TGD view of the gravitational hum as gravitational diffraction

The revolution in cosmology is continuing. The latest breakthrough was announced yesterday (see this). See also the popular article. There is a collection of articles related to the discovery.

The dicovery

Scientists from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) have now officially made the first detections of the gravitational wave background. This gravitational hum was not detected by Earth bound instruments.

The wavelength of the oscillations makes itself visible as correlations between the variations of the spinning  rates  for pulsars having relative  distances measured using a light year as a unit.   The wavelength of the oscillations is measured in light years. In the LIGO experiment  the  periods are measured as fractions of a second.  

Where could this length scale come from? What might make bells ringing is that the star nearest to the Sun is at a distance of 4 light years and the typical distance between stars is 5 light years.

Near to the end of the talk also the wavelength scale of millions of light years is mentioned. This scale corresponds to a typical distance between galaxies, which is few Mpc, pc= 3.26 ly.

Remark: I am grateful to Marko Manninen for noticing a rather stupid mistake: I talked about a period of millions of light years for the detected gravitational radiation. The period is of course a few years as is obvious from the fact that it is not easy to find graduate students able to stay motivated for millions of years.

The unexpectedly large amplitude of the oscillations motivates the hypothesis that pairs of galactic supermassive blackholes or interacting groups of them could generate the gravitational hum. There are candidates for these pairs but no established pair. The group hypothesis seems to work better.

TGD explanation in terms of astrophysical gravitational quantum coherence and diffraction in hyperbolic tesselation

TGD suggests a radically different hypothesis based on TGD view of gravitational quantum coherence an diffraction in a hyperbolic tessellation.

1. TGD predicts quantum gravitational coherence in astrophysical scales characterized by gravitational Planck constants h_gr = GMm/β₀ characterizing big mass M and small mass m. β₀=v₀/c<1 is a velocity parameter. The Equivalence Principle is realized as the independence of the gravitational Compton length Λ_gr= GM/β₀= r_s/2β₀ on mass m.
   1. For the Sun Λ_gr is 1/2 of Earth radius. If the TGD proposal, which explains Cambrian explosion in terms of rapid increase of the Earth radius by factor 2, this scale is the radius of Earth before the explosion (see this).
   2. For the Earth Λ_gr is .45 cm and the size scale of a snowflake, which is a zoomed version of the unit cell of the ice crystal: a fact which still remains a mystery.
   3. For the galactic black hole, Λ_gr is about 1.2×10⁷ km=1.2× 10^-2 light seconds and corresponds to a frequency of about 100 Hz, the upper bound of EEG frequencies by the way (which might put bells ringing!). For β₀=1 Λ_gr happens to correspond to the radius of the lowest Bohr orbit for Sun Λ_gr in Bohr orbit model for planetary orbit (another bell ringing!) and defines only a lower bound for the quantum coherence scale.
2. Where could the wavelength of order of distance between neighboring stars emerge? TGD strongly suggests that the tessellations (lattices) associated with hyperbolic 3-space identified light-cone proper time a= constant surface play a key role in all scales, in particular in biology.

   There could exist a fractal hierarchy of hyperbolic tessellations (see this) formed by astrophysical objects of various mass scales. Could the stars with average distance of 5 light years form tessellations of this kind analogous to lattices in a condensed matter system. The wavelength for the diffracted gravitational waves in cubic tessellation would have the upper bound 2d, d the lattice constant, which would be now about 5 light years.

3. There is empirical evidence for these tessellations. So called cosmic fingers, discovered by Halton Arp (see this or this), correspond to astrophysical objects appearing at single light of sight (first mystery) and having redshift coming as multiples of a basic redshift (second mystery). This could serve as a direct signature of the hyperbolic counterpart for a line of atoms located along a lattice. Redshift is proportional to distance and also to the recession velocity, which would therefore be quantized in the observed manner.
4. What kind of tessellations could be involved? There is an infinite number of tessellations for H³ but only 4 regular uniform honeycombs. For two of these the unit cell is a dodecahedron, for 1 of them it is an icosahedron and for 1 of them it is a cube. Note that in Euclidian 3-space one has just one regular honeycomb consisting of cubes.

   There are also more general uniform honeycombs involving several cell types. There is a unique "multicellular" honeycomb for which all cells are Platonic solids. This is icosatetrahedral (or more officially, tetrahedral-icosatetrahedral) honeycomb for which the cells are tetrahedrons, octahedrons, and icosahedrons (see this). All faces are triangles and I have proposed a universal realization of genetic code in which genetic codons correspond to the triangular faces of icosahedra an tetrahedra (see this).

The key prediction is gravitational diffraction in this cosmic lattice.

1. In diffraction in the lattice the diffracted amplitude concentrates in specific directions corresponding to the reciprocal lattice. Something analogous should happen for tessellations in hyperbolic 3-space. Already the concentration to beams would mean an amplification effect (note that the lowest order prediction for the intensity of the radiation does not depend on the value of the effective Planck constant).

