Beltrami flows and holography = holomorphy vision

Beltrami flows (see this) appear in several contexts. Google AI informs that Beltrami flow is a force-free flow field at 3-sphere. The simplest Hopf fibration (see this) is from 3-sphere to 2-sphere. The inverse images of the points of and there are numerous generations of Hopf fibration: the fibration S⁵→ CP₂ is of special interest in TGD.

Some background

Some background about Beltrami flows is in order.

1. For the Beltrami flow (see this) velocity field satisfies curl(v) = Λ×v so that curl(v) is parallel to v. In fluid dynamics Beltrami flow corresponds to a flow for which vorticity ω= ∇× v and velocity v are parallel. ω× v=0 gives ω =∇× v= α (x,t)v. Beltrami flows in S³ satisfy this condition and are exact solutions to Euler equations.
2. In magnetohydrodynamics one can replace velocity field with magnetic field B and of the current j satisfies j= ∇× B= α B implying the vanishing of the Lorentz force j× B. The current flows along field lines and in TGD the flow of particles along monopole flux tubes is the counterpart for this flow. These Beltrami flows involve the linking and knotting of magnetic field lines. Similar situation prevails in hydrodynamics.

Jenny Lorraine Nielsen has proposed that the Hopf fibration S¹→ S⁹→ CP₄ could provide a theory of everything and that Beltrami flows (see this) associated with this kind of fibrations play a key role in physics. The scalar Λ, which depends on position, appearing in the definition of Beltrami flow has dimensions of 1/length. Mass has dimension of ℏ/length so that 1/Λ should be identified as an analog of Compton length. These flows are topologically very interesting and involve linking and knotting of the flow lines.

The claim of Jenny Nielsen is that it is possible to understand particle massivation in terms of Beltrami flows. Higgs expectation defining the mass spectrum in the standard model is identified as hbarΛ for the eigenvalue Λ of the lowest eigenmode of Beltrami flow. It would seem that Λ is assumed to be constant: this is not necessary. It must be possible to relate Λ to the radius of S³ and one chooses it suitably to get Higgs vacuum expectation. To get masses of fermions one must put them in by hand as couplings of fermions to Higgs so that one does not really predict fermion masses: the situation remains the same as in the standard model.

Beltrami flows in TGD

The generalization of Beltrami flows to 4-D context is one of the key ideas of TGD (see for instance this and this) but I have not discussed them explicitly in the recent framework based on holography = holomorphy vision (H-H) ) (see for instance this and this and this).

1. The motivation is that TGD is formally hydrodynamics in the sense that field equations express local conservation of isometry charges of M⁴× CP₂. There is actually infinite-dimensional algebra of conserved charges. The proposal is that in TGD, the Beltrami flows become genuinely 4-dimensional and correspond to classical field configuration for which the 4-D Lorentz force involving electric components vanishes.
2. The definition of the Beltrami flow is however different since one cannot regard the magnetic field as a vector field in 4 dimensions. For field equations Kähler current typically vanishes but can be also light-like. The counterpart of Beltrami flow states that Kähler current is proportional to the corresponding axial current:

   j=D_νJ^μν = α × ε^{μν αβ}A_νJ_αβ.

   The divergence of j^μ vanishes and this must be true also for the instanton current unless α=0 holds true This is the case if the CP₂ projection of the space-time surface is at most 3-dimensional. If it is 4-D the parameter α must vanish since the divergence of the axial current gives instanton density ε^μναβ J_μνJ_αβ, which is non-vanishing for CP₂ and by self-duality proportional to J^μν J_μν. Hence the only option is α=0 for D=4.

3. If these Beltrami flows are integrable, they can give a physical realization of some, perhaps all, space-time coordinates as coordinates varying along the flow lines of some isometry current. The time component of 4-force has interpretation as dissipation power and also vanishes. These non-dissipative configurations play a key role in TGD and are natural when space-time surfaces are identified as quantum coherence regions.
4. The key idea sharpening dramatically the notion of Beltrami flow supported by H-H vision is that complex analytic maps f: z→ f(z) allow us to construct integrable flows. What matters physically would be singularities: poles and zeros. Without them these maps would be mere general coordinate transformations.

   In TGD, this generalizes to 4 dimensions by the introduction of generalized complex structure in H=M⁴ × CP₂. The presence of hypercomplex coordinates in M⁴ motivates the term "generalized". In 4-D context, poles and zeros as singularities of a flow correspond to string world sheets and partonic 2-surfaces. The second key idea is that fermions at the flow lines serve as markers and provide information about the flow. In the cognitive sector they realize Boolean logic.

Flows in the complex plane

Flows in the plane are usually regarded as interesting Beltrami flows since in this case the condition ∇ × v = α v cannot be satisfied unless vorticity and eigenvalue α vanish. It is however possible to consider the situation α=0 also in the D=2 case. What is remarkable is that this brings in the notion of holomorphy. Moreover, the integrability is the key notion in TGD and means that flow lines have interpretation as coordinate lines.

One can start from flows in plane, in particular integrable flows.

1. Integrability means that the flow lines of the flow define coordinate lines. This requires that the velocity v for the flow line is a gradient grad(phi) of the coordinate in question. This condition is very strong and implies irrotationality so that a rotational flow is only possible in a global sense. Without integrability, the flow would be more like a random motion analogous to the motion of gas particles. Integrability brings in smoothness and the flow looks like a fluid flow.

   Most importantly, exotic smooth structures possible in TGD would correspond to flows for which smoothness fails at singularities to make possible fermionic interactions, although fermions are free in TGD. But this is possible only for 4-D space-time.

2. One can go even further and require that there are two integrable coordinates. They could be assigned with velocity v and vorticity curl(v). Both would define gradient flows apart from singularities. These conditions give Cauchy-Riemann conditions expressing complex analyticity. The flow can be expressed as an analytic map z→ f(z) of the complex plane and the flow lines correspond to coordinate lines of the new coordinates defined by f. Locally the conditions state that the flow is locally incompressible and irrotational apart from singularities. Globally this need not be the case.

   These maps however have poles and zeros as singularities. Poles act as sources and sinks at which the flow fails to be incompressible. Zeros correspond to vortex cores at which the flow velocity must approach zero.

3. One can also allow cuts. They appear if a complex analytic map is many-valued, such as fractional power and it is made discontinuous by taking only a single branch. Second option is to allow a covering in which case the complex plane becomes many-sheeted. In TGD, this picture is generalized to a 4-D situation.

