Tuesday, August 30, 2022

Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole

The theoretical framework behind TGD involves several different strands and the goal is to unify them to a single coherent whole. TGD involves number theoretic and geometric visions about physics and M8-H duality, analogous to Langlands duality, is proposed to unify them. Also quantum classical correspondence (QCC) is a central aspect of TGD. One should understand both the M8-H duality and QCC at the level of detail.

The following mathematical notions are expected to be of relevance for this goal.

  1. Von Neumann algebras, call them M, in particular hyperfinite factors of type II1 (HFFs), are in a central role. A both the geometric and number theoretic side, QCC could mathematically correspond to the relationship between M and its commutant M'.

    For instance, symplectic transformations leave induced Kähler form invariant and various fluxes of Kähler form are symplectic invariants and correspond to classical physics commuting with quantum physics coded by the super symplectic algebra (SSA). On the number theoretic side, the Galois invariants assignable to the polynomials determining space-time surfaces are analogous classical invariants.

  2. The generalization of ordinary arithmetics to quantum arithmetics obtained by replacing + and × with ⊕ and ⊗ allows us to replace the notions of finite and p-adic number fields with their quantum variants. The same applies to various algebras.
  3. Number theoretic vision leads to adelic physics involving a fusion of various p-adic physics and real physics and to hierarchies of extensions of rationals involving hierarchies of Galois groups involving inclusions of normal subgroups. The notion of adele can be generalized by replacing various p-adic number fields with the p-adic representations of various algebras.
  4. The physical interpretation of the notion of infinite prime has remained elusive although a formal interpretation in terms of a repeated quantization of a supersymmetric arithmetic QFT is highly suggestive. One can also generalize infinite primes to their quantum variants. The proposal is that the hierarchy of infinite primes generalizes the notion of adele.
The formulation of physics as Kähler geometry of the "world of classical worlds" (WCW) involves of 3 kinds of algebras A; supersymplectic isometries SSA acting on δ M4+× CP2; affine algebras Aff acting on light-like partonic orbits; and isometries of light-cone boundary δ M4+, allowing hierarchies of subalgebras An.

The braided Galois group algebras at the number theory side and algebras {An} at the geometric side define excellent candidates for inclusion hierarchies of HFFs. M8-H duality suggests that n corresponds to the degree nof the polynomial P defining space-time surface and that the n roots of P correspond to n braid strands at H side. Braided Galois group would act in An and hierarchies of Galois groups would induce hierarchies of inclusions of HFFs. The ramified primes of P would correspond to physically preferred p-adic primes in the adelic structure formed by p-adic variants of An with + and × replaced with ⊕ and ⊗.

See the article Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole or the chapter with the same title.

Monday, August 22, 2022

TGD view of Krebs cycle

This article was inspired by the YouTube video (see this) in which biologist Nick Lane talked of Krebs cycle, also known as citric acid cycle. The title of the video was "How the Krebs cycle powers life and death?".

Krebs cycle is central in the metabolism of animal cells, liberating metabolic energy from glucose and leading to the emergence of the basic building blocks of fundamental biomolecules. Lane talks also of the reverse Krebs cycle appearing in photosynthesis. Lane proposes a vision of how life could have evolved from in-organic chemistry in thermal vents. Lane emphasizes the importance of charge separation at the level of the cell and even at the level of Earth.

The objections against Lane's view give a good motivation for developing a TGD based view about Krebs cycle. This view is based on some basic ideas of TGD inspired quantum biology. In particular the zero energy ontology (ZEO) in which Krebs cycle and its reversal could be seen as time reversal of each other at the control level; the quantum gravitational view of metabolism and evolution of life; the TGD inspired view about how Pollack effect induces charge separations leading also to a view of genetic code, which at fundamental level would be realized in terms of both dark proton and dark photon triplets; and the TGD proposal for what happened in Cambrian explosion in which oxygenated oceans and highly developed multicellulars emerged apparently out of nowhere.

The discussion leads to a more precise view of metabolism before the Cambrian explosion, according to which the dark photons generated by the Earth's core would have provided the photons for photosynthesis in underground oceans and led to their oxygenation.

See the article Krebs cycle from TGD point of view or the chapter Quantum gravitation and quantum biology in TGD Universe.

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

Articles related to TGD.

Wednesday, August 17, 2022

Some TGD inspired questions and thoughts about hyperfinite factors of type II1

I have had a very interesting discussion with Baba Ilya Iyo Azza about von Neumann algebras. I have a background of physicists and have suffered a lot of frustration in trying to understand hyperfinite factors of type II1 (HFFs) by trying to read mathematicians' articles.

I cannot understand without a physical interpretation and associations to my own big vision TGD. Yesterday I again stared at the basic definitions, ideas and concepts trying to build a physical interpretation. I try to summarize what I possibly understood.

  1. One starts from the algebra of bounded operators in Hilbert space B(H). von Neumann algebra is a subalgebra of B(H). Already here an analog of inclusion is involved (see this). There are also inclusions between von Neumann algebras.

    What could the inclusion of von Neumann algebra to B(H) as subalgebra mean physically?

  2. In the TGD framework, I can find several analogies. Space-time is a 4-surface in H=M4× CP2: analog of inclusion reducing degrees of freedom. Space-time is not only an extremal of an action, but also satisfies holography so that this 4-surface is almost uniquely defined by a 3-surface. I talk about preferred extremals (PEs).

    Clearly, there is an analogy with von Neumann algebras, in particular HFFs with extremely nice mathematical properties, as a subalgebra of B(H) and quantum classical correspondence suggests that this analogy is not accidental.

The notion of the commutant M' of M is essential. Also M' defines HFF.What could be its physical interpretation?
  1. In TGD, one has indeed an excellent candidate for the commutant. Supersymplectic symmetry algebra (SSA) of δ M4+× CP2 (δ M4+ denotes the boundary of a future directed light-cone) is proposed to act as isometries of the "world of classical worlds" (WCW) consisting of space-time surfaces as PEs (very, very roughly).

    Symplectic symmetries are generated by Hamiltonians, which are products of Hamiltonians associated with δ M4+ (metrically sphere S2) and CP2. Symplectic symmetries are conjectured to act as isometries of WCW and gamma matrices of WCW extend symplectic symmetries to super-symplectic ones.

    Hamiltonians and their super-counterparts generate the super-symplectic algebra (SSA) and quantum states are created by using them. SSA is a candidate for HFF. Call it M. What about M ?

  2. The symplectic symmetries leave invariant the induced Kähler forms of CP2 and contact form of δ M4+ (assignable to the analog of Kähler structure in M4).
  3. The wave functions in WCW depending of magnetic fluxes defined by these Kähler forms over 2-surfaces are physically observables which commute SSA and with M. These fluxes are in a central role in the classical view about TGD and define what might perhaps be regarded as a dual description necessary to interpret quantum measurements.

    Could M' correspond or at least include the WCW wave functions (actually the scalar parts multiplying WCW spinor fields with WCW spinor for given 4-surface a fermionic Fock state) depending on these fluxes only? I have previously talked of these degrees of freedom as zero modes commuting with quantum degrees of freedom and of quantum classical correspondence.