   Furthermore, by quantum coherence the scattered amplitude is proportional to N² rather than N, where N is the number of atoms in the lattice, now stars in the tessellation. Could these two amplification effects explain why the observed effect is so much larger than expected? Professionals could easily find whether this idea fails at the quantitative level.

   TGD view suggests that the dark gravitational radiation propagates along the monopole flux tubes connecting stars.

2. In the ordinary diffraction from a cubic lattice in Euclidian space E³, the condition of constructive interference for the two rays scattered from to neighboring points of the cubic lattice states, requires that the difference of lengths for the paths travelled is a multiple of the wavelength of the incoming radiation. This gives the Bragg condition: sin(θ)= nλ/2d, where θ is the glance angle defined as the angle of incoming ray with respect to the normal direction of the lattice plane. The condition gives λ <2d/n and implies λ <2d for n=1. Therefore the diffraction occurs only for frequencies ω > nω_n, ω_n>c/2d.

   In the case of gravitational radiation, this would give for a cubic lattice λ<2d/n, d ≈ 5 light years, which conforms with the scale of few years for the periods. The lower bound for the period T would be about T_min=10 years. The condition that the scattered beams connect lattice points, gives an additional quantization condition to the glance angle θ. Most naturally it would correspond to a line connecting lattice points.

See the for instance the articles Magnetic Bubbles in TGD Universe: Part I and Magnetic Bubbles in TGD Universe: Part II.

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

Clumpiness paradox of cold dark matter scenario from the TGD point of view

Clumpiness paradox is one of the many problems plaguing the cold dark matter scenario (see this).

Clumpiness parameter (see this) is in principle deducible from the weak gravitational lensing caused by dark matter. In halo models it affects the annihilation rate of dark matter particles. Since the predicted rate is proportional to mass density squared, the annihilation rate increases for clumpy mass distribution.

If I understand correctly, the clumpiness paradox states that the clumpiness, which is determined by the size of dark matter clumps, depends on the scale in which observations are carried out. Clumpiness is smaller in long length scales, which means that the observed clumps are larger in long scales. In long scales, corresponding to recent cosmology, the sizes of clumps assignable are larger and the clumpiness parameter is .83. In shorter length scales corresponding to the age of the Universe about 380 thousand years the clumpiness parameter is smaller: .76.

In long length scales, a proposed explanation for the small value of clumpiness, i.e. a large size of clumps, is in terms of identification of dark matter as ultralight axions with very large Compton length determining the size scale of clumps.

This does not explain why the clumpiness depends on scale. Furthermore, clumps have been now observed in considerably smaller scales than earlier (see this). The strange looking conclusion is that cold dark matter is colder in short scales: the naive expectation would be just the opposite since it is the hot dark matter particles, which should form only small clumps. Something seems to go wrong.

The clumpiness paradox suggests a fractal distribution of dark matter. Indeed, in the TGD framework, cosmic strings thickened to monopole flux tubes would be responsible for gravitational lensing and the thickness of the monopole flux tubes would characterize the lensing.

The explanation for the large size of the clumps in long scales would be the large size of the Compton length proportional to effective Planck constant h_eff=nh₀. In the case of gravitational Planck constant h_eff= h_gr= GMm/β₀, β₀ a velocity parameter, assignable to the monopole flux tubes connecting pairs formed by a large mass M and small mass m, the gravitational Compton length is equal to Λ_gr= GM/β₀= r_s/2β₀, r_s Schwartshild radius of M increasing with the size scale of structure (note that there is no dependence on m). The larger the scale of the studied astrophysical object, the larger Λ_gr as minimal gravitational quantum coherence length is, and the smaller the clumpiness in this scale.

See the articles Magnetic Bubbles in TGD Universe: Part I, Magnetic Bubbles in TGD Universe: Part II and TGD view of the paradoxical findings of the James Webb telescope.

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

James Webb telescope suggests a possible mechanism for how Universe became transparent

I received a link to a very interesting article titled "JWST Unveils How Galaxies Made the Universe Transparent: A Cosmic Mystery Solved!" (see this).

The analysis of the findings of Jame Webb Telescope lead to the conclusion that some galaxies would have been surrounded by bubbles of ionized hydrogen  with a radius of millions of light years (analogous with Fermi bubbles having a size scale of 50,000 light years?). They would have expanded and merged. But why only some galaxies?

TGD  suggests a fractal network formed by gravitational flux tubes connecting astrophysical objects and  carrying dark matter with a huge value of gravitational Planck constant ℏ_gr= GMm/β₀, where β₀=v₀/c ≤1  is a velocity parameter and the large mass M an small mass m are connected by  gravitational monopole flux tubes.

The large value of ℏ_gr  makes  possible gravitational quantum coherence possible in astrophysical scales.  Dark photon radiation would have propagated along the flux tubes and transformed to ordinary photons  in detection making the early Universe visible. Cosmos would be like a network of candles connected by electric wires in a Christmas tree (see this).

