspot minimum. The equatorial contribution is maximal at solar minimum. The spectral index of the equatorial contribution is harder and higher energies are present. The energy range is maximal during spot minima. Gamma flux is reduced during sun spot maxima.

How the observed gamma rays could be produced in TGD Universe?
  1. Gamma rays cannot cannot be gammas produced by nuclear reactions as ordinary gammas since nuclear energy scale is much below the scale of gamma rays extending to 100 GeV at least. Even the hadronic energy scale is too low. The gamma rays could be cosmic rays having already high energies: the spectral indices are however different. This leaves acceleration of charged particles producing gamma rays as the most plausible mechanism irrespective of whether the particle come from solar core or are cosmic rays.

  2. Dark magnetic flux tubes are basic notion of TGD and could serve as the channels along which charged particles could propagate to the surface without losing their energies in collisions. An interesting hypothesis considered already earlier is that solar magnetic field has flux tubes carrying monopole flux. This would predict that the flow is not evenly distributed but reflects the structure of the flux tube distribution.

    Charged particles could accelerate in the electric field of flux tube as they travel along flux tubes and generate gamma rays by some mechanism. The energy would be the increment of Coulomb energy if dissipation is neglected. A simple modification of flux tube type extremals allows the presence of helical magnetic and electric fields along flux tube orthogonal to each other. I have proposed the same mechanism to explain the gamma rays and high energy electrons at MeV energies associated with lightnings: in standard physics framework dissipative losses do not allow them.

  3. What could be the production mechanism of gamma rays? If flux tubes have sharp kinks, charged particles should experience large deceleration in the kinks and could emit high energy gamma ray in the process. The highly relativistic charge particle itself could leak out (one cannot exclude nuclei from solar core). Large deflection angles however requires transfer of momentum also to flux tube degrees of freedom.

  4. What could be the origin of the gap around 30-50 GeV? If the acceleration takes place in the electric fields assignable to the closed flux tubes assignable to solar dipolar magnetic field, the charged particle could travel several times around the loop giving rise to several energy bands explaining the gap and suggesting several of them. The flux loop would act as a particle accelerator.

    A possible mechanism producing cosmic rays could be pair-annihilation of pairs of M89 pions with mass about 70 GeV to gamma ray pairs or charged particles with energies 35 MeV. Could the dip observed in the energy range around 30-50 GeV somehow relate to the charged decay products of M89 pions accelerating in the electric fields of flux tubes? Could the dip be gap without the decays of M89 pions?

  5. The charged particles could be provided by the solar core or they could be cosmic rays. The order of magnitude for gamma ray intensity is 5 times larger than in cosmic ray model, which encourages the identification as cosmic rays (see this). The origin of cosmic rays is however also a mystery and neutron stars, supernovae, active galactic nuclei, quasars, and gamma-ray bursts have been proposed as sources of cosmic rays.

    In TGD the model for the formation of galaxies, quasars, and active galactic nuclei, and even stars, and planets relies on the formation of loopy tangles along long thickening cosmic strings analogous to magnetic dipole field. Galactic matter would be produced by the decay of the flux tube energy to particles as analog of the decay of inflaton field. This could generate both charged particles and gamma radiation in the solar core and in neutron stars. The acceleration could be much more effective due to the strong magnetic and electric fields involved. Also charged particles can leak out from the flux tubes and cosmic rays could be produced by this mechanism. Cosmic rays could move along the highways defined by the long magnetic flux tubes connecting galaxies.

The understanding of the correlations with the solar cycle requires a model for the polarization flip. One can consider several options but the model based on reconnection splitting dipole loops from the flux tube tangle representing the analog dipole field is the simplest one. The simplest variant of the model requires zero energy ontology (ZEO) and quantum coherence at dark flux tubes in solar length scales and that long galactic string defines wormhole magnetic field with two sheets (type I and II) connected by wormhole contacts separated from each other in the sense that M4 projections are disjoint.
  1. Let us denote the numbers of dipole loops of type i=I,II by ni. Assume that in the initial situation one has (nI=nmax,nII=0). B as maximum value Bmax. The arrows of time at the two sheets are assumed to be opposite during cycles.

  2. The transition leading B=Bmax to B=0 would be "big" state function reduction (BSR) changing the arrow of time at sheets of both type I and II. BSR would generate maximum number of new dipole flux loops of type II: nII→ nmax so that one has nI= nII= nmax and B=0.

  3. After that dipole loops of type I begin to split away by reconnections in "small" state function reductions (SSRs) so that nI decreases. They split further in pieces and leak out from Sun whereas nII remains unchanged since it corresponds to the passive boundary of CD - this is essential. Net B increases until one has B=-Bmax.