The 2-dimensional flows related to the simplest Hopf fibration S³→ S²

Consider first the Hopf fibration S³→ S². The fibers associated with the points S² correspond to linked, nonintersection circles in S³. The twist or linkage is characterized by an integer known as Chern number.

A simple visualization of the fibration is in terms of the inverse images of the circles S¹ of S² in S³ under bundle projection. For the visualization purposes, one can represent S² as E² and S³ as E³. The inverse images of the circles S¹⊂S² with a constant latitude θ define a slicing of E³ with z-axis excluded, by tori S¹⊂S¹ the origin of E³ and projecting to a circle with center point at the origin of E². Poles correspond to tori which degenerate to a single point, the origin E³.

The flows of S³ consistent with the Hopf fibration are unions of toric flows at the tori S¹× S¹ characterized by 2 winding numbers (n₁,n₂) project to circles S¹⊂S². Note that the flow in S² is not geodesic flow. The flows of charged particles along closed cosmic strings with homologically trivial S²⊂CP₂ as cross section and define analogs of these flows.

Besides Betrami flows ∇× v=α v in S³, also other flows S² related to Hopf fibrations and its generalization are interesting in the TGD framework. Since S² has complex and K\"ahler structures, the integrable flows of S² should be reducible to analytic maps f: z→ f(z) S²→ S². Apart from vortex and pole singularities these flows are incompressible gradient flows with a vanishing vorticity and divergence. From the TGD point of view, especially interesting flows flow are magnetohydrodynamics geodesic flows of CP₁ (and CP₂) coupled to its K\"ahler form as U(1) field for which S³ (S⁵) define the fiber of U¹ bundle.

1. At the fermionic the presence of the S¹ as fiber of S³ brings in a coupling of S² spinors to a covariantly constant Kähler form of S², which corresponds to a U(1) symmetry assignable to S¹. In the case of S², the coupling is not necessary but in the case of CP₂ the Hopf fibration S⁵→ CP₂ allows Spin_c structure and leads to the standard model couplings and symmetries in TGD.
2. S² with Kähler structure can be visualized for the standard embedding S² → E³ as a covariantly constant magnetic field B orthogonal to S². Another way to describe B is as a covariantly constant antisymmetric 2-tensor in S².
3. At the hydrodynamical level, one can consider hydrodynamics in which geodesic free motion couples to the magnetic field defined by the Kähler form via Lorentz force. The magnetic force causes a twisting so that the motion is not anymore along a big circle. The flow lines tend to turn towards the North Pole or South Pole and approach/or leave the poles from South or North. Chiral symmetry is clearly violated.

   For the lift of this flow to S³ flow lines define a union of non-intersecting linked circles S¹ as fibers of S³→ S². If the S² flow is integrable, it is possible to label the fiber circles by a time coordinate so that they define a smooth 2-D manifold. Vortex singularities must correspond to single fiber S¹, possibly contracted to a point.

4. Therefore the basic question is whether a given flow is integrable rather than a random motion of gas molecules. One needs two coordinates defined by the flow and there are several candidates, acceleration defined by the Lorentz force, velocity and vorticity. Complex and Kähler structures make sense also for S². The conclusion is that analytic maps z→ f(z) of a complex coordinate of S² define an integrable flow. The real and imaginary parts of f(z) define the velocity field v.
5. There are two kinds of singularities at which the analyticity fails: zeros correspond to vortices and poles to sources and sinks. Everywhere else the flow is locally incompressible and irrotational so that both the divergence and rotor of the velocity field vanish. If the flow has no singularities it can be regarded as a mere coordinate change. Singularities contain the physics.It would seem that only integrable flows allow a lift to flows in S³.

Hopf fibration S⁵→ CP₂

In TGD the projection S⁵→ CP₂ is the crucial Hopf fibration since it makes it possible to provide CP₂ with a respectable spinor structure. The Kähler coupling gives rise to the standard model couplings and symmetries and H=M⁴× CP₂ is physically unique: weak interactions are color interactions in CP₂ spin degrees of freedom (charge and weak isospin). What is essential is the coupling of the Kähler gauge potential to spinors. This in turn leads to a Dirac equation in H=M⁴× CP₂ and the induced Dirac equation at the space-time surface X⁴.

1. At the hydrodynamical level one has geodesic flow coupled to the self-dual Kähler form of CP₂ consisten with its complex structure. One has Euclidian analogs of constant electric and magnetic fields, which are of the same magnitude. They would be orthogonal in E⁴ but in CP₂ their inner product gives constant instanton density. Since Kähler form defines the flow, there are good hopes that the flow is integrable and allows a lift to S₅. In this case the inverse images of the flow lines not linked.
2. Also now complex analytic maps f: CP₂→ CP₂ define i×ntegrable flows with singularities. There are two complex coordinates and one can have poles with respect to both of them. Both poles and zeros are replaced with 2-D surfaces and also the analogs of cuts appearing if many-valued maps f are allowed.

CP₂ type extremals

At the next level one can consider CP₂ type extremals, which are deformations of the canonical embedding of CP₂ as an Euclidean 4-surface of H=M⁴× CP₂ for which M⁴ coordinates are constant. They can be said to define basic building bricks of particles in TGD. The CP₂ type extremal has locally the same induced metric and Kähler structure as CP₂ but its M⁴ projection is a light-like curve, light-like geodesic in the simplest situation. It also ends, that is holes realized as 3-surfaces.

1. The above situation for which time is time parameter as 5:th coordinate is replaced with M⁴ time coordinate u varying along the light-like curve. Also now the complex analytic functions f: CP₂ → CP₂ define integrable flows. Time coordinate labels 3-D sections of the flow.
2. Now these flows would carry real physics. Induced Dirac equation effectively reduces to 1-D Dirac equation for fermion lines identified and holomorphy solves it, very much like in string models.

   The physical interpretation is very concrete. The addition of fermions to fermion lines serves as an addition of a marker making the flow visible. Fermions as markers allow to get information about the underlying geometric flow making itself visible via the time evolution of the many-fermion state.

   In TGD, fermions also realize Boolean logic at quantum level and the time evolutions between fermionic states can be seen as logical implication A→ B. Spinor structure as square root of metric structure fuses logic and geometry to a larger structure.

Integrable flows at Minkowskian space-time surfaces X⁴ ⊂ H

In holography = holomorphy vision space-time surfaces are roots for a pair f=(f₁,f₂): H→ C² of two generalized analytic functions f_i of one real hypercomplex coordinate u of M⁴, and the remaining 3 complex coordinates of H. Let us denote one of the complex coordinates by w, which can be either an M⁴ or CP₂ coordinate.