But why would the flux tubes be associated only with the  galaxies having the ionized bubbles? Is this necessary? If these ionized bubbles w ere present, were  they formed as analogs of Fermi bubbles in the collisions  of very long cosmic strings?

Cosmic strings are 4-D surfaces X²× Y² ⊂ H= M⁴ × CP2, which are unstable against the thickening of their 2-D Minkowski space projection X². In a collision of  very long  cosmic strings,  portions of colliding cosmic strings  thickened and   dark energy was  transformed to ordinary   and dark matter (this is an analog of inflaton decay). Therefore  a flux tube spaghetti giving rise to a galaxy would have formed.  If all galaxies were formed in this way, all of them would have an ionized bubble. Did most of the galaxies  emerge in some other way?

I have proposed that very  astrophysical objects could have  formed in explosions (mini Big Bangs) throwing out magnetic bubbles  consisting of gravitational flux tubes. They would be  involved with the thickenings of the cosmic strings and flux tubes. Also radial flux tubes mediating gravitational interaction would be present.

See the articles Magnetic Bubbles in TGD Universe: Part I, Magnetic Bubbles in TGD Universe: Part II and TGD view of the paradoxical findings of the James Webb telescope.

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

Master formula for the scattering amplitudes: finally?

Most pieces that have been identified over the years in order to develop a master formula for the scattering amplitudes are as such more or less correct but always partially misunderstood. Maybe the time is finally ripe for the fusion of these pieces to a single coherent whole. I will try to list the pieces into a story in the following.

1. The vacuum functional, which is the exponential Kähler function defined by the classical bosonic action defining the preferred extremal a an analog of Bohr orbit, is the starting point. Physically, the Kähler function corresponds to the bosonic action (e.g. EYM) in field theories.

   Because holography is almost unique, it replaces the path integral by a sum over 4-D Bohr trajectories as functional integral over 3-surfaces plus discrete sum.

2. However, the fermionic part of the action is missing. I have proposed a long time ago a super symmetrization of WCW K hler function by adding to it what I call modified Dirac action. It relies on modified gamma matrices modified gamma matrices Γ^α, which are contractions Γ_kT^{α k} of H gamma matrices Γ_k with the canonical momentum currents T= ∂ L/∂_∂αh^k defined by the Lagrangian L. Modified Dirac action is therefore determined by the bosonic action from the requirement of supersymmetry. This supersymmetry is however quite different from the SUSY associated with the standard model and it assigns to fermonic Noether currents their super counterparts.

   Bosonic field equations for the space-time surface actually follow as hermiticity conditions for the modified Dirac equation. These equations also guarantee the conservation of fermion number(s). The overall super symmetrized action that defines super symmetrized Kähler function in WCW would be unambiguous. One would get exactly the same master formula as in quantum field theories, but without the path integral.

3. The overall super symmetrized action is sum of contributions assignable to the space-time surface itself, its 3-D light-like parton orbits as boundaries between Minkowskian regions and Euclidian wormhole contact, 2-D string world sheets and their 1-D boundaries as orbits of point-like fermions. These 1-D boundaries are the most important and analogous to the lines of ordinary Feynman diagrams. One obtains a dimensional hierarchy.
4. One can assign to these objects of varying dimension actions defined in terms of the induced geometry and spinor structure. The supersymmetric actions for the preferred extremals analogous to Bohr orbit in turn give contributions to the super symmetrized Kähler function as an analogue of the YM action so that, apart from the reduction of path integral to a sum over 4-D Bohr orbits, there is a very close analogy with the standard quantum field theory.

However, some problems are encountered.

1. It seems natural to assume that a modified Dirac equation holds true. I have presented an argument for how it indeed emerges from the induction for the second quantized spinor field in H restricted to the space-time surface assuming modified Dirac action.

   The problem is, however, that the fermionic action, which should define vertex for fermion pair creation, disappears completely if Dirac's equation holds everywhere! One would not obtain interaction vertices in which pairs of fermions arise from classical induced fields. Something goes wrong.

2. If one gives up the modified Dirac equation, the fermionic action does not disappear? In this case, one should construct a Dirac propagator for the modified Dirac operator. This is an impossible task in practice.

   Moreover, the construction of the propagator is not even necessary and in conflict with the fact that the induced spinor fields are second quantized spinors of H restricted to the space-time surface and the propagators are therefore well-defined and calculable and define the propagation at the space-time surface.

   Should we conclude that the modified Dirac equation cannot hold everywhere? What these, presumably lower-dimensional regions of space-time surface, are and could they give the interaction vertices as topological vertices?

The key question is how to obtain emission of fermion pairs and bosons as their bound states?

1. I have previously derived a topological description for reaction vertices. The fundamental 1 → 2 vertex (for example e → e+ gamma) generalizes the basic vertex of Feynman diagrams, where a fermion emits a boson or a boson decays into a pair of fermions. Three lines meet at the ends.