  4. Next occurs BSR generating maximum number of new flux loop portions of type I leading nI= nII= nmax and B=0 and same is repeated except that now nII decreases.

  5. One can understand the sunspot cycle in terms of split dipole loops leaving the Sun: their intersection with the solar surface would define sunspot pair and the distance of members of the pair would decrease to zero during the cycle.

The model leads to rather dramatic predictions.
  1. Various magnetic structures are predicted to appear in pairs with members related by an approximate Z2 symmetry. For the magnetic field of the Sun this symmetry would be naturally inversion symmetry with respect to the surface of Sun (or of dipole core). Also reflection symmetry can correspond to Z2. This symmetry should be universal and the predictions are in sharp contrast with the locality principle of classical physics. One could even understand the mysterious "Axis of Evil" associated as anomaly of CMB and apparently giving special role for solar system (see this).

  2. Also unexpected connections with TGD inspired views about biology and consciousness emerge. Magnetic body (MB) is the intentional agent in living system Z2 realized as inversion could related the parts of MB in the interior and exterior of Earth: could the idea about intra-terrestrial life introduced originally half-jokingly make sense - at the level of MBs at least? ZEO based theory of consciousness predicts that conscious entities can have both arrows of time and death means reincarnation with opposite arrow of time. But where do these ghostly selves with opposite arrow of time reside? Could Z2 - possibly realized as inversion - relate relates these selves to each other.

See the article Solar surprise, the chapter with the same title or the chapter TGD and Astrophysics "Physics in Many-Sheeted Space-Time: part II".

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

Articles and other material related to TGD.

Wednesday, May 01, 2019

Twistor lift of TGD and WCW geometry

In the following a view about WCW geometry forced by twistor lift of TGD is summarized. Twistor lift brings to the action a volume term but without breaking conformal invariance and without introducing cosmological constant as a fundamental dimensional dynamical coupling. The proposed construction of the gamma matrices of WCW giving rise to Kähler metric as anti-commutators is now in terms of the Noether super charges associated with the super-symplectic algebra. This I dare to regard as a very important step of progress. pu

Possible weak points of the earlier vision

To make progress it is wise to try to identify the possible weak points of the earlier vision.

  1. The huge vacuum degeneracy of Kähler action defining the Kähler function of WCW Kähler metric is analogous to gauge degeneracy of Maxwell action and coded by symplectic transformations of CP2. It implies that the degeneracy of the metric increases as one approaches vacuum extremals and is maximal for the space-time surfaces representing canonical imbeddings of Minkowski space: Kähler action vanishes up to fourth order in deformation. The original interpretation was in terms of 4-D spin glass degeneracy assumed to be induced by quantum degeneracy.

    One could however argue that classical non-determinism of Kähler action is not acceptable and that a small term removing the vacuum degeneracy is needed to make the situation mathematically acceptable. There is an obvious candidate: a volume term having an interpretation in terms of cosmological constant. This term however seems to mean the presence of length scale as a fundamental constant and is in conflict with the basic lesson learned from gauge theories teaching that only dimensionless couplings can be allowed.

  2. The construction of WCW Kähler metric relies on the hypothesis that the basic result from the construction of loop space geometries generalizes: the Kähler metric should be essentially unique from the condition that the isometry group is maximal - this guarantees the existence of Riemann connection. For D=3 this condition is expected to be even stronger than for D=1.

    The hypothesis is that in zero energy ontology (ZEO) the symplectic group acting at the light-like boundaries of causal diamond (CD) (one has CD= cd× CP2, where cd is the intersection of future and past directed light-cones) acts as the isometries of the Kähler metric.

    It would be enough to identify complexified WCW gamma matrices and define WCW metric in terms of their anti-commutators. The natural proposal is that gamma matrices are expressible as linear combinations of fermionic oscillator operators for second quantized induced spinor fields at space-time surface. One could even ask whether fermionic super charges and conserved fermionic Noether charges are involved with the construction.

    The explicit construction of gamma matrices has however been based on somewhat ad hoc formulas, and what I call effective 2-dimensionality argued to follow from quantum criticality is somewhat questionable as exact notion.

Twistor lift of TGD and ZEO

Twistor lift of TGD and ZEO meant a revolution in the view about WCW geometry and spinor structure.

  1. The basic idea is to replace 4-D Kähler action with dimensionally reduced 6-D Kähler for the analog of twistor space of space-time surface. The induction procedure for the spinors would be generalized so that it applies to twistor structure. The twistor structure of the imbedding space is identified as the product of twistor spaces M4× S2 of M4 and SU(3)/U(1)× U(1) of CP2. In momentum degrees of freedom the twistor space of M4 would be the usual CP3.