  4. Note that there are also number theoretic degrees of freedom, which naturally appear from the number theoretic M8 description mapped to H-description: Galois groups and their representations, etc...
There are further algebraic notions involved. The article of John Baez (see this) describes these notions nicely.
  1. The condition M'' = M is a defining algebraic condition for von Neumann algebras. What does this mean? Or what could its failure mean? Could M'' be larger than M? It would seem that this condition is achieved by replacing M with M''.

    M''=M codes algebraically the notion of weak continuity, which is motivated by the idea that functions of operators obtained by replacing classical observable by its quantum counterpart are also observables. This requires the notion of continuity. Every sequence of operators must approach an operator belonging to the von Neumann algebra and this can be required in a weak sense, that is for matrix elements of the operators.

  2. There is also the notion of hermitian conjugation defined by an antiunitary operator J: a= JAJ. This operator is absolutely essential in quantum theory and in the TGD framework it is geometrized in terms of the Kä form of WCW. The idea is that entire quantum theory, rather than only gravitation or gravitation and gauge interactions should be geometrized. Left multiplication by JaJ corresponds to right multiplication by a.
  3. The notion of factor as a building brick of more complex structures is also central and analogous to the notion of simple group or prime. It corresponds to a von Neumann algebra, which is simple in the sense that it has a trivial center consisting of multiples of unit operators. The algebra is direct sum or integral over different factors.
  4. A highly non-intuitive and non-trivial axiom relating to HFFs is that the trace of the unit operator equals to 1. The intuitive idea is that the density matrix for an infinite-D system identified as a unit operator gives as its trace total probability equal to one. These factors emerge naturally for free fermions. For factors of type I associated with three bosons, the trace equals n in the n-D case and ∞ in the infinite-D case.

    The factors of type I are tensor products of factors of type I and HFFs and could describe free bosons and fermions.

    In quantum field theory (QFT), factors of type III appear and in this case the notion of trace becomes useless. These factors are pathological and in QFT they lead to divergence difficulties. The physical reason is the idea about point-like particles, leading in scattering amplitudes to powers of delta functions having no mathematical meaning. In the TGD framework, the generalization of a point-like particle to 3-surface saves from these difficulties and leads to factors of type I and HFFs.

    Measurement resolution implies unique number theoretical discretization and further simplifies the situation in the TGD framework. In particular, "hyperfinite" expresses the fact that the approximation of a factor with its finite-D cutoff is an excellent approximation.

One cannot avoid philosophical considerations related to the interpretations of quantum measurement theory. The standard interpretations are known to lead to problems in the case of HFFs.
  1. An important aspect related to the probabilistic interpretation is that physical states are characterized by a density matrix so that quantum theory reduces to probability theory, which would become in some sense non-commutative for von Neumann algebras.

    The problem is that no pure normal states as counterparts of quantum states do not exist for HFFs. Furthermore, the phenomenon of interference central in quantum theory does not have a direct description. One can of course argue that in practice the system studied is entangled with the environment and that this forces the description in terms of a density matrix even when pure states are realized at the fundamental level.

  2. TGD strongly suggests the generalization of the state as density matrix to a "complex square root" of density matrix proportional to exponent of a real valued Kähler function of WCW identified as Kähler action for the space-time region as a preferred extremal and a phase factor defined by the analog of of action exponential. The quantum state would be proportional to an exponent of Kähler function of WCW identified as Kähler action for space-time surface as a preferred extrema.
  3. There are also problems with the interpretations of quantum theory, which actually strongly suggest that something is badly wrong with the standard ontology.

    This requires a generalization of quantum measurement theory (see this and this) based on zero energy ontology (ZEO) and Negentropy Maximization Principle (NMP) \cite{allb/nmpc}. The key motivation is that ZEO is implied by an almost exact holography forced by general coordinate invariance for space-times as 4-surface. That holography and, as a consequence, classical determinism are not quite exact, has important implications for the understanding of the space-time correlates of cognition and intentionality in the TGD framework.

    In the TGD framework, the basic postulate is that quantum measurement as a reduction of entanglement can in principle occur for any entangled system pair.

Consider now the standard construction leading to a hierarchy of HFFs and their inclusions.
  1. One starts from an inclusion M⊂ N of HFFs. I will later consider what these algebras could be in the TGD framework.
  2. One introduces the spaces L2(M) resp. L2(N) of square integrable functions in M resp. N.

    From the physics point of view, bringing in L2 is something extremely non-trivial. Space is replaced with wave functions in space: this corresponds to what is done in wave mechanics, that is quantization! One quantizes in M, particles as points of M are replaced by wave functions in M, one might say.

  3. At the next step one introduces the projection operator e as a projection from L2(N) to L2(M): this is like projecting wave functions in N to wave functions in M. I wish I could really understand the physical meaning of this. The induction procedure for second quantized spinor fields in H to the space-time surface by restriction is completely analogous to this procedure.

    After that one generates a HFF as an algebra generated by e and L2(N): call it < L2(N), e>. One has now 3 HFFs and their inclusions: M0== M, M1== N, and < L2(N), e>== M2.

    An interesting question is whether this process could generalize to the level of induced spinor fields?

  4. Even this is not enough! One constructs L2(M2)== M3 including M2. One can continue this indefinitely. Physically this means a repeated quantization.

    One could ask whether one could build a hierarchy M0, L2(M0),..., L2(L2...(M0))..): why is this not done?

    The hierarchy of projectors ei to Mi defines what is called Temperley-Lieb algebra involving quantum phase q=exp(iπ/n) as a parameter. This algebra resembles that of S but differs from it in that one has projectors instead of group elements. For the braid group ei2=1 is replaced with a sum of terms proportional to ei and unit matrix: mixture of projector and permutation is in question.

  5. There is a fascinating connection in TGD and theory of consciousness. The construction of what I call infinite primes (see this) is structurally like repeated second quantization of a supersymmetric arithmetic quantum field theory involving fermions and bosons labelled by the primes of a given level I conjectured that it corresponds physically to quantum theory in the manysheeted space-time.

    Also an interpretation in terms of a hierarchy of statements about statements about .... bringing in mind hierarchy of logics comes to mind. Cognition involves generation of reflective levels and this could have the quantization in the proposed sense as a quantum physical correlate.

Connes tensor product is natural for modules having algebra as coefficients. For instance, matrix multiplication has an interpretation as Connes tensor product reduct tensor product of matrices to a matrix product. The number of degrees of freedom is reduced.
  1. Inclusion of Galois group algebra of extension to its extension could define Connes tensor product. Composite polynomial instead of product of polynomials: this would describe interaction physically: the degree of composite is product of degrees of factors and the same holds true for the product of polynomials. This rule for the dimensions holds also for the tensor product. Composite structure implies correlations and formation of bound states so that the number of degrees of freedom is reduced.
  2. Also the inclusion SSAn+1 to SSAn should define Connes tensor product. Note that the inclusions are in different directions. Could it be that these two inclusion sequences correspond to the sequences assignable to M and M'?

    What about the already mentioned "classical" degrees of freedom associated with the fluxes of the induced Kähler form? Should one include the additional degrees of freedom to M' or are they dual to the number theoretic degrees of freedom assignable to Galois groups. How does the M8-H duality, relating number theoretic and geometric descriptions in analogy with Langlands duality, relate to this?