   In TGD, this vertex can topologically correspond to the decomposition of a 3-surface into two 3-surfaces, the decomposition of a partonic 2-surface into two, the decomposition of a string into two, and finally, the turning of the fermion line backwards from time. One can say that the n-surfaces are glued together along their n-1-dimensional ends, just like the 1-surfaces are glued at the vertex in the Feynman diagram.

2. In the earlier posting, I already discussed how to identify vertex for fermion-antifermion pair creation as a V-shaped turning point of a 1-D fermion line. The fermion line turns back in time and fermion becomes an antifermion. Now, however, the quantized boson field at the vertex is replaced by a classical boson field. This description is basically the same as in the ordinary path integral where the gauge potentials are classical.

   The problem was that if the modified Dirac equation holds everywhere, there are no pair creation vertices. The solution of the problem is that the modified Dirac equation at the V-shaped vertex cannot hold true.

   What this means physically is that fermion and antifermion numbers are not separately conserved in the vertex. The modified Dirac action for the fermion line can be transformed to the change of antifermion number as operator (or fermion number at the vertex) expressible as the change of the antifermion part of the fermion number. This is expressible as the discontinuity of a corresponding part of the conserved current at the vertex. This picture conforms with the appearance of gauge currents in gauge theory vertices. Notice that modified gamma matrices determined by the bosonic action appear in the current.

3. This argument was limited to 1-D objects but can be generalized to higher-dimensional defects by assuming that the modified Dirac equation holds true everywhere except at defects represented as vertices, which become surfaces. The modified Dirac action reduces to an integral of the discontinuity of say antifermion current at the vertex, i.e. the change of the antifermion charge as an operator.

What remains to be understood more precisely is the connection with the exotic smooth structures possible only in 4-D space-time.

1. As already explained, towards the end of last year I realized that this V-shaped defect could correspond to a point-like defect of an exotic 4-D smooth structure. In general relativity as also in TGD, causal loops are associated with these defects. In TGD, the causal anomaly would mean that the direction of time is reversed in the vertex since antifermions and fermions can be thought of as moving in opposite directions of time. What is so remarkable is that this interpretation is possible only in 4-D space-time; in higher dimensions irreducible exotic smooth structures are impossible.
2. The next step is to ask whether a generalization is possible. Exotic smooth structures reduce to standard ones except in a set of defects having measure zero. The interpretation is that the dimension of defects, in the case that they are surfaces, is less than 4. Also non-point-like defects might be possible in contrast to what I assumed at first. If not, then only the direction of fermion lines could change.

   If the generalization is possible, also 1-D, 2-D, and 3-D defects are possible. In the 1→ 2 vertex the orbit of an n<4- dimensional surface would turn back in the direction of time. These are exactly the various topological vertices that I have previously arrived at, but guided by a physical intuition.

   An entire hierarchy of particles of different dimensions is possible. As a matter of fact, in topological condensed matter physics, they are commonplace. One talks about bulk states, boundary states, edge states and point-like singularities.

   All in all, exotic smooth structures would give vertices without vertices assuming only free fermions fields and no primary boson fields! And this is possible only in space-time dimension 4!

See the article Exotic smooth structures at space-time surfaces and master formula for scattering amplitudes in TGD} , the earlier article Intersection form for 4-manifolds, knots and 2-knots, smooth exotics, and TGD or the chapter Does M⁸ H duality reduce classical TGD to octonionic algebraic geometry?: Part II .

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

Is a master formula for the scattering amplitudes possible?

Marko Manninen asked whether TGD can in some sense be reduced to a single equation or principle is very interesting. My basic answer is that one could reduce TGD to a handful of basic principles. However, at the level of classical physics, one could perhaps say that general coordinate invariance → holography ← 4-D generalization of holomorphy reduce the representations of preferred extremals as analogs of Bohr orbits for particles as 3-surfaces to a representation analogous to that of a holomorphic function.

Can one hope something analogous to happen at the level of scattering amplitudes? Is some kind of a master formula possible? I have considered many options, even replacing the S-matrix with the Kähler metric in the fermionic degrees of freedom (see this). The motivation was that the rows of the matrix defining Kähler metric define unit vectors allowing interpretation in terms of probability conservation. However, it seems that the concept of zero energy state alone makes the definition unambiguous and unitarity is possible without additional assumptions.

1. In standard quantum field theory, correlation functions for quantum fields give rise to scattering amplitudes. In TGD, the fields are replaced by the spinor fields of the "world of classical worlds" (WCW) which can regarded as superpositions of pairs of multi-fermion states restricted at the 3-D surfaces at the ends of the 4-D Bohr orbits at the boundaries of CD.

   These 3-surfaces are extremely strongly but not completely correlated by holography implied by 4-D general coordinate invariance. The modes of WCW spinor fields at the 3-D surfaces correspond to irreducible unitary representations of various symmetries, which include supersymplectic symmetries of WCW and Kac-Moody type symmetries. Hence the inner product is unitary.