    Remarkably, M4 and CP2 are the only spaces allowing twistor space with Kähler structure. In the case of M4 the Kähler structure is a generalization of that for E4. TGD would be unique from the existence of twistor lift. This predicts CP breaking at fundamental level possibly responsible for CP breaking and matter-antimatter asymmetry.

  2. One would still have Kähler coupling strength αK as the only single dimensionless coupling strength, whose spectrum is dictated by quantum criticality meaning that it is analogous to critical temperature. All coupling constant like parameters would be determined by quantum criticality. Cosmological constant would not be fundamental constant and this makes itself visible also in the concrete expressions for conserved Noether currents. The breaking of the scale invariance removing vacuum degeneracy of 4-D Kähler action would be analogous to spontaneous symmetry breaking and would remove vacuum degeneracy and classical non-determinism.

    The volume term would emerge from dimensional reduction required to give for the 6-surface the structure of S2 bundle having space-time surfaces as base space. Cosmological constant would be determined by dynamics and depend on p-adic length scale depending in the average on length scale of space-time sheet proportional to the cosmic time sense like 1/a2, a cosmic time. This would solve the problem of large cosmological constant and predict extremely small cosmological constant in cosmic scales in the recent cosmology. This suggests that in long length scales one still has spin glass degeneracy realized in terms of many-sheeted space-time.

  3. In ZEO 3-surface correspond to a union of 3-surfaces at the ends of space-time surfaces at boundaries of CD. There are many characterizations of quantum criticality.

    1. Preferred extremal property and quantum criticality would mean that one has simultaneously an extremal of both 4-D Kähler action and volume term except at singular 2-surfaces identified as string world sheets and their boundaries. In accordance with the universality of quantum critical dynamics, one would have outside singularities local dynamics without dependence on Kähler coupling strength. The interpretation would be as geometric generalization of massless fields also characterizing criticality.

    2. Another characterization of preferred extremal is as a space-time surfaces using sub-algebra Sm of symplectic algebra S for which generators have conformal weights coming as m-tuples of those for the full symplectic algebra. Both Sm and [S,Sm] would have vanishing Noether charges. For the induced spinor fields analogous condition would hold true. Effectively the infinite number of radial conformal weights of the symplectic algebra associated with the light-like radial coordinate of δ M4+/- would reduce to a finite number.

    3. A further characterization would be in terms of M8-H duality. Preferred extremals in H would be images of of space-time surfaces in M8 under M8-H duality. The latter would correspond to roots of octonionic polynomials with coefficients in an extension of rationals. Therefore space-time surfaces in H satisfying field equations plus preferred extremal conditions would correspond to surfaces described by algebraic equations in M8. Algebraic dynamics would be dual to differential dynamics.

    4. In adelic physics the hierarchy of Planck constants heff/h0=n with n having an interpretation as dimensions of Galois group of extension of rationals would define further correlate of quantum criticality. The scaled up Compton lengths proportional to heff would characterize the long range fluctuations associated with quantum criticality.

The revised view about WCW metric and spinor structure

In this framework one can take a fresh approach to the construction of the spinor structure and Kähler metric of WCW. The basic vision is rather conservative. Rather than inducing ad hoc formulas for WCW gamma matrices one tries to identify Noether the elements super-algebra as Noether charges containing also the gamma matrices as Noether super charges.

  1. The simplest guess is that the algebra generated by fermionic Noether charges QA for symplectic transformations hk→ hk+ε jAk assumed to induce isometries of WCW and Noether supercharges Qn and their conjugates for the shifts Ψ→ Ψ+ε un, where un is a solution of the modified Dirac equation, and ε is Grassmann number are enough to generate algebra containing the gamma matrix algebra.

  2. The commutators ΓAn=[QA,Qn] are super-charges labelled by (A,n). One would like to identify them as gamma matrices of WCW. The problem is that they are labelled by (A,n) whereas isometry generators are labelled by A only just as symplectic Noether charges. Do all supercharges ΓAn except ΓA0 corresponding to u0=constant annihilate the physical states so that one would have 1-1 correspondence? This would be analogous to what happens quite generally in super-conformal algebras.

  3. The anti-commutators of ΓA0 would give the components of the Kähler metric. The allowance of singular surfaces having 2-D string world sheets as singularities would give to the metric also stringy component besides 3-D component and possible 0-D components at the ends of string. Metric 2-D property would not be exact as assumed originally.

This construction can be blamed for the lack of explicitness. The general tendency in the development of TGD has been replacement of explicit but somewhat ad hoc formulas with principles. Maybe this reflects to my own ageing and increasing laziness but my own view is that principles are what matter and get abstracted only very slowly. The less formulas, the better!

See the article Twistor lift of TGD and WCW geometry or the chapter Recent View about Kähler Geometry and Spin Structure of WCW of "Physics as WCW geometry".

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

Articles and other material related to TGD.