I do not have an intuitive grasp about category theory. In any case, one would have a so-called 2-category (see this). M and N correspond to 0-morphisms (objects). One can multiply L2(M) and L2(N) by M or N. The bimodules ML2(M)M, NL2(N)N correspond to 1-morphisms which are units whereas the bimodules MMN, and NMM correspond to generating 1-morphisms mapping M into N. Bimodule map corresponds to 2-morphisms. Connes tensor product defines a tensor functor.

Extended ADE Dynkin diagrams for ADE Lie groups, which correspond to finite subgroups of SU(2) by McKay correspondence, characterize inclusions of HFFs. For a subset of ADE groups not containing E7 and D2n+1, there are inclusions, which correspond to Dynkin diagrams of finite subgroups of the quantum group SU(2)q. What is interesting that E6 (tetrahedron) and E8 (icosahedron/dodecahedron) appear in the TGD based model of bioharmony and genetic code but not E7 (see this).

  1. Why finite subgroups of SU(2) (or SU(2)q) should appear as characterizers of the inclusions in the tunnel hierarchies with the same value of the quantum dimension Mn+1:Mn of quantum algebra.

    In the TGD interpretation Mn+1 reduces to a tensor product of Mn and quantum group, when Mn represents reduced measurement resolution and quantum group the added degrees of freedom. Quantum groups would represent the reduced degrees of freedom. This has a number theoretical counterpart in terms of finite measurement resolution obtained when an extension....of rationals is reduced to a smaller extension. The braided relative Galois group would represent the new degrees of freedom.

  2. The identification of HFF as tensor product of GL(2,c) or GL(n,C) and the identification as analog of McKay graph for the irreps of a closed subgroup defines an invariant characterizing the fusion rules involved with the reduction of the tensor product is involved but I do not really understand this. What comes to mind is that all the essential features of tensor products of HFFs reduce to tensor products of finite subgroups of SU(2) or of SU(2)q.
  3. In the TGD framework, SU(2) could correspond to a covering group of quaternionic automorphisms and number theoretic discretization (cognitive representations) would naturally lead to discrete and finite subgroups of SU(2).
What could HFFs correspond to in TGD?
  1. Braid group B(G) of group (say Galois group as subgroup of Sn) and its group algebra would correspond to B(G) and L2(B(G)).
  2. Braided Galois group and its group algebra could correspond to B(G) and L2(B(G)). Composite polynomials define hierarchies of Galois groups such that the included Galois group is a normal subgroup. This kind of hierarchy could define an increasing sequence of inclusions of braided Galois groups.
  3. Elements of SSA are labelled by non-negative integers. One can construct a hierarchy of subalgebras SSAn , such that elements with large conformal weight annihilate the physical state and also their commutators with SSAn do this. SSAn+1 is included by SSAn and one has a kind of reversed sequence of inclusions.
  4. Braided Galois groups and a hierarchy of SSAn could correspond to commuting algebras M and M'.
  5. Question: Does the standard construction bring in something totally new to these hierarchies or is the resulting structure equivalent with that given by the standard construction?
For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD.

Sunday, August 14, 2022

Do the inclusion hierarchies of extensions of rationals correspond to inclusion hierarchies of hyperfinite factors?

I have enjoyed discussions with Baba Ilya Iyo Azza about von Neumann algebras. Hyperfinite factors of type II1 (HFF) (see this) are the most interesting von Neumann algebras from the TGD point of view. One of the conjectures motivated by TGD based physics, is that the inclusion sequences of extensions of rationals defined by compositions of polynomials define inclusion sequences of hyperfinite factors. It seems that this conjecture might hold true!

Already von Neumann demonstrated that group algebras of groups G satisfying certain additional constraints give rise to von Neumann algebras. For finite groups they correspond to factors of type I in finite-D Hilbert spaces.

The group G must have an infinite number of elements and satisfy some additional conditions to give a HFF. First of all, all its conjugacy classes must have an infinite number of elements. Secondly, G must be amenable. This condition is not anymore algebraic. Braid groups define HFFs.

To see what is involved, let us start from the group algebra of a finite group G. It gives a finite-D Hilbert space, factor of type I.

  1. Consider next the braid groups Bn, which are coverings of Sn. One can check from Wikipedia that the relations for the braid group Bn are obtained as a covering group of Sn by giving up the condition that the permutations sigmai of nearby elements ei,ei+1 are idempotent. Could the corresponding braid group algebra define HFF?

    It is. The number of conjugacy classes gn σign-1, gn == σ n+1 is infinite. If one poses the additional condition ei2= U× 1, U a root of unity, the number is finite. Amenability is too technical a property for me but from Wikipedia one learns that all group algebras, also those of the braid group, are hyperfinite factors of type II1 (HFFs).

  2. Any finite group is a subgroup G of some Sn. Could one obtain the braid group of G and corresponding group algebra as a sub-algebra of group algebra of Bn, which is HFF. This looks plausible.
  3. Could the inclusion for HFFs correspond to an inclusion for braid variants of corresponding finite group algebras? Or should some additional conditions be satisfied? What the conditions could be?
Here the number theoretic view of TGD comes to rescue.
  1. In the TGD framework, I am primarily interested in Galois groups, which are finite groups. The vision/conjecture is that the inclusion hierarchies of extensions of rationals correspond to the inclusion hierarchies for hyperfinite factors. The hierarchies of extensions of rationals defined by the hierarchies of composite polynomials Pn ˆ ...ˆ P1 have Galois groups which define a hierarchy of relative Galois groups such that the Galois group Gk is a normal subgroup of Gk+1. One can say that the Galois group G is a semidirect product of the relative Galois groups.
  2. One can decompose any finite subgroup to a maximal number of normal subgroups, which are simple and therefore do not have a further decomposition. They are primes in the category of groups.
  3. Could the prime HFFs correspond to the braid group algebras of simple finite groups acting as Galois groups? Therefore prime groups would map to prime HFFs and the inclusion hierarchies of Galois groups induced by composite polynomials would define inclusion hierarchies of HFFs just as speculated.

    One would have a deep connection between number theory and HFFs. This would also give a rather precise mathematical formulation of the number theoretic vision.

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

    Articles related to TGD.

Friday, August 12, 2022

Does the phenomenon of super oscillation challenge energy conservation?

The QuantaMagazine popular article "Puzzling Quantum Scenario Appears Not to Conserve Energy" (see this) told about puzzling observations the quantum physicists Sandu Popescu, Yakir Aharonov and Daniel Rohrlich made 1990 (see this). These findings challenge energy conservation at the level of quantum theory.

The experiment of authors starts from the purely mathematical observation that a function can behave faster than any of the Fourier components in its Fourier transform when restricted to a volume smaller than the domain of Fourier transform. This is rather obvious since representing the restricted function as a Fourier transform in the smaller domain one obtains faster Fourier components. This phenomenon is called super oscillation.

Does this phenomenon have a quantum counterpart? The naive replacement of Fourier coefficients with oscillation operators for photons need not make sense. If one makes the standard assumption that classical states correspond to coherent states, also super-oscillations should correspond to a coherent state.