2. Whatever the detailed form of the 3-D parts of the modes of WCW spinor fields at the boundaries of CD is, they can be constructed from ordinary many fermion states. These many-fermion state correspond in the number theoretic vision of TGD to Galois singlets, which are states constructed at the level of M⁸ from fermion with momenta whose components are possibly complex algebraic integers in the algebraic extension of rational defining the 4-D region of M⁸ mapped to H by M⁸-H duality. Complex momentum means that the corresponding state decomposes to plane waves with a continuum of momenta.

   Galois confined states have momenta, whose components are integers in the momentum scale defined by the causal diamond (CD). Galois confinement defines a universal mechanism for the formation of bound states. The induced spinor fields are second quantized free spinor fields in H and their Dirac propagators are therefore fixed. This means an enormou calculational simplification.

3. The inner products of these WCW spinor fields restricted to 3-surfaces determine the scattering amplitudes. They are non-trivial since the modes of WCW spinor fields are located at opposite boundaries of CD. These inner products define the zero energy state identifiable as such as scattering amplitudes. This is the case also in wave mechanics and quantum TGD is indeed wave mechanics for particles identified as 3-surfaces.
4. There is also a functional integral of these amplitudes over the WCW, i.e. over the 4-D Bohr orbits. This defines a unitary inner product. The functional integral replaces the path integral of field theory and is mathematically well-defined since the Kähler function, appearing in the exponent defining vacuum functional, is a non-local function of the 3-surface so that standard local divergences due to the point-like nature of particles disappear. Also the standard problems due to the presence of a Hessian coming from a Gaussian determinant is canceled by the square foot of the determinant of the Kähler metric appearing in the integration measure.
5. The restriction of the second quantized spinor fields to 4-surfaces and zero-energy ontology are absolutely essential. Induction turns free fermion fields into interacting ones. The spinor fields of H are free and define a trivial field theory in H. The restriction to space-time surfaces changes the situation. Non-trivial scattering amplitudes are obtained since the fermionic propagators restricted to the space-time surface are not anymore free propagators in H. Therefore the restriction of WCW spinors to the boundaries of CD makes the fermions interact in exactly the same way as it makes the induced spinor connection and the metric dynamical.

There are a lot of details involved that I don't understand, but it would seem that a simple "master formula" is possible. Nothing essentially new seems to be needed. There is however one more important "but".

Are pair production and boson emission possible?

The question that I have pondered a lot is whether the pair production and emission of bosons are possible in this picture. In this process the fermion number is conserved, but fermion and antifermion numbers are not conserved separately. In free field theories they are, and in the interacting quantum field theories, the introduction of boson fermion interaction vertices is necessary. This brings infinities into the theory.

1. In TGD, the second quantized fermions in H are free and the boson fields are not included as primary fields but are bound states of fermions and antifermions. Is it possible to produce pairs at all and therefore also bosons? For example, is the emission of a photon from an electron possible? If a photon is a fermion-antifermion pair, then the fermion and antifermion numbers cannot be preserved separately. How to achieve this?
2. If fundamental fermions correspond to light-like curves at light-like orbit of partonic 2-surfaces, pair creation requires that that fermion trajectory turns in time direction. At this point velocity is infinite and this looks like a causal anomaly. There are two options: the fermion changes the sign of its energy or transforms to antiferion with the same sign of energy.

   Different signs of energy is not possible since the annihilation operator creating the fermion with opposite energy would annihilate either the final state or some fermion in the final state so that both fermion and antifermion numbers of the final state would be the same as those of the initial state.

   On the other hand, it can be said that positive energy antifermions propagate backwards in time because in the free fermion field since the terms proportional to fermion creation operators and antifermion annihilation operators appear in the expression of the field as sum of spinor modes.

   Therefore a fermion-antifermion pair with positive energies can be created and corresponds to a pair of creation operators. It could also correspond to a boson emission and to a field theory vertex, in which the fermion, antifermion and boson occur. In TGD, however, the boson fields are not included as primary fields. Is such a "vertex without a vertex" possible at all?

3. Can one find an interpretation for this creation of a couple that is in harmony with the standard view. Space-time surfaces are associated with induced classical gauge potentials. In standard field theory, they couple to fermion-antifermion pairs, and pairs can be created in classical fields. The modified Dirac equation and the Dirac equation in H also have such a coupling. Now the modified Dirac equation holds true at the fermion lines at the light-like orbits of the partonic 2-surface. Does the creation of pairs happen in this way? It might do so: also in the path integral formalism of field theories, bosons basically correspond to classical fields and the vertex is just this except that in TGD fermions are restricted to 1-D lines.

Fundamental fermion pair creation vertices as local defects of the standard smooth structure of the space-time surface?

Here comes the possible connection with a very general mathematical problem of general relativity that I have discussed here.