1. The roots give space-time surfaces as minimal surfaces solving the field equations for any classical action as long as it is general coordinate invariant and constructible in terms of induced geometry. The extremely nonlinear field equations reduce to local algebraic conditions and Riemannian geometry to algebraic geometry.
2. X⁴ shares one hypercomplex coordinate and one complex coordinate with H and both X⁴ and H have generalized complex structure. X⁴ has hypercomplex coordinate u (u=t-z of M² in the simplest situation) and complex coordinate w (coordinate of complex plane E² in the simplest situation). This defines the Hamilton-Jacobi structure of X⁴.
3. Complex analytic maps of X⁴ are of the form by (u→ f(u), w→ g(u,w)). Integrable flows are induced by these maps. If there are no singularities they correspond to general coordinate transformations. The map by f having singularities generates a new Hamilton-Jacobi structure.
4. Poles and zeros in the w-plane correspond to 2-D string world sheets. The counterparts of zeros and poles for hypercomplex plane, parameterized by a discrete set of values of the real hypercomplex coordinate u correspond to singular partonic 2-surfaces with complex coordinate w at the light-like orbit of a partonic 2-surface. These singular partonic 2-surfaces can be identified as TGD counterparts analogs of vertices at which fermionic lines can change their direction. At these surfaces the trace H of the second fundamental form vanishing everywhere else by minimal surface property has a delta function like singular. Its CP₂ part has an interpretation as analog of Higgs vacuum expectation value. The claim of Jenny Nielsen is analogous to this result. In TGD also the M⁴ part of H is non-vanishing and corresponds to a local acceleration concentrated at the singularity. An analog of Brownian motion is in question.

   One could very loosely say that the parameter α for Beltrami flow vanishes everywhere except at singularities where it has interpretation as value of the analog of Higgs expectation as the trace of the second fundamental form.

   String world sheets in turn mediate interactions since they connect to each other the light-like orbits of partonic 2-surfaces. This view conforms with the basic physical picture of TGD.

To sum up, the new elements brought by the holography = holomorphy principle are as follows.

1. It would seem that the flows in CP₁ and CP₂ are more important than flows in S³ and S⁵ but that the integrable flows allow a lift of the flow lines to smooth manifolds of the total space. The spheres provide the needed Kähler form guaranteeing the twisting of the flow and making in the case of S² possible arbitrarily complex flow topologies as knotting, braiding, and linking. Also 2-knots are possible in 4-D context.
2. The flows with a coupling to the induced Kähler form have a clear physical interpretation and the fermion lines central in the TGD based view of scattering amplitudes could correspond to the flow lines. The flows without singularities define general coordinate transformations. What about the Kähler flows expected to have singularities? Could they have some physical interpretation?

   String world sheets are identifiable as intersections of two space-time surfaces with the same H-J structure, this applies also to self-intersections. Partonic 2-surfaces in turn are counterparts of vertices at which the TGD counterparts of Feynman lines meet (see this). These singularities play a key role in the construction of scattering amplitudes in the TGD framework. Also the singularities of the complex flows in the presence of Kähler force have this kind of singularities as counterparts vortices and sinks and sources. Could the flow singularities correspond to self intersections and partonic 2-surfaces?

3. Could the analytic maps with singularities defined by Kähler flow allow to define Hamilton-Jacobi structure in geometric terms using the information about its singularities as self-intersections.
4. The realization that fermion lines very concretely serve as markers of a hydrodynamic flow.

See the article Beltrami flows and holography = holomorphy hypothesis or the chapter Beltrami flows and holography = holomorphy hypothesisHolography=holomorphy vision in relation to quantum criticality, hierarchy of Planck constants, and M⁸−H duality.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Are the standard candles so standard after all?

Sabine Hossenfelder told about findings suggesting that the notion of dark energy might not be needed after all (see this). The analysis of 100 supernovae known as standard candles by Perlmutter, Schmidt and Reese led to the Nobel prize 2011. The recent study by Son et al involving more than 3000 supernovae that should be standard candles however suggested that the Nobel prize was premature.

The article titled Strong Progenitor Age-bias in Supernova Cosmology. II. Alignment with DESI BAO and Signs of a Non-Accelerating Universe (see this) concludes on basis of empirical data that the expansion, although it has been accelerating, is not accelerating anymore and might be even decelerating. The conclusion would be that there is no need for dark energy or at least that the cosmological constant is decreasing now.

Perlmutter, Schmidt and Reese studied supernovae of type Ia SNe known as standard candles assumed to have a peak luminosity, which does not depend on their age or the galaxy in which they belong. These supernovae typically have as progenitors which dwarfs, which are dead stars. These stars do not shine anymore. Since they can be regarded as the final states of stellar evolution, one can argue that their explosions yield the same peak luminosity so that they can serve as standard candles allowing a reliable determination of their distance from the redshift. If this were not the case, one should have a reliable model for the luminosity to deduce the distance.

The analysis of Son et al has, however, led to a conclusion that the luminosity of the standard candle correlates with the age of their progenitor. The younger the progenitor, the lower the peak luminosity. This conclusion is at 5.5 σ level. Therefore the distances estimated on the basis of standard candle assumption using redshift are too large. The actual distances would be smaller and no acceleration would be needed in the recent cosmology. Already the earlier findings by DESI suggested that acceleration has been decreasing which could be understood as a decrease of the cosmological constant Λ. If these findings are true they mean that the Λ CDM model is in grave difficulties. Even stellar models might be in difficulties if the properties of a white dwarf depend on the galactic environment they reside in. The abstract of the article of Son et al gives a more technical summary.

Supernova (SN) cosmology is based on the key assumption that the luminosity standardization process of Type Ia SNe remains invariant with progenitor age. However, direct and extensive age measurements of SN host galaxies reveal a significant (5.5σ) correlation between standardized SN magnitude and progenitor age, which is expected to introduce a serious systematic bias with redshift in SN cosmology. This systematic bias is largely uncorrected by the commonly used mass-step correction, as progenitor age and host galaxy mass evolve very differently with redshift. After correcting for this age-bias as a function of redshift, the SN dataset aligns more closely with the w0waCDM model recently suggested by the DESI BAO project from a combined analysis using only BAO and CMB data. This result is further supported by an evolution-free test that uses only SNe from young, coeval host galaxies across the full redshift range. When the three cosmological probes (SNe, BAO, CMB) are combined, we find a significantly stronger (>9σ) tension with the ΛCDM model than that reported in the DESI papers, suggesting a time-varying dark energy equation of state in a currently non-accelerating universe.