Coherent states are eigenstates of the annihilation operator and proportional to exponential exp(α a)|0>, where "0" refers to the ground state an a to creation operator. These states contain N-photon states with an arbitrarily large photon number. For some number of photons the probability is maximum.

This raises several questions.

  1. Coherent states are not eigen-states of energy: can one really accept this? This kind of situation is encountered also in the model of superconductivity assuming coherent state of Cooper pairs having an ill-defined fermion number.
  2. Could the super oscillation correspond to the presence of N-photon states with a large number of photons? Could the state of n parallel photons behave like a Bose-Einstein condensate having N-fold total energy in standard physics or its modification, such as TGD?
Authors tested experimentally whether the super-oscillation has a quantum counterpart. In an ideal situation one would have a single photon inside an effectively 1-D box. One opens the box for time T and inserts a mirror inside the box to the region where super oscillation takes place and the photon looks like a short wavelength photon. The mirror reflects the photon with some probability out of the box. If T is long one expects that the procedure does not affect the photon appreciably. What was observed were photons with the energy of a super photon rather than energy of any of its low energy components.

In the experiment described in the popular article, red light would correspond to photons with energy around 2 eV and gamma rays to photons with energies around MeV, a million times higher energy. The first guess of standard quantum theorists would be that the energies of mirrored photons are the same as for the photons in the box. Second guess would be that, if the coherent state corresponds to the super oscillation as a classical state, then the measured high energy photons could correspond to or result from collinear n-photon states present in the coherent state.

In the TGD framework zero energy ontology (ZEO) provides a solution to the problem related to the conservation of energy. In ZEO, quantum states are replaced by zero energy states as pairs of states assignable to the boundaries of causal diamond (intersection of light-cones with opposite time directions) with opposite total quantum numbers. By Uncertainty Principle this is true for Poincare charges only at an infinite volume limit for the causal diamond but this has no practical consequences. The members of the pair are analogs of initial and final states of a particle reaction. In ZEO, it is possible to have a superposition of pairs for which the energy of the state at either boundary varies. In particular, coherent states have a representation which does not lead to problems with conservation laws.

What about the measurement outcome? The only explanation for the finding that I can invent in TGD is based on the hierarchy phases of ordinary matter labelled by effective Planck constants and behaving like a hierarchy of dark matter predicted by the number theoretical vision of TGD.

  1. Dark photons with heff= nh0 > h can be formed from ordinary photons with heff= h. The energy would be by a factor heff/h larger than for an ordinary photon with the same wavelength. Note that dark photons play a key role in the TGD based view of living matter.

    TGD also predicts dark N-photons as analogs of Bose-Einstein condensates. They are predicted by number theoretic TGD and there is empirical evidence for them (see this). This would require a new kind of interaction and number theoretical view about TGD predicts this kind of interaction based on the notion Galois confinement giving rise to N-photons as Galois confined bound states of virtual photons with energies give by algebraic integers for an extension of rationals defined by a polynomial defining the space-time region considered.

    I have proposed an analogous energy conserving transformation of dark photon or dark N-photon to ordinary photon as an explanation for the mysterious production of bio-photons in biomatter. The original model for dark photons is discussed here. Now the value of heff could be much larger: as large as heff ≈ 1014: in this case the wavelength would be of order Earth size scale.

  2. What comes to mind is that an N-photon state present in the coherent state can transform to a single photon state with N-fold energy. In the standard model this is not possible. On the other hand, in the experiments, discussed from the TGD point of view in here, it is found that N-photon states behaving like a single particle are produced. Could the N-photon states present in a coherent state be Galois confined bound states or could they transform to such states with some probability?

    In the recent case, the dark photons would have the same wavelength as red photons in the box but energy would be a million times higher. Could a dark photon or N-photon with Nheff/h ≈ 106 be reflected from the mirror and transform to an ordinary photon with gamma ray energy.

    One must notice that the real experiment must use many-photon states N-photons might be also formed from N separate photons.

To sum up, new physics would be involved. ZEO is needed to clarify the issues related to energy conservation and the number theoretic physics predicting dark matter hierarchy is needed to explain the observation of high energy photons.

See the article TGD and condensed matter of the chapter with the same title.

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

Articles related to TGD.

Wednesday, August 10, 2022

Chemical bonds as flux tube links and realization of dark codons using only dark protons

In the proposed model of dark DNA, one must assume that the dark codon is formed by a triplet of dark nucleons (proton and neutron). In the TGD framework one could justify the presence of neutrons by the large value of Planck constant increasing the weak scale to at least atomic length scale so that weak bosons would behave like massless particles in atomic scales at the MB. Therefore the dark protons could transform to dark neutrons easily. Neutron would be connected to either neighbor by a meson-like flux tube bond which is positively charged so that each codon would have a charge of 3 units neutralized by an opposite charge of 3 phosphates.

The introduction of neutrons brings in an additional bit. Therefore one could use only dark protons, if one could bring in this additional bit in some way. An obvious candidate would be the direction of a monopole magnetic flux assignable to the letter of the codon as a closed flux tube with respect to reference direction defined by the DNA sequence. If the letters of codon are closed linked flux tubes containing dark protons forming dark DNA as a chain, this kind of option might work. Consider first the topology of the monopole flux tubes.

  1. Magnetic monopole flux tubes correspond to closed 3-surfaces in the TGD framework. They are closed because the boundary conditions do not allow boundaries with a monopole charge nor boundaries at all. In dimension 3, these flux tubes can become knotted and closed flux tubes can get linked.
  2. If one has a braiding of N flux tubes, one can connect the ends of the N flux tubes. There are many manners to connect the ends, and one obtains at most N linked closed flux tubes, which are knots. The simplest option is that the ends of each braid strand are connected so that one has N linked flux tubes. This corresponds to the "upper" ends as a trivial permutation of the "lower" ends.
  3. Any permutation in the permutation group SN is possible. A given permutation can be expressed as a product of permutations such that each permutation leaves invariant a subset. Permutations are therefore characterized by a partition of N objects to subsets such that the given set consist of Ni objects with ∑ Ni=N and that these sets do not decompose to smaller subsets. The allowed permutations for Ni objects correspond to elements of the cyclic group ZNi. These cyclic permutations give rise to a single closed tube when the ends of the braid ends and permuted braid ends are connected. The number of closed flux tubes is therefore the number of summands in ∑ Ni=N. These permutations are obtained by reconnections from the permutation corresponding to N closed loops so that there are two levels: the level of braiding and the level of reconnections behind the stages not visible in the properties of the braiding.
Linking is a metaphor for bonding. One speaks of the chain of generations, of a weak link in the chain, etc.
  1. Chemical bonds are classified into ionic bonds, valence bonds involving delocalization of electrons, and hydrogen bonds involving delocalization of protons. Chemical bonds are not well-understood in the framework of standard chemistry. TGD suggests that they involve space-time topology: monopole flux tube pairs would be associated with the bonds and the splitting of the bond would correspond to a reconnection splitting the pair to two U-shaped flux tubes. Flux tubes and connecting molecules as nodes are proposed to form a network.
  2. I have not considered in detail how the U-shaped flux tubes are associated with the nodes. Bonding=linking metaphor encourages a crazy question. The members of the flux tube pairs, which are proposed to connect molecules, which serve as nodes of a network . These flux tubes must close and could be linked with shorter closed flux tubes assignable to molecules.
  3. Could this linking bind the molecules and atoms to a single topological structure. If so, both chemistry and topological quantum computation (TQC) in the TGD framework would involve linking, braiding, and reconnections as new topological elements. Biomatter at molecular level would consist of chains of closed flux tubes which can be also stretched and give rise to braids.