1. Causal anomalies as time loops that break causality are more the rule than an exception in general relativity the essence of the causal anomaly is the reversal of the arrow of time. Causal anomalies correspond to exotic diffeo-structures that are possible only in dimension D=4! Their number is infinite.
2. Quite generally, the exotic diffeo-structures reduce to local point-like defects of the usual differentiable structure. Exotic differentiable structures are also possible in TGD, and I have proposed that the associated defects correspond to a creation of fermion-fermion pairs for emission of fermion pairs of of gauge bosons and Higgs particle identified in TGD as bound states of fermion-antifermion pairs. This picture generalizes also to the case of gravitons, which would involve a pair of vertices of this kind. The presence of 2 vertices might relate to the weakness of the gravitational interaction.

   The reversal of the fermion line in time direction would correspond to a creation of a fermion-antifermion pair: fermion and antiferion would have the same sign of energy. This would be a causal anomaly in the sense that the time direction of the fermion line is reversed so that it becomes an antifermion.

   I have proposed that this causal anomaly is identifiable as an anomaly of differentiable structure so that emission of bosons and fermion pairs would only be possible in dimension 4: the space-time dimension would be unique!

3. But why would a point-like local defect of the differentiable structure correspond to a fermion pair creation vertex. In TGD, the point-like fermions correspond to 1-D light-like curves at the light-like orbit of the partonic 2-surface.

   In the pair creation vertex in presence of classical induced gauge potentials, one would have a V-shaped world line of fermion turning backwards in time meaning that antifermion is transformed to fermion. The antifermion and fermion numbers are not separately conserved although the total fermion number is. If one assumes that the modified Dirac equation holds true along the entire fermion worldline, there would be no pair creation.

   If it holds true only outside the V-shaped vertex the modified Dirac action for the V-shaped fermion libe can be transformed to a difference of antifermion number equal to the discontinuity of the antifermion part of the fermion current identified as an operator at the vertex. This would give rise to a non-trivial vertex and the modified gamma matrices would code information about classical bosonic action.

See the article Exotic smooth structures at space-time surfaces and master formula for scattering amplitudes in TGD} , the earlier article Intersection form for 4-manifolds, knots and 2-knots, smooth exotics, and TGD or the chapter Does M⁸ H duality reduce classical TGD to octonionic algebraic geometry?: Part II .

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

TGD view of the paradoxical finding of the James Webb telescope

I found a fascinating Youtube video this) in LAB360 with the title "James Webb Telescope Detect more than 700 Galaxies at the Edge of Our Universe" summarizing the findings of the James Webb telescope.

Summary of the findings of the James Webb telescope

The existence of more than 700 galaxies a few hundred million years after BB is in sharp conflict with the standard Big Bang Model although it is consistent with the cosmic expansion. Distance measurements indeed use cosmic redshift to deduce the distances of the galaxies. In any case, the James Webb telescope is profoundly shaking the foundations of cosmology. It seems that one can safely forget the standard story about the formation of stars and galaxies and also inflation as the generally accepted story of what happened before that.

In the standard picture, the epoch of reionization starts 1 billion years after the BB as the fog of gas is cleared by reionization so that photons can propagate. No signals hould arrive from the epoc preceding reionization. These 700 galaxies should not be there since they are too young, existing 370-500 million years after BB.

The mass of the galaxy serves as a measure for the age of the galaxy but 6 galaxies with age .5 Gy and 10 times bigger than the Milky Way have been found! This makes one wonder, what will be found when one goes farther back in time?

JW can see galaxies as extended objects with visible structures and this provides a lot of additional information about the composition of these too-early birds.

1. Complex organic molecules, found also in smoke/fog, were found: this is 1 billion years too early! These molecules, polycyclic aromatic hydrocarbons (PAHs) (see this), are big molecules, containing hundreds of atoms. What adds to the mystery, is that PAHs were found in regions where there are no stars or star formation but not in regions where stars are forming! PAH world hypothesis states that PAHs have played a key role in prebiotic life leading the emergence of RNAs (see this).
2. Also the locations of these molecules can be determined by JW in terms of their spectra. The distribution of the molecules is not uniform as one might expect. These galaxies can have the same mass as the Milky Way. The mass serves as a measure for the age of the galaxy but the age of these galaxies, according to standard cosmology, is only 10 percent of that of the Milky Way. This creates a paradox.
3. One particular galaxy, GN-z11 (see this) is observed as it existed 13.3 Gy ago.
   1. GN-z11 is found to contain an exceptionally high proportion of nitrogen and abundance of stars.
   2. Birth of globular star clusters (see this) have been found in GN-z11. This finding is especially paradoxical since they are regarded as very old objects! The compositions of O,N, Na, and Al vary inside globular clusters. These anomalies have been known for a long time (see this). One however expects that the stars of the cluster should have the same origin and age in the early universe.
   3. Also supermassive stars (see this), having masses of few hundred solar masses, have been found in globular clusters (see this). Also multiple globular clusters have been found.

TGD explanation of the paradoxical findings of the James Webb telescope

What goes wrong with the standard cosmology? Could TGD inspired cosmology suggest an answer? Consider first zero energy ontology (ZEO) and the TGD view of dark matter.