What could be the interpretation of this finding in the TGD framework. Consider first the TGD based view of cosmology.

1. In the TGD Universe cosmological constant-like parameter appears as a multiplier of the volume term of the action containing also Kähler action if the twistor lift of TGD, fixing the choice of H=M⁴× CP₂ is accepted. Λ is inversely proportional to the square of the p-adic length scale characterizing the size scale of the space-time sheet and is proposed to satisfy the p-adic length scales hypothesis favor primes near powers of 2. An entire hierarchy of cosmological constants is predicted (see this). If the observations determine the value of the cosmological constant reflect the p-adic size scale of the observable Universe at the moment when the radiation was emitted. Since this p-adic size scale correlates with the cosmic age, the observed cosmological constant should decrease with cosmic time. This could explain DESI observations.
2. Primordial cosmology is dominated by cosmic strings, unstable against thickening to monopole flux tubes. Flux tubes are characterized by thickness and length (see this). The scale defined by the cosmological constant emerging naturally in the twistor lift of TGD \cite{allb/twistquestions} corresponds to the p-adic length assignable to the length of the cosmic string. The flux tube thickness corresponding to the cosmological constant for standard cosmology is estimated to be about 10^-4 meters. Also thinner and thicker flux tubes are possible and one cannot exclude space-time regions, which are small deformations of pieces of M⁴ with a non-vanishing cosmological constant. Long cosmic strings explain galactic dark matter as energy of a cosmic string or a bundle of them transversal to the galactic plane.
3. Instead of gravitational condensation, the formation mechanism for the galaxies and stars in the TGD Universe is the thickening of the cosmic string leading to a liberation of its energy and the formation of flux tube tangles. This process would have been initiated by the topologically unavoidable collisions of cosmic strings. This mechanism is analogous to inflation (see this,this, this,this and this) but quantum coherence in astrophysical scales due the arbitrarily large values of gravitational and electric Planck constants (see this and this) makes exponential expansion un-necessary.

TGD also suggests a radical modification of stellar physics and stellar evolution (see this) based on new physics predicted by TGD (see this). This new view leads to a view of how standard candles fail to be so standard.

1. TGD also allows to consider a radically new view of the Sun itself (see this) based on the TGD based generalization of the standard model predicting a hierarchy of fractally scaled variants of the standard model (see this) The surface layers in which a phase transition transforming M₈₉ hadrons to ordinary hadrons would produce solar wind and solar energy, rather than the fusion in the stellar core.
2. There would be the analog of metabolic energy feed as M₈₉ hadrons from the galactic nucleus to the surface of the Sun. Interestingly, the spin axis of the galactic blackhole points towards the Earth.
3. In the Universe of the standard model, star ages as nuclear fusion burns the nuclear fuel in the core. In the TGD Universe, the fuel would be M₈₉ hadrons decaying to ordinary nuclei, producing solar wind and radiation, and forming a layer at the surface of the star rather than in its core. The heavier nuclei in the layer would sink to lower depths just as in the case of Earth. This suggests that the thickness of the layer of ordinary nuclei at the surface of the star increases with its age.
4. What could prevent the gravitational collapse of the star? Do the ordinary nuclei at the surface generate the pressure opposing gravitational force? There is indeed evidence for a solid phase in the surface of the Sun (see this). In the white dwarfs of the standard model, the fusion has ceased and they produce only thermal radiation as they cool to eventually collapse to form a supernova. Also in the TGD framework, gravitational collapse leading to a supernova explosion occurs when the feed of M₈₉ hadrons from the galactic nucleus has stopped and the star becomes a white dwarf.
5. The star with too low metabolic energy feed from the galactic blackhole starves and dies. Could stars die also at the young age, just as we can do? If so, there would be a spectrum of white dwarfs and standard candles characterized by their life spans.
6. Why would the liberated energy, or at least the peak luminosity, be lower in the supernova explosion of the white dwarfs in galaxies of the earlier Universe? Could the reason be that they have not had enough time to collect ordinary matter at their surface serving in a role analogous to fat forming lipid layers of cells before the M₈₉ hadron feed ceased? The biological analogy suggests that "cold fusion" as dark fusion at the surface layers could act like fat and produce energy and perhaps even solar wind and radiation energy when the M₈₉ hadron feed has ceased.

   What is important, that the very selection of the white dwarf in early cosmology would select a star that died at a young age! In old galaxies the still existing white dwarfs would have reached a higher age!

7. Why should the metabolic energy feed relate to the activity of the galaxies? Dead galaxies do not give rise to a formation of stars. Is the reason that the metabolic energy source in f the galactic blackhole has depleted? Or have the long monopole flux tube pairs feeding M₈₉ hadrons split by reconnections to short closed fluxed tubes? This mechanism could also explain solar spots and the solar cycle and also the changes of the orientation of the Earth's magnetic field. Could the ceasing of metabolic energy feed also explain the death of a star?

This view would conform with the gradually emerging vision that life, death and consciousness are present in all scales and that the basic phenomena of biology could have counterparts even in stellar and galactic physics.

See the article Are standard candles so standard after all? or the chapter About the recent TGD based view concerning cosmology and astrophysics.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this. tps://tgdtheory.fi/tgdmaterials/curri.html">this.

The story about tetraquark, which measurably existed at two places simultaneously

There has been strange post rotating in the web. It claims that a tetraquark with very strange properties has been discovered in CERN. Very probably, this is only one example of the nonsense filling the web nowadays and belongs to the same category as the many miracles related to 3I/ATLAS.

The post makes the weird claim that the LHC tetraquark has been detected at two places simultaneously at a distance of 1.4 meters. This is claimed to demonstrate that quantum coherence in this scale is involved. Standard quantum mechanics however says that the position measurement localizes the particle so that this is not possible. The post claims that the source is CERN Large Hadron Collider, Physical Review Letters 2025. There is no such report. Physical Review Letters. Tetraquark has been discovered but everything seems to be business as usual. There is however a strange co-incidence related to the TGD view of quantum physics, predicting the possibility of quantum coherence in arbitrarily long length scales and this motivated the writing of this post.

Just for fun, suppose there indeed is evidence that a tetraquark with a lifetime of about τ=about 10^-23 seconds was detected at a distance of L=1.4 m.