    Note that 2 U-shaped flux tubes can reconnect and this transition can lead to a pair of flux tubes or to a linked pair of U-shaped flux tubes so that 3 different states are possible.

  4. I have proposed that the pairing of molecules by a pair of monopole flux tubes serves as a correlate for entanglement. If dark protons are associated with closed flux tubes, they must entangle. Could also the linking of the U-shaped flux tubes give rise to entanglement? Stable linking correlates the positions of the flux tubes but this need not mean entanglement since wave function can be a product of wave functions in cm coordinates and relative coordinates.
Linking as an additional topological element inspires some quantum chemical and -biological speculations.
  1. Could the presence of valence-/hydrogen bonds involve a closed flux tube at which the electron (pair)/proton is delocalized and that this flux tube is linked with another such flux tube. This picture is consistent with the proposed role of quantum gravitation in metabolism (see this) and generation of the predecessor of the nervous system (see this) based on ver,y long variants of hydrogen bonds characterized by gravitational Planck constant. In this view, living matter would be an extremely highly organized structure whereas in the standard chemistry organism would be a soup of biomolecules.
  2. What comes to mind as an example, is the secondary structure of proteins (see this) involving α- helices, β-strands and β-sheets. Tertiary structure refers to 3-D structure created by a single protein molecule. It can have several domains. There are also quaternary structures formed by several polypeptide chains. Proteins consist of relatively few substructures known as domains, motives and folds. Could these structures involve braided and linked flux tube structures with dynamical reconnections?
Consider now a possible model of dark DNA involving only dark protons.
  1. One can imagine that dark protons are associated with closed flux tubes acting as hydrogen bonds, such that 3 closed flux tubes as letters are linked to form a dark codon. The dark codons could in turn be linked to form genes as sequences of codons. The direction of the magnetic flux can be opposite or parallel to that of the chain so that each closed flux tube represents a bit of topological information. The chains of links would define sequences of bits and even qubits. Could this define the predecessor of the genetic code for which letter represents a single bit?
  2. If one has only dark protons, one obtains only 32 dark codons. An additional bit is required to get 64 codons. Could the direction of the closed flux tube in the chain provide the missing bit?
It is known that the genetic code has a slightly broken symmetry with respect to the last letter of the codon. For almost all RNA codons U and C resp. A and G define code for the same amino-acid. An attractive interpretation of the symmetry is that this symmetry is that U-C pair and A-G pair correspond to the bits defined by magnetic flux so that the sign of magnetic flux would not matter much at the level of proteins. For this interpretation, the additional bit would not mean much at the level of proteins.

This need not be the case at the level of dark codons. In (see this) it was found that the earlier 1-1 correspondence between dark codons and ordinary genetic codons is unnecessarily strict and a modification of the earlier picture of the relation between dark and chemical genetic code and of the function of dark genetic code was considered.

  1. Dark DNA (DDNA) strand is dynamical and has the ordinary DNA strand associated with it and dark gene state can be in resonant interaction with ordinary gene only when it corresponds to the ordinary gene. This applies also to DRNA, DtRNA and DAA (AA is for amino acids).

    This would allow DDNA, DRNA, DtRNA and DAA to perform all kinds of information processing such as TQC by applying dark-dark resonance in quantum communications. The control of fundamental biomolecules by their dark counterparts by energy resonance would be only one particular function.

  2. Most importantly, flux tubes magnetization direction could define qubit. If the additional qubit corresponds to nucleon isospin, it is not clear whether this is the case. One can also allow superpositions of the dark genes representing 6-qubit units. A generalization of quantum computation so that it would use 6-qubits units instead of a single qubit as a unit, is highly suggestive.
  3. Genetic code code could be also interpreted as an error code in which dark proteins correspond to logical 6-qubits and the DNA codons coding for the protein correspond to the physical qubits associated with the logical qubit.
  4. The teleportation mechanism discussed in (see this) could make possible remote replication and remote transcription of DNA by sending the information about the ordinary DNA strand to the corresponding dark DNA strand by energy resonance. After that, the information would be teleported to a DNA strand in a ferromagnetic ground state at the receiver. After this, ordinary replication or transcription, which would also use the resonance mechanism, would take place.
See the article The Realization of Genetic Code in Terms of Dark Nucleon and Dark Photon Triplets or the chapter with the same title.

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

Articles related to TGD.

Tuesday, August 09, 2022

Ultradiffuse galaxies as a problem of cold dark matter and MOND scenarios

The existence of ultradiffuse galaxies for which the velocity of distant rotating stars is extremely low (see this), means difficulties for the cold dark matter scenario since in some cases there seems to be no dark matter at all, and in some cases there seems to be only dark matter. These objects has been proposed as a support for MOND, but also MOND has grave difficulties with them.

The problem in the case of galaxy AGC 114905 is(see this) is dcussed in a popular article "In a Wild Twist, Physicists Have Revived an Alternative Theory of Gravity" published in Science-Astronomy (this). This galaxy is of the same size as Milky Way and seems to have very small amount of dark matter, if any.

Mancera Pina et al (see this)argue that both cold dark matter scenario and MOND fail to explain the anomalously low value of the rotation velocity of distant stars. The proposal of Banik et al (see this) is that the inclination between the galactic disc and skyplane is overestimated, which leads to a too small estimate for the estimate for the rotation velocity so that MOND could be saved.

In the TGD framework (see this, this, and this), the rotation velocity is proportional to the square root of the product GT, where T is the string tension of a long magnetic flux tube formed from a cosmic string carrying dark energy and possibly also matter. In the ordinary situation, the flux tube would be considerably thickened only in a tangle associated with the galaxy as part of volume- and magnetic energies would have decayed to ordinary matter, in analogy with the decay of inflaton field.

If the flux tube itself has a very long thickened portion such that ordinary matter has left this region by free helical motion along the string or by gravitational attraction of some other object, the string tension T is small and very small velocity is possible. Ordinary bound state of matter is not necessary since the gravitational force of the flux tubes binds the stars. This might explain why the galaxy can be ultradiffuse.

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

Articles related to TGD.

Is pair creation really understood in the twistorial picture?

Twistorialization leads to a beautiful picture about scattering amplitudes at the level of M8 (see this). In the simplest picture, scattering would be just a re-organization of Galois singlets to new Galois singlets. Fundamental fermions would move as free particles.

The components of the 4-momentum of virtual fundamental fermion with mass m would be algebraic integers and therefore complex. The real projection of 4-momentum would be mapped by M8-H duality to a geodesic of M4 starting from either vertex of the causal diamond (CD) . Uncertainty Principle at classical level requires inversion so that one has a= ℏeff/m, where ab denotes light-cone proper time assignable to either half-cone of CD and m is the mass assignable to the point of the mass shell H3⊂ M4⊂ M8.