1. TGD suggests that the prevailing view about the notion of time is wrong. TGD forces a new ontology of quantum theory, which I call zero energy ontology (ZEO) (see this). Causal diamond (CD) as a state-determined and dynamical quantization volume has two boundaries and zero energy states are in fermionic degrees of freedom superpositions of pairs of 3-D states asociated with these two.

   Zero energy state corresponds also to a superposition of space-time surfaces connecting the two boundaries of CD. By the almost deterministic holography implied by the 4-D general coordinate invariance, the space-time analogs 4-D analogs of Bohr orbits of particles as 3-D surfaces. In ZEO, subjective time and geometric time are not the same thing but are strongly correlated. This new ontology solves the basic paradox of quantum measurement theory.

   There are two kind of state functions reductions (SFRs): "Small" SFRs (SSFRs) corresponding to repeated measurements in Zeno effect and "big" SFRs (BSFRs) corresponding to ordinary SFRs. CD has two kind of boundaries; active and passive. In SSFRs, the active boundary and states at it change whereas the passive boundary and the states at it remain unaffected. This is the counterpart of the Zeno effect: the state changes slighty but the arrow of time is preserved. SSFRs also correspond to weak measurements in quantum optics.

   In BSFRs the arrow of time changes. BSFR occurs when the set of observables measured in SSFR a the active boundary of CD does not commute with those measured earlier at the passive boundary of CD. CD increases in size in a statistical sense during the sequence of SSFRs since the active boundary drifts farther from the passive one. This gives rise to the correlation of subjective time a sequence of SSFRs with geometric time a distance between the tips of CD.

2. TGD also predicts quantum coherence in arbitrarily long scales and gravitational quantum coherence corresponds to the longest, even astrophysical, quantum coherence scales gravitational interactio has infinite range and is unscreened (see this).
3. The change of arrow of time in BSFRs implies dramatic effects even in astrophysical scales. Even astrophysical objects can live forth and back in geometric time. The ageing in the physical sense occurs in both directions of geometric time so that the physical age is total time spent in this moving forth and back. Since the passive boundary is stationary, the physical ageing in ZEO is faster than ageing in the standard ontology.

   During this process the physical system ages. Although the size of CDs increases in statistical sense, the ageing occurs in both directions of time so that the age is total time spent in this forth and back in time process. Hence ageing in ZEO is faster than ageing in the standard ontology.

Consider first the time anomalies.

1. ZEO explains stars and galaxies older than the Universe.
2. ZEO also predicts the variation of the ages of galaxies and stars in the very early Universe. Since galaxies and stars can be born at different periods in this life forth and back in geometric time, they can have different ages in the sense of ZEO. This explains why the abundances of atoms associated with the stars of star clusters are found to vary. The life forth and back in time also explains the appearance of globular star clusters, which are very old and are not possible in standard cosmology.

What about PAHs which appear in the regions where star formation does not occur and do not appear in the region containing stars?

1. The TGD view of nuclear physics, originally inspired by the findings about "cold fusion", and based on the notion of dark nuclei, identified scaled up analogs of ordinary nuclei, leads to a model of prestellar evolution based on dark fusion (explaining also "cold fusion", see this, this, and this).

   "Dark" means that the nucleons of these nuclei have non-standard values of Planck constant h_eff=nh₀. In the number theoretic vision of TGD, n has interpretation in terms of dimension of extension of rationals associated with a polynomial with integer coefficient defining a space-time region (see this,this, and this).

   Dark fusion generates dark nuclei as sequences of dark protons at monopole flux tubes having size scale of electron Compton length. Their binding energy is much smaller than the binding energy of the ordinary nuclei. Dark nuclei can therefore transform to ordinary nuclei and liberate most of the nuclear binding energy in the process, this give rise to "cold fusion". The temperature of the dark fusion region increases in the process and eventually reaches the temperature at which ordinary nuclear fusion can start.

   Even chemistry and complex molecules can emerge before the ordinary nuclear fusion is ignited. This could explain the presence of PAHs, in particular their presence in regions where there is no star formation or stars.

2. Why signals from the period preceding the reionization are possible? One reason is that there was a reionization. TGD also allows us to consider the possibility that the signals arrive as dark photons along monopole flux tubes of a cosmic flux tube network acting as an analog of the nervous system. Also in the TGD based model of the brain dark photon signals propagating between the central nervous system and magnetic body play a key role.

I have considered the findings of James Webb telescope from the TGD point of view here. The TGD view of cosmology and astrophysics is discussed in various articles (see this, this, this, this, and this).

See the article TGD view of the paradoxical findings of the James Webb telescope or the chapter TGD View of the Engine Powering Jets from Active Galactic Nuclei.

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

Neil Gersching's vision of self-replicating robots from TGD point of view

The video of Lex Fridman interviewing Neil Gerching (see this) is highly inspiring for anyone interested in what is happening in the High Tech frontier nowadays.