1. This is impossible since the maximal distance that tetra quark can travel is about d= c×τ= 3×10^-15 meters, which corresponds to the length scale of proton. The ratio L/d= 1.4×10¹⁵/3 so that tetraquark should survive for time t= L/c= .5×10^-8 s.
2. Could time dilation explain this? The lifetime of tetraquark is τ in the rest system. The lifetime T detected in the lab is longer than τ by dilation factor gamma= 1/(1-v²/c²)^1/2 giving γ= T T/τ= L/d∼ 3×10^-15, of order about 10¹⁵×m_T, where m_T is tetraquark mass of order proton mass. The energy of the tetraquark should be about 10¹² times the proton mass. The energy of protons in the cm system (lab) is a few hundred proton masses. Clearly, this option makes no sense.
3. What about TGD? TGD predicts a hierarchy of effective Planck constants h_eff and the lifetime for a particle with h_eff is scaled up by h_eff/h and for large values of h_eff the particle can be very long. And now comes the motivation for this post: the gravitational Planck constant is h_gr/h ∼ 10¹⁴ assignable to Earth particle pair and playing key role in TGD inspired quantum biology, corresponds to the ratio L/d. If the finding were true it would mean a direct and very dramatic support for the basic prediction of TGD. Knowing that the web is totally corrupted by fake news after the removal of fact checking, I do not take this possibility seriously.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

The recent view of TGD inspired theory of consciousness and quantum biology

This article is a summary of TGD inspired theory of consciousness and  its applications to quantum biology as they are towards the end of 2025.   In the TGD framework, it is not possible to discuss consciousness without the TGD view of space-time and quantum. Also the applications to quantum biology and neuroscience have been essential in the development of ideas. The basic inspiration has come from the deep philosophical problems of recent day physics and philosophy of consciousness. The TGD view of consciousness can be seen as a generalization of quantum measurement theory: the observer as an outsider becomes a part of the system.

The basic new elements are zero energy ontology (ZEO) as a new quantum ontology forced by the new view of space-time as 4-surfaces analogous to Bohr orbits of particles as 3-D surfaces. The dynamics of the classical space-time obeys holography = holomorphy principle. The failure of a strict classical determinism provides geometric correlates of intention and cognition. ZEO allows us to solve the basic problem of quantum measurement theory, allows free will, and provides a new view of the relation between geometric time and subjective time.

Physical existence, identified as the mathematical existence of quantum states: one can speak of quantum Platonia. Conscious existence is identified as quantum jumps between them and can be seen as two different kinds of existence. The classical non-determinism gives rise to quantum jumps giving rise to conscious entities, selves, and the ordinary quantum jumps are predicted to change the arrow of time. This means death and reincarnation of self with an opposite arrow of time.

Also the number theoretic visions of TGD is central. A key implication of the number theoretic vision is a hierarchy of Planck constants h_eff making possible quantum coherence in arbitrarily long scales crucial for the coherence of living matter. p-Adic length scale hierarchy is the second number theoretic prediction. The applications to quantum biology and neuroscience rely on these hierarchies.

In this article, the key notions and ideas of TGD, especially those relevant to consciousness and quantum biology, are summarized. The  TGD view of consciousness emphasizing recent progress is  summarized. The basic ideas and applications to  quantum biology are also described.

See the article The recent view of TGD inspired theory of consciousness and quantum biology and the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

The anomalies of cosmic microwave background from the TGD point of view

I have not previously systematically considered the CMB anomalies from the point of view of TGD. Cosmological Principle (CP) makes strong predictions. Inflationary cosmology explains the approximate constancy of the CMB temperature and predicts a scaling invariant spectrum for density perturbations: this predicts the angular dependence of the CMB temperature fluctuations.

This prediction is however plagued by small anomalies. The CMB dipole is due to the motions of the solar system with respect to CMB. There is also a "matter" anomaly for galaxies and clusters in the scale of megaparsecs. Also there is also recent evidence for the so-called quasar anomaly. There is also evidence for dark flow in even longer scales larger than the horizon size.

The Axis of Evil anomaly is in sharp conflict with CP. The quadrupole coefficients are unexpectedly small and the directions assignable to the octupole and quadrupole coefficients are aligned and parallel to the and parallel to ecliptic which means a strong violation of CP. Besides this there are fluctuation anomalies: in particular, hemispherical asymmetry for the fluctuation strengths.

In TGD, Cosmological Principle fails at the level of space-time surfaces but is replaced with Poincare invariance at the level of H=M⁴× CP₂: space-time sheets are like moving particles with each having its own CMB. The holography= holomorphy principle generalizes the scaling invariance to holomorphy of analytic functions of hypercomplex and 3 complex coordinates of H so that one has a generalization of conformal invariance to 4 dimensions. The quantum coherence possible in arbitrarily long scales and assigned to gravitational field bodies allows us to get rid of exponential expansion. This has also implications for the understanding of CMB. This picture leads to models of various CMB anomalies.

See the article The anomalies of cosmic microwave background from the TGD point of view or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Considerable progress in the understanding of M8-H duality

The idea of M⁸-H duality (H=M⁴× CP₂) has progressed through frustratingly many several twists and turns. The evolution of the ideas Consider first the development of the key ideas and the related problems.

1. The first key idea (see this, this and this) was that one can interpret octonions O as Minkowski space M⁸ (see this) by using the number theoretic inner product defined by the real part Re(o₁o₂) of the octonion product. Later I gave up this assumption and considered complexified octonions, which do not form a number field, but finally found that the original option is the only sensible option.
2. The second key idea was that if either the tangent spaces T or normal spaces N of Y⁴ ⊂ M⁸ are quaternionic and therefore associative, and also contain a commutative subspace C, they can be parameterized by points of CP₂ and mapped to H=M⁴× CP₂. This would be the first half or M⁸-H duality.
3. How to map the M⁴ ⊂ M⁸ projection to M⁴× CP₂? This question did not have an obvious answer. The simplest map is direct identification whereas the inversion with respect to the cm or tip of causal diamond cd⊂ M⁴⊂ H is strongly suggested by Uncertainty Principle and the interpretation of M⁸ coordinates as components of 8-momentum (see this. Note that one can considerably generalize the simplest view by replacing the fixed commutative subspace of quaternion space M⁴ with an integrable distribution of them in M⁸.
4. I considered first the T option in which T was assumed to be associative. The cold shower was that there might be very few integrable distributions of associative tangent spaces (see this and this). As a matter of fact, M⁴ and E⁴ were the only examples of associative 4-surfaces that I knew of. On the other hand, any distribution of quaternionic normal spaces is integrable and defines an associative surface Y⁴. This led to a too hasty conclusion that only the N option might work.
5. If M⁸ is not complexified, the surfaces Y⁴ in M⁸ are necessarily Euclidean with respect to the number theoretic metric (see this). This is in sharp conflict with the original intuitive idea that Y⁴ has a number theoretic Minkowski signature. Is it really the normal space N , which must have a Minkowskian signature? Is also T possible.
6. The minimal option in which M⁸-H duality determines only the 3-D holographic data as 3-surfaces Y³⊂ M⁸ mapped by M⁸-H duality to H. The images of Y³ could define holographic data consistent with the holography = holomorphy (H-H) vision (see this, this, this, this and this). Both M⁸ and H sides of the duality would be necessary.