The geodesic would intersect the a=ℏeff/m 3-surface and also other mass shells and the opposite light-cone boundaries of CDs involved. The mass shells and CDs containing them would have a common center but Uncertainty Principle at quantum level requires that for each CD and its contents there is an analog of plane wave in CD cm degrees of freedom.

One can however criticize this framework. Does it really allow us to understand pair creation at the level of the space-time surfaces X4⊂ H?

  1. All elementary particles consist of fundamental fermions in the proposed picture. Conservation of fermion number allows pair creation occurring for instance in the emission of a boson as fermion-antifermion pair in f→ f+b vertex.
  2. The problem is that if only non-space-like geodesics of H are allowed, both fermion and antifermion numbers are conserved separately so that pair creation does not look possible. Pair creation is both the central idea and source of divergence problems in QFTs.
  3. One can identify also a second problem: what are the anticommutation relations for the fermionic oscillator operators labelled by tachyonic and complex valued momenta? Is it possible to analytically continue the anticommutators to complexified M4⊂ H and M4⊂ M8? Only the first problem will be considered in the following.
Is it possible to understand pair creation in the proposed picture based on twistor scattering amplitudes or should one somehow bring the bff 3-vertex or actually ff fbar fbar vertex to the theory at the level of quark lines? This vertex leads to a non-renormalizable theory and is out of consideration.

One can first try to identify the key ingredients of the possible solution of the problem.

  1. Crossing symmetry is fundamental in QFTs and also in TGD. For non-trivial scattering amplitudes, crossing moves particles between initial and final states. How should one define the crossing at the space-time level in the TGD framework? What could the transfer of the end of a geodesic line at the boundary of CDs to the opposite boundary mean geometrically?
  2. At the level of H, particles have CP2 type extremals - wormhole contacts - as building bricks. They have an Euclidean signature (of the induced metric) and connect two space-time sheets with a Minkowskian signature.

    The opposite throats of the wormhole contacts correspond to the boundaries between Euclidean and Minkowskian regions and their orbits are light-like. Their light-like boundaries, orbits of partonic 2-surfaces, are assumed to carry fundamental fermions. Partonic orbits allow light-like geodesics as possible representation of massless fundamental fermions.

    Elementary particles consist of at least two wormhole contacts. This is necessary because the wormhole contacts behave like Kähler magnetic charges and one must have closed magnetic field lines. At both space-time sheets, the particle could look like a monopole pair.

  3. The generalization of the particle concept allows a geometric realization of vertices. At a given space-time sheet a diagram involving a topological 3-vertex would correspond to 3 light-like partonic orbits meeting at the partonic 2-surface located in the interior of X4. Could the topological 3-vertex be enough to avoid the introduction of the 4-fermion vertex?
Could one modify the definition of the particle line as a geodesic of H to a geodesic of the space-time surface X4 so that the classical interactions at the space-time surface would make it possible to describe pair creation without introducing a 4-fermion vertex? Could the creation of a fermion pair mean that a virtual fundamental fermion moving along a space-like geodesics of a wormhole throat turns backwards in time at the partonic 3-vertex. If this is the case, it would correspond to a tachyon. Indeed, in M8 picture tachyons are building bricks of physical particles identified as Galois singlets.
  1. If fundamental fermion lines are geodesics at the light-like partonic orbits, they can be light-like but are space-like if there is motion in transversal degrees of freedom.
  2. Consider a geodesic carrying a fundamental fermion, starting from a partonic 2-surface at either light-like boundary of CD. As a free fermion, it would propagate to the opposite boundary of CD along the wormhole throat.

    What happens if the fermion goes through a topological 3-vertex? Could it turn backwards in time at the vertex by transforming first to a space-like geodesic inside the wormhole contact leading to the opposite throat and return back to the original boundary of CD? It could return along the opposite throat or the throat of a second wormhole contact emerging from the 3-vertex. Could this kind of process be regarded as a bifurcation so that it would correspond to a classical non-determinism as a correlate of quantum non-determinism?

  3. It is not clear whether one can assign a conserved space-like M4 momentum to the geodesics at the partonic orbits. It is not possible to assign to the partonic 2-orbit a 3-momentum, which would be well-defined in the Noether sense but the component of momentum in the light-like direction would be well-defined and non-vanishing.

    By Lorentz invariance, the definition of conserved mass squared as an eigenvalue of d'Alembertian could be possible. For light-like 3-surfaces the d'Alembertian reduces to the d'Alembertian for the Euclidean partonic 2-surface having only non-positive eigenvalues. If this process is possible and conserves M4 mass squared, the geodesic must be space-like and therefore tachyonic.

    The non-conservation of M4 momentum at single particle level (but not classically at n-particle level) would be due to the interaction with the classical fields.

  4. In the M8 picture, tachyons are unavoidable since there is no reason why the roots of the polynomials with integer coefficients could not correspond to negative and even complex mass squared values. Could the tachyonic real parts of mass squared values at M8 level, correspond to tachyonic geodesics along wormhole throats possibly returning backwards along the another wormhole throat?
How does this picture relate to p-adic thermodynamics (see this) as a description of particle massivation?
  1. The description of massivation in terms of p-adic thermodynamics suggests that at the fundamental level massive particles involve non-observable tachyonic contribution to the mass squared assignable to the wormhole contact, which cancels the non-tachyonic contribution.

    All articles, and for the most general option all quantum states could be massless in this sense, and the massivation would be due the restriction of the consideration to the non-tachyonic part of the mass squared assignable to the Minkowskian regions of X4.

  2. p-Adic thermodynamics would describe the tachyonic part of the state as "environment" in terms of the density matrix dictated to a high degree by conformal invariance, which this description would break. A generalization of the blackhole entropy applying to any system emerges and the interpretation for the fact that blackhole entropy is proportional to mass squared. Also gauge bosons and Higgs as fermion-antifermion pairs would involve the tachyonic contribution and would be massless in the fundamental description.
  3. This could solve a possible and old problem related to massless spin 1 bosons. If they consist of a collinear fermion and antifermion, which are massless, they have a vanishing helicity and would be scalars, because the fermion and antifermion with parallel momenta have opposite helicities. If the fermion and antifermion are antiparallel, the boson has correct helicity but is massive.

    Massivation could solve the problem and p-adic thermodynamics indeed predicts that even photons have a very small thermal mass. Massless gauge bosons (and particles in general) would be possible in the sense that the positive mass squared is compensated by equally small tachyonic contribution.

  4. It should be noted however that the roots of the polynomials in M8 can also correspond to energies of massless states. This phase would be analogous to the Higgs=0 phase. In this phase, Galois symmetries would not be broken: for the massive phase Galois group permutes different mass shells (and different a=constant hyperboloids) and one must restrict Galois symmetries to the isotropy group of a given root. In the massless phase, Galois symmetries permute different massless momenta and no symmetry breaking takes place.
See the article About TGD counterparts of twistor amplitudes: part II or the chapter About TGD counterparts of twistor amplitudes.

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

Articles related to TGD.

Monday, August 08, 2022

Universe as a dodecahedron?: two decades later

I encountered a link to a popular article in Physics World with the title "Is the Universe a dodecahedron" (see this) telling about the proposal of Luminet et al that the Universe has a geometry of dodecahedron. I have commented on this finding almost 20 years ago (see this). A lot has happened during these two decades and it is interesting to take a fresh TGD inspired view.