The key topic of discussion were self-replicating machines that are built from a few "Lego blocks" that contain their own building instructions and are analogous to genes or proteins. Function and 3-D structure are the same. The building blocks themselves would be robot-like and would build more complex robots. One can say that this Lego set would self-assemble itself. Also the ability to disassemble would be important and make error correction possible. This brings in mind what happens in living systems.

There would be a whole hierarchy of these structures. The basic structures would be analogous to 20 amino acids. Biology of course suggests also the presence of DNA and cell nucleus could be seen as the basic lego block containing instructions and having the ability to replicate. The vision is that someday our technology could transform to artificial life.

Gersching criticized the complete separation of software and hardware (program tape and the reading head of the Turing machine) which he called Turing's error. Gersching also proposed that information should be the starting point concept of physics rather than geometry which leads to the recent physics based on partial differential equations.

In this article I will compare the vision of Gersching to TGD based vision of, not only life, but the entire Universe as a self-organizing entity.

1. In the TGD framework, Lego Universe emerges naturally. 4-D general coordinate invariance implies holography: Legos are almost deterministic Bohr orbit-like 4-surfaces. Holography suggests a concrete identification of basic building bricks in terms of fundamental regions associated with hyperbolic 3-manifolds at 3-D mass shells defining the boundary data for number theoretical holography in M⁸. The strengthening of 3→ 4 holography to almost 2→ 4 holography reduces further the number of building bricks of space-time surfaces.

   The analogy with genes and proteins as building bricks might be much more than analogy. The mass shell as hyperbolic 3-space allows an infinite number of tessellations and one of them is icosa tetrahedral tessellations in terms of which it seems to be possible to understand the genetic code. Genetic code in this sense might be present in all scales and be induced to 3-surfaces. The fermions associated with the "unit cells" of the icosahedral tessellation could realize genetic code.

   The fusion of building blocks might reduce to the analog of crystal growth by fusing the fundamental regions of tessellations and also DNA replication, transcription, and translation could reduce to crystal growth.

2. In TGD holography implies that at space-time level a given 3-D surface defining the data of holography has an almost unique "fate", goal one might say. Holography forces what I call zero energy ontology (ZEO). Quantum states are superpositions of 4-D space-time surfaces analogous to Bohr orbits and state function reductions (SFRs) take place between these superpositions. The basic paradox of quantum measurement theory disappears.

   The sequence of "small" SFRs (SSFRs) defines "self" as the TGD counterpart for the Zeno effect. Each SSFR replaces this superposition with a new one and changes the state but in such a way that measured observables commute with those whose eigenstate the states associated with the passive boundary of causal diamond (CD) are.

   "Big" SFRs (BSFRs) change the arrow of geometric time correlating with subjective time as a sequence of SSFRs and change the roles of the active and passive boundaries of CD. This means the "death" of self and its reincarnation with an opposite arrow of time. Pairs of BSFRs define temporary changes of the arrow of time and would make possible a trial-and error process so that the self-organizing system would be analogous to a self-assembling conscious machine able to also disassemble if necessary to reach the goal.

3. In TGD there is no need to choose between information based physics and physics based on partial differential equations: these views would be complementary. TGD relies on two complementary visions. In number theoretic vision everything in discrete and algebraic equations characterize physical states. In the geometric vision structures are continuous and partial differential equations define the time evolution. These views are related by M⁸-H duality as a generalization of momentum-position duality forced by the replacement of point-like particles with 3-surfaces.
4. Gersching does not seem to regard consciousness as a crucial element of biology. The TGD view is completely different and in TGD quantum measurement theory based on ZEO extends to a theory of consciousness.

Besides this, the possible role of quantum gravitation for both biological systems and computer consciousness is discussed although this is not directly relevant to the basic topic. My defence is that the structures able to self assemble must also be computer-like systems.

1. The notion of a magnetic body (MB) carrying dark matter as h_eff=nh₀ phases of ordinary matter is essential. For the gravitational monopole flux tubes the value of h_eff=h_gr would be enormous and imply quantum coherence in arbitrarily long scales. Gravitational MBs could control both living matter and computers.
2. A criterion characterizing the critical clock frequency or its biological analog for the transformation of living system to a conscious and living system is deduced. This transition would mean that the statistical determinism fails due to the possibility of quantum coherence in time scales longer than the clock period.
3. Also an attempt to identify various quantum gravitational Compton lengths Λ_gr and frequencies f_gr with frequencies, which appear in the TGD inspired quantum biology, is made. Λ_gr and f_gr appear also in the TGD inspired physical model of computers.
4. The emerging view could be blamed for the return to astrology. Indeed, the gravitational flux tubes mediating the gravitational interactions between Sun and planets, between planets, between Earth and Moon, and even between the galactic blackhole and solar system could play a key role since the interactions are mediated along the flux tube network. However, the numerous strange numerical coincidences for quantum gravitational coherence scales and corresponding frequencies force us to take this view seriously.

See the chapter Neil Gersching's vision of self-replicating robots from TGD point of view or the article with the same title.

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