Interpretational problems

There are also interpretational problems.

1. The proposed physical interpretation for the 4-surface Y⁴⊂ M⁸ was as the analog of momentum space for a particle identified as a 3-D surface. In this interpretation the Y⁴ would be an analog of time evolution with time replaced with energy. A more concrete interpretation of the 3-D holographic data would be as a dispersion relation and Y⁴ could also represent off-mass shell states. Momentum space description indeed relies on dispersion relations and space-time description to the solutions of classical field equations.
2. For N option Y⁴ must be Euclidean in the number theoretic metric. Therefore the momenta defined in terms of the tangent space metric are space-like. What does this mean physically?

   Could the problem be solved if the momentum assignable to a given point of Y⁴ is identified as a point of its quaternionic normal space as proposed in (see this).

   Or should one accept both T and N options and interpret the Euclidean Y⁴ as as a counterpart of a virtual particle with space-like momenta and of CP₂ type extremals at the level of H. At vertices belonging to Y⁴₁∩ Y⁴₂ me, quaternionic N(Y⁴₁) would contain points of quaternionic T(Y⁴₂) so that the earlier proposal would not be completely wrong.

3. A further criticism against the M⁸-H duality is that its explicit realization has been missing. For N option, the distributions of the quaternionic normal spaces N are always integrable but their explicit identification has been the problem. For T option even the existence of integrable distributions of T has remained open.

A possible solution of the problems of the earlier view

Consider now how the view to be described could solve the listed problems.

1. There are two options, which could be called T and N: either the local tangent space T or normal space N is quaternionic. Which one is correct or are both correct?

   Any integrable distribution of quaternionic normal spaces is allowed whereas for tangent spaces this is not the case. This does not mean that non-trivial solutions would not exist. Perhaps the rejection of the T option was too hasty.

   Furthermore, for X⁴⊂ H both Minkowskian and Euclidean signatures of the induced metric are possible: could T and N option be their M⁸ counterparts?

2. Holography= holomorphy vision (H-H) allows an explicit construction of the space-time surfaces X⁴⊂ H. For Y⁴⊂ M⁸ the situation has been different. The very nature of duality concept suggests that the explicit construction must be possible also at the level of H.
3. Is M⁸-H duality between 4-D surfaces Y⁴⊂ M⁸ and space-time surfaces X⁴⊂ H or only between the 3-D holographic data Y³⊂ H and X³⊂ M⁸-H?

It turns out that a modification of the original form of the M⁸-H duality, formulated in terms of a real octonion analytic functions f(o):O→ O, leads to a possible solution of these problems.

1. All the conditions f(o)=0, f(o)=1 and Imf)(o)=0, and Ref)(o)=0 are invariant under local G₂ acting as as a dynamical spectrum generating symmetry group since f_º g₂= g_2º f holds true. The task reduces to that of finding the 4-surfaces with a constant quaternionic T or N.
2. In particular, M⁴⊂ M⁸ has been hitherto the only known Y⁴ of type T and the action of local G₂ generates a huge number of Y⁴ of type T. Both T and N option are possible after all! G₂ symmetry applies also to the N option for which E⁴ is the simplest representative!
3. The roots of Im(f)(o)=0 resp. Re(f)(o)=0 are unions ∪_o0S⁶(o₀) of 6-spheres, where o₀ is octonionic real coordinate o₀. The 3-D union Y⁴= ∪_o0S⁶(o₀) ∩ M⁴=S²(o₀)⊂ M⁴ has quaternionic tangent space T=M⁴. The interpretation as holographic data and the M⁸ counterpart of a partonic orbit is suggestive.
4. The Euclidean 3-surface Y³= S⁶(o₀) ∩ E⁴(o₀)=S³(o₀) could serve as a holographic data for Y⁴ with quaternionic normal spaces and with an Euclidean number theoretic signature of the metric. Obviously, the option Y⁴=∪_o0 Y³(o₀) fails to satisfy this condition. The interpretation would be as the M⁸ counterpart of CP₂ type extremal with a Euclidean signature of the induced metric. The identification as the M⁸ counterpart of a virtual particle with space-like momentum is suggestive.

   If T resp. N contains a commutative hyper-complex subspace, it corresponds to a point of CP₂. Hence Y⁴ can be mapped to X⁴⊂ H=M⁴× CP₂ as M⁸-H duality requires.

5. What could be the counterpart of H-H vision in M⁸? One can choose the function f(o) to be an analytic function of a hypercomplex coordinate u or v of M⁴ and 3 complex coordinates of M⁸. The natural conjecture is that the image X⁴ of Y⁴ has the same property and satisfies H-H.

This view solves the interpretational problems.

1. The proposed physical interpretation for the 4-surface Y⁴⊂ M⁸ was as the analog of momentum space for a particle identified as a 3-D surface. The interpretation the Y⁴ as the analog of time evolution with time replaced with energy looks range. A more concrete interpretation of the 3-D holographic would be as a dispersion relation emerges and Y⁴ could also represent off-mass shell states. Momentum space description indeed relies on dispersion relations and space-time description to the solutions of classical field equations.

   Number theoretic discretization as a selection of points as elements of the extensions of rationals defining the coefficient field for f(o) and the replacement of fermions to the "active" points of discretization would realize many fermion states at the level of H. Galois confinement (see this and this) stating that the total momenta are rational numbers would provide a universal mechanism for the formation of bound states.

2. For N option Y⁴ must be Euclidean in the number theoretic metric. Therefore the momenta defined in terms of the tangent space metric are space-like. What does this mean physically?