In the TGD framework, one can imagine two starting points concerning the explanation of the findings.

  1. Could there be a connection with the redshift quantization along some lines ("God's fingers"") proposed by Halton Arp (see this) and Fang-Sato. I have considered several explanations for the quantization. In TGD cosmic=time constant surface corresponds to hyperbolic 3-space H3 of Minkowski space in TGD. H3 allows an infinite number of tessellations (lattice-like structures).

    I have proposed an explanation for the redshift quantization in terms of tessellations of H3. The magnetic bodies (MBs) of astrophysical objects and even objects themselves could tend to locate at the unit cells of the tessellation.

  2. Icosa-tetrahedral tessellation (lattice-like structure in hyperbolic space H3) plays a key role in the TGD model of genetic code (see this) suggested to be universal. Lattice-like structures make possible diffraction if the incoming light has a wavelength, which is of the same order as the size of the unit cell.
In the sequel I will consider only the latter option.
  1. In X ray diffraction, the diffraction pattern reflects the structure of the dual lattice: the same should be true now. Only the symmetries of the unit cell are reflected in diffraction. If CMB is diffracted in the tessellation, the diffraction pattern reflects the symmetries of the dual of the tessellation and does not depend on the value of the effective Planck constant heff. Large values of Planck constant make possible large crystal-like structures realized as part of the magnetic body having large enough size, now realized at the magnetic body (MB).
  2. Icosatetrahedral tessellation plays a key role in the TGD inspired model of the genetic code. Dodecahedron is the dual of icosahedron and tetrahedron is self-dual! [Note however that also the octahedron is involved with the unit cell although "icosa-tetrahedral" does not reflect its presence. Cube is the dual of the octahedron.]

    So: could the gravitational diffraction of CMB on a local crystal having the structure of icosa-tetrahedral tessellation create the illusion that the Universe is a dodecahedron?

Could the possible dark part of the CMB radiation diffract in local tessellations assigned with the local MBs?
  1. In diffraction, the wavelength of diffracted radiation must correspond to the size of the unit cell of the lattice-like structure involved. The maximum wavelength of CMB intensity as function of wavelength corresponds to a wavelength of about .5 cm. Can one imagine a tessellation with the unit cell of size about .5 cm?
  2. The gravitational Planck constant ℏgr =GMm/β0, where M is large mass and m a small mass, say proton mass (see this, this, this, this and this). Both masses are assignable to the monopole flux tubes mediating gravitational interaction. β0=v0/c is velocity parameter and near to unity in the case of Earth.
  3. The size scale of the unit cell of the dark gravitational crystal would be naturally given by Λgr = ℏgr/m= GM/β0 and would be depend on M only and would be rather large and depend on the local large mass M, say that of Earth. Λgr does not depend on m (Equivalence Principle).
  4. For Earth, the size scale of the unit cell would be of the order of Λgr= GME0 ≈ .45 cm, where β0= 0=v0/c ≈ 1 is near unity from the experimental inputs emerging from quantum hydrodynamics (see this) and quantum model of EEG (see this) and quantum gravitational model for metabolism (see this and this). Λgr could define the size of the unit cell of the icosa-tetrahedral tessellation. Note that Earth's Schwartschild radius rS=2GM≈ .9 cm.

    Encouragingly, the wavelength of CMB intensity as a function of wavelength around .5 cm to be compared with Λgr ≈ .45 cm! Quantum gravitational diffraction might take place for dark CMB and give rise to the diffraction peaks!

  5. Diffraction pattern would reflect astroscopic quantum coherence, and the findings of Luminet et al could have an explanation in terms of the geometry of local gravitational MB rather than the geometry of the Universe! Diffraction could also explain the strange deviations of CMB correlation functions from predictions for large values of the angular distance. It might be also possible to understand the finding that CMB seems to depend on the features of the local environment of Earth, which is in a sharp conflict with the cosmological principle. According to Wikipedia article (see this), even in the COBE map, it was observed that the quadrupole (l=2, spherical harmonic) has a low amplitude compared to the predictions of the Big Bang. In particular, the quadrupole and octupole (l=3) modes appear to have an unexplained alignment with each other and with both the ecliptic plane and equinoxes.
  6. Could the CMB photon transform to a gravitationally dark photon in the diffraction? This would be a reversal for the transformation of dark photons to ordinary photons interpreted as biophotons. Also in quantum biology the transformation of ordinary photons to dark ones takes place. If so the wave length for a given CMB photon would be scaled up by the factor ℏgr/ℏ =(GMEm/β0)/ℏ ≈ 3.5× 1012 for proton. This gives Λ=1.75 × 107 km, to be compared with the radius of Earth about 6.4× 106 km.
See the chapter TGD and cosmology.

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

Articles related to TGD

Thursday, August 04, 2022

Antipodal duality and TGD

The so called antipodal duality has received considerable attention. The calculations of Dixon et al based on the earlier calculations of Goncharow et al suggests a new kind of duality relating color and electroweak interactions. The calculations lead to an explicit formula for the loop contributions to the 6-gluon scattering amplitude in N=4 SUSY. The new duality and relates 6-gluon amplitude for the forward scattering to a 3-gluon form factor of stress tensor analogous to a quantum field describing a scalar particle. This amplitude can be identified as a contribution to the scattering amplitude h+g→ g+g at the soft limit when the stress tensor particle scatters in forward direction. The result is somewhat mysterious since in the standard model strong and electroweak interactions are completely separate.

In TGD, there are indeed quite a number of pieces of evidence for this kind of duality but the possibility that only electroweak or color interactions could provide a full description of scattering amplitudes. The number-theoretical view of TGD could however come into rescue.

See the article Antipodal duality and TGD or the chapter About TGD counterparts of twistor amplitudes.

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

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Wednesday, August 03, 2022

Quantization of cosmic redshifts in the TGD framework

In a FB discussion Jivan Coquat asked for my opinion about Halton Arp (see this).

Halton Arp brings to my mind redshift quantization along lines, which has been considered also by Fang-Sato, who talked of "God's fingers". I have considered several explanations for the quantization.

  1. To my opinion, the most convincing explanation is in terms of lattice-like structures, tessellations, in hyperbolic space H3, which corresponds to cosmic time a= constant hyperboloid of future light-one (see this).
  2. H3 allows an infinite number of tessellations, which correspond to discrete subgroups of Lorentz group SO(1,3) having as covering SL(2,C) (spinors). In E3 only 17 lattices are possible. The so called icosa-tetrahedral tessellation is in a key role in TGD model of genetic code realized at a deeper level in terms of dark (heff=nh0>h) proton triplets and flux tubes of magnetic body (see this).
  3. For lattices in the Euclidean space E3, the radial distance from origin is quantized. For H3 redshift proportional to H3 distance replaces Euclidian radial distance and the tessellation gives redshift quantization. Astrophysical objects would tend to be associated with the unit cells of the tessellation.
  4. The tessellation itself could be associated with the magnetic (/field) body carrying dark matter in the TGD sense as heff=nh0>h phases: this is a prediction of number theoretic vision about physics as dual of geometric vision. Very large values of heff =hgr= GMm/v0 (Nottale hypothesis for gravitational Planck constant, see this) assignable to gravitational flux tubes are possible, and this makes these tessellations possible as gravitationally quantum coherent structures even in cosmological scales. This is a diametric opposite to what superstring models where quantum gravitation appears only in Planck length scale, suggests.
See the chapter (see Quantum Theory of Self-Organization.