   Could the problem be solved if the momentum assignable to a given point of Y⁴ is identified as a point of its quaternionic normal space as proposed in (see this).

   Or should one accept both T and N options and interpret the Euclidean Y⁴ as as a counterpart of a virtual particle with space-like momenta and of CP₂ type extremals at the level of H.

   At 2-D vertices belonging to the intersection Y⁴₁∩ Y⁴₂, quaternionic N(Y⁴₁) would contain points of quaternionic T(Y⁴₂) so that the first proposal would not be completely wrong.

3. Could the TGD analogs of Feynman diagrams be built by gluing together T and N type surfaces Y⁴ along 3-surfaces Y³ defining analogs of vertices. In the role of consciousness theorist, I have called them "very special moments in the life of self" (see this) at which the non-determinism of the classical field equations in H-H vision is localized. At these 3-surfaces the smoothness of Y⁴ fails and could give a connection to the notion of exotic smooth manifold (see this, this, and this), conjectured to make possible particle vertices and fermion pair creation in TGD despite the fact that fermions in H are free (see this, this and this).

See the article Still about M⁸-H duality or the chapter chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Did Google quantum computer change the arrow of time?

The latest FB news is that Google quantum computer has changed the arrow of time for a period of about 1 second. There is no publication of this yet but IBM made a similar announcement in 2019 (see this). It remains unclear to me what they have achieved without knowing what they mean with the time reversal.

1. Time reversal can be interpreted as a time reflection, which is a slightly broken discrete symmetry in fundamental physics. Do they construct a time revered time evolution in which initial and final states are permuted? Since complex conjugation is associated with the time reversal, a positive Hamiltonian can induce the time-reversed time evolution and no new physics would be involved.
2. Time reversal can be also interpreted as a thermodynamical time reversal. The reversal of the thermodynamical arrow of time is thought to be impossible in standard thermodynamics. There are however anomalies suggesting that this is possible. Phase conjugate laser rays are a basic example. In biology Pollack effect suggests the reversal of the arrow of time in the negatively charged exclusion zone. The inpurities are cleaned out of the system whereas thermodynamics suggests the reversal. Dissipation with a reversed arrow of time.
3. In TGD, time reversal occurs in "big" state function reductions (BSFRs) occurring in quantum measurement and induce a thermodynamical time reversal. In "small" SFRs (SSFRs), which have interpretation as internal quantum measurements of the system involving no external observer and assumed to give rise to cognition and consciousness, this does not happen. These measurements would take place in the discrete degrees of freedom predicted to be associated with the non-determism, of the classical dynamics. The sequence of SSFRs defines a conscious entity self, which would die and reincarnate with an opposite arrow of time in BSFR. Falling asleep or biological death would be familiar examples of this.

By writing "Google's quantum computer reversed the arrow of time" to Google, one learns more. AI claims that the thermodynamic arrow was not really changed. A quantum computational feat would be in question. But what does it really mean? The computer is externally controlled and the time evolution A→B is continued so that one has A→B→A. This means that a quantum measurement by an external system takes place at time T when the B→A starts.

In the TGD framework this would mean that the control inducing what looks B→A corresponds to a BSFR at time T, which reverses the arrow of geometric time. A time evolution to the geometric past by SSFRs begins at time T-ΔT₁ and eventually at time T-ΔT₂ a second BSFR occurs and the evolution with the standard arrow of time time by SSFRs begins, not at T but, at T+ΔT. ΔT would be about 1 second. The same happens as we fall asleep: we wake-up after, say, ΔT=12 hours but make a time travel to the geometric past during sleep lasting for say, 12 hours. If this interpretation is correct, the experiment could provide a direct support for the zero energy ontology of TGD.

However, a more precise TGD view of what happened is needed. In TGD cognition is predicted to be present in all scales so that I will approach the question from the point of view of TGD inspired theory of consciousness.

1. There are very delicate details involved. Second law says that the entropy S(S) of a closed system S increases. Now S is the quantum computer. There is also the entanglement entropy S(S-O) between S and that observer O. It is reported that the entropy of the quantum computer decreased during the period B→ A. It is not clear to me whether this entropy was S(S) or S(O,S)? If the system was closed during this period, the decrease of S(S) would allow us to conclude that the arrow of time was effectively changed.
2. What does the period B→ A does correspond to in TGD? Suppose that it corresponds to [T-Δ T₁, T-Δ T₂ when geometric time decreases. What does the entropy correspond to. Does it correspond to the entanglement entropy of the system + observer or to the sum of this entropy and system's internal entropy? Or is also the system s internal entropy basically entanglement entropy?
3. Intuitively it looks obvious that the first BSFR increases the information of an external observer of the system and reduces S(S-O) to zero. If the internal degrees of freedom are not entangled with external degrees of freedom, BSFR leaves S(S) unaffected. The time reversed time evolution would increase S(S) but in the opposite time direction. If S(S-O) is generated, it is reduced to zero in the second BSFR. S(S) would increase during the period [T-Δ T₁, T-Δ T₂. If an observer O with a standard arrow of time were able to observe S during this period, it would see this as a decrease of S(S).

   Also in the second BSFR the entropy would have decreased and the evolution in standard direction would have started at T+Δ T. It is difficult to say whether the entropy increased or decreased. If this was the case, the experiment would provide direct support for the zero energy ontology of TGD.

4. To gain some insight, one can compare the situation to what happens during sleep. Sleep has positive effects, perhaps due to the fact that it reduces the entropy of the sleeper. These positive effects are however felt also subjectively, rather than perceived by the external observer. Should one identify O as the field body of the system observing the biological body or is some other interpretation more appropriate?
5. There is a further delicacy involved. In TGD, the fundamental objects are 4-surfaces as slightly non-deterministic analogs of Bohr orbits for particles identified as 3-surfaces. The discrete degrees of freedom associated with the non-determinism are identified as cognitive degrees of freedom. Therefore it might make sense to speak of cognitive entropy S(cogn) associated with them.

   S(cogn) would increase as we get tired and would be reduced during sleep. Could S(cogn) correspond to entanglement entropy between cognitive degrees of freedom and those of the external world? If so, S(cogn) would contribute also to S(S-O). In BSFR also S(cogn) would be reduced to zero. If this view holds true, then the second BSFR would be responsible for the decrease of entanglement entropy.

Note that there are also other kinds of entanglements involved. Consider two systems A and B.