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

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The mysterious precession of the Earth's spin axis from the TGD point of view

These comments were inspired by two interesting Youtube videos by Sören Backman (see this and this) with a provocative title "Gravity's biggest failure - precession, what is it hiding". The precession of the Earth's spin axis cannot be explained as an effect caused by other planets and Sun and even the nearest stars are too far in order to explain the precession as an effect caused by them. Precession is therefore a real problem for the standard view of gravitation.

The proposal for the explanation of the precession of Earth discussed in the videos is inspired by the notion of Electric Universe, and has several similarities with the TGD inspired model. I could expect this from my earlier discussions with the proponents of Electric Universe. About 3 years ago, I wrote a chapter inspired by these discussions (see this).

My view is that the extremist view that gravitation reduces to electromagnetism is wrong but that electromagnetism, in particular magnetic fields, have an important role even in cosmological scales. In standard physics, magnetic fields in long scales would require coherent currents, which tend to be random and dissipate. Even the understanding of the stability of the magnetic field of Earth is a challenge, to say nothing of the magnetic fields able to survive in cosmological scales. In TGD, monopole flux tubes define magnetic fields which need no currents as sources.

Consider first monopole flux tubes, which are present in all length scales in the TGD Universe and distinguish TGD from both Maxwell's electrodynamics and general relativity.

  1. Flux tubes can carry monopole flux, in which case they are highly stable. The cross section is not a disk but a closed 2-surface so that no current is needed to create the magnetic flux. The flux tubes with vanishing flux are not stable against splitting.
  2. Flux tubes relate to the model for the emergence of galaxies (see this and this) and explain galactic jets propagating along flux tubes (see this). Dark energy and possible matter assignable to the cosmic strings predicts correctly the flat velocity spectrum of stars around galaxies.
  3. In the MOND model it is assumed that the gravitational force transforms for certain critical acceleration from 1/r2 to 1/r force. In TGD this would mean that the 1/ρ forces caused by the cosmic string would begin to dominate over the 1/rho2 force. The predictions of MOND TGD are different since in TGD the motion takes place in the plane orthogonal to the cosmic string.
  4. The flux tubes can appear as torus-like circular loops. Also flux tube pairs carrying opposite fluxes, resembling a DNA double strand, are possible and might be favoured by stability. Flux tubes are possible in all scales and connect astrophysical structures to a fractal quantum network. The flux tubes could connect to each other nodes, which are deformations of membrane-like entities having 3-D M4 projections and 2-D E3 projections (time= constant) (also an example of "non-Einsteinian" space-time surface).
  5. Pairs of monopole flux tubes with opposite direction of fluxes can connect two objects: this could serve as a prerequisite of entanglement. The splitting of a flux tube pair to a pair of U-shaped flux tubes by a reconnection in a state function reduction destroying the entanglement. Reconnection would play an essential role in bio-catalysis.
  6. Flux tube pairs can form helical structures and stability probably requires helical structure. Cosmic analog of DNA could be in question: fractality and gravitational quantum coherence in arbitrarily long scales are a basic prediction of TGD so that monopole flux tubes should appear in all scales. Also flux tubes inside flux tubes inside and hierarchical coilings as for DNA are possible.
A possible TGD inspired solution of the precession problem relies on the TGD view about the formation of galaxies and stellar systems.
  1. Just like galaxies, also the stellar systems would have been formed as local tangles of a long monopole flux tube (thickened cosmic string), which itself could be part of or have been reconnected from a tangle of flux tube giving rise to the galaxy. The thickening liberates dark energy of cosmic strings and gives rise to the ordinary matter and is the TGD counterpart of inflation involving no inflaton fields.
  2. In the same way as galaxies, stellar systems would be like pearls along string. This predicts correlations in the dynamics and positions of distant stars and galaxies and there is evidence for these correlations.
  3. The flux tubes could connect the solar system to some distant stellar system. A good candidate for this kind of system is Pleiades, a star cluster located at a distance of 444 light years (the nearest star has a distance of 4 light years). There would also be an analog of solar wind along this flux tube giving for the solar magnetosphere a bullet-like shape.
  4. The transversal gravitational force of the flux tube would cause the precession of the solar system around the flux tube. The entire solar system, as a tangle of the flux tube, would precess like a bullet-like top around the direction of this flux tube. The details of this picture are discussed in this and this .
  5. The TGD analogs of Birkeland currents and the analogy of solar wind would flow along the monopole flux tubes, perhaps as dark particles in the TGD sense, that is having effective Planck constant heff=nh0 which can be much larger than h, even so large that gravitational quantum coherence is possible in astrophysical and even cosmological scales.
See the the chapter TGD and astrophysics.

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

Articles related to TGD.

MOND and TGD view of dark matter

The TGD based model explains the MOND (Modified Newton Dynamics) model of Milgrom for the dark matter. Instead of dark matter, the model assumes a modification of Newton's laws. The model is based on the observation that the transition to a constant velocity spectrum in the galactic halos seems to occur at a constant value of the stellar acceleration equal to acr =about 10-11g, where g is the gravitational acceleration at the Earth. MOND theory assumes that Newtonian laws are modified below acr.
  1. In TGD, dark energy plus magnetic energy would be associated with cosmic strings, which are "non-Einsteinian" 4-surfaces of M4× CP2 with 2-D M4 projection. Cosmic strings are unstable agains thickening of the M4 projection so that one obtains Einsteinian monopole flux tube.

    In accordance with the observations of Zeldovich, galaxies would correspond to tangles along a long cosmic string at which the string has thickened and liberated its energy as ordinary matter (TGD counterpart for the decay of the inflaton field). The flux tubes create 1/ρ type gravitational field orthogonal to string and this gives rise to the observed flat velocity spectrum (see this, this, and this).

  2. In MOND theory, it is assumed that gravitation starts to behave differently when it becomes very weak and predicts the critical acceleration. In the TGD framework, the critical acceleration would be of the same order of magnitude as the acceleration created by the gravitational field of the cosmic string and would also define a critical distance depending only on the string tension.
  3. If 1/r2 changes to 1/r in MOND, model one obtains the same predictions as in TGD for the planar orbits orthogonal to the long string along which galaxies correspond to a flux tube tangled. The models are not equivalent. In TGD, general orbit corresponds to a helical motion of the star along the cosmic string so that the concentration on a preferred plane is predicted. This has been recently reported as an anomaly of dark matter models (see this).
  4. The critical acceleration predicted would correspond to acceleration of the same order of magnitude as the acceleration caused by cosmic string. From M2/Rcr= GM/R2cr= TG/Rcr (assuming that dark matter dominates) one obtains the estimate Rcr=M/T and acr =GT2/M, where M is the visible mass of the object - for instance the ordinary matter of a galaxy. If critical acceleration is always the same, one would have T=(acrM/G)1/2 so that the visible mass would scale like M∝ T2 if acr is constant of Nature.

See the chapter TGD and astrophysics.

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

Articles related to TGD