1. The IDF of A need not entangle with the ODF of A although the ODF of A and B can entangle. Could this relate to sensory perception?
2. The IDF of A can entangle with the ODF B. Could this make possible psychokinesis and hypnosis?
3. The IDF of A and B can entangle. Could this relate to telepathy?
4. Entanglement can also occur between the IDF and ODF of A. Could this relate to the realization of intentions in motor degrees of freedom?

See the article Are Conscious Computers Possible in TGD Universe? or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

The most distant known galaxy JADES-GS-z14-0 has high metallicity and 10 times higher oxygen content than expected

The popular article with title "Oxygen Has Been Discovered In The Most Distant Known Galaxy JADES-GS-z14-0" (see this) tells that the most distant known Galaxy JADES-GS-z14-0 existed about 300 million years after Big Bang. It was discovered by James Webb and ALMA telescope has continued the observations. What is totally surprising is that the stars of JADES-GS-z14-0 have high metallicity. In particular, the oxygen content is 10 times higher than expected. In the standard view of stellar evolution, this requires that the stars have suffered several supernova explosions. This is not possible.

There is an article by Schouws et al in arXiv with title "Detection of [OIII]88μm in JADES-GS-z14-0 at z=14.1793" (see this). Here is the abstract of the article.

We report the first successful ALMA follow-up observations of a secure z>10 JWST-selected galaxy, by robustly detecting (6.6σ) the [OIII]88μm line in JADES-GS-z14-0 (hereafter GS-z14). The ALMA detection yields a spectroscopic redshift of z=14.1793+/- 0.0007, and increases the precision on the prior redshift measurement of z=14.32^+0.08_-0.20 from NIRSpec by ≥ 180×. Moreover, the redshift is consistent with that previously determined from a tentative detection (3.6σ) of CIII]1907,1909 (z=14.178+/- 0.013), solidifying the redshift determination via multiple line detections. We measure a line luminosity of L[OIII]88=(2.1+/- 0.5)× 10⁸L_Sun, placing GS-z14 at the lower end, but within the scatter of, the local L[OIII]88-star formation rate relation.

No dust continuum from GS-z14 is detected, suggesting an upper limit on the dust-to-stellar mass ratio of < 2× 10^-3, consistent with dust production from supernovae with a yield y_d<0.3M_Sun. Combining a previous JWST/MIRI photometric measurement of the [OIII]λλ 4959,5007 Angstrom and Hβ lines with Cloudy models, we find GS-z14 to be surprisingly metal-enriched (Z∈ [0.05,0.2]Z_Sun), a mere 300 Myr after the Big Bang. The detection of a bright oxygen line in GS-z14 thus reinforces the notion that galaxies in the early Universe undergo rapid evolution.

This finding conforms with the general TGD based view of the formation of galaxies and stars (see this and this). Galaxies would not be formed by gravitational condensation but by the thickening of tangles of a cosmic string leading to the liberation of energy giving rise to ordinary matter, somewhat like inflation theory. Also the intersections of two cosmic strings and self intersections could be involved and generate galactic nuclei. The model explains the flat galactic rotation curves in terms of dark energy assignable to cosmic strings.

Also stars would be formed by a similar mechanism (see this). That no dust continuum created by supernova explosions was observed, is consistent with the assumption that no supernova explosions have occurred as standard model requires in order to explaing the high metallicity.

This explosive process can be considerably faster than the formation by gravitational condensation and dominate in the very early cosmology. TGD leads also to a model of stars based on new physics predicted by TGD and differing dramatically from the standard view (see this) and could change profoundly the views about stellar evolution.

See the article ANITA anomaly, JWST observation challenging the interpretation of CMB, star formation in the remnant of a star, and strange super nova explosion or the chapter About the recent TGD based view concerning cosmology and astrophysics.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

The internal degrees of freedom related to the classical non-determinism and consciousness

In TGD, consciousness and cognition are assigned with the internal degrees of freedom (IDF) assignable with the classical non-determinism. Ordinary SFRs (BSFRs) are assigned with the ordinary degrees of freedom (ODF) assignable to the entire Bohr orbits and measured in the ordinary quantum measurements. Several questions related to the relationship of IDF and ODF) come to mind.

Consider two systems A and B.

1. The IDF of A need not entangle with the ODF of A although the ODF of A and B can entangle. Could this relate to sensory perception?
2. The IDF of A can entangle with the ODF B. Could this make possible psychokinesis and hypnosis?
3. The IDF of A and B can entangle. Could this relate to telepathy?
4. Entanglement can also occur between the IDF and ODF of A. Could this relate to the realization of intentions in motor degrees of freedom?

The precise role of quantum criticality should be understood. Conservation laws pose strong restrictions here: a stable particle like proton or electron serves as an example. The intuitive idea is that a perturbation is needed to trigger a BSFR, which transforms intention realized as entanglement to a motor action or to an action affecting the external world. Is the quantum entanglement of IDF with its ODF enough to trigger a BSFR of the system: a spontaneous decay of an unstable particle would be an example now.

See the article The problem of time and the TGD counterpart of F= ma or the chapter Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Is cognition present at elementary particle level and are particle reactions intentional actions?

An innocent looking question "What F=ma means in TGD?", posed by Lawrence B. Crowell in a FB discussion, can be abstracted to the question how the transfers of conserved isometry charges of H=M⁴× CP₂ are realized at the level of fundamental interactions. At this level, the question is about how the conserved charges associated with the initial state particles are redistributed between the final state particles.

Somewhat surprisingly, TGD based quantum ontology implies that quantum non-determinism is an essential part of the answer to the question. Equally surprisingly, also a connection with the theory of consciousness and cognition emerges at the fundamental elementary particle level.

In the TGD view, the weak violation of the classical non-determinism in holography = holomorphy vision of TGD leads to the identification of self as a sequence of "small" state function reductions (SSFRs) identified as TGD counterparts of repeated measurements of the same observables: now however the observables related to the non-determinism are measured in SSFRs and give rise to the correlates of cognition. By quantum criticality, a "big" state function reduction (BSFR) as the TGD counterpart of what occurs in quantum measurement, can take place. BSFR means the death of self and its reincarnation with an opposite arrow of time.

Quantum criticality of the TGD Universe, realized in terms of holography = holomorphy principle, would be essential for this. For instance, particle decay involving topological changes could correspond to this process and all particle interactions would basically be due to the quantum criticality so that instead of SSFR, BSFR takes place. Intention is transformed to action at fundamental level. Cognition is dangerous in the TGD Universe!

See the article The problem of time and the TGD counterpart of F= ma or the chapter Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.