From the problem of time in general relativity to the TGD counterpart of F= ma

This contribution was inspired by a posting of Lawrence B. Crowell related to one particular problem related to the notion of time in general relativity: the general coordinate invariance implies interpretational problems since it is difficult to identify any preferred time coordinates used by observers. The identification of spatial coordinates is problematic for the same reason.

There are also other deep problems. In curved space-time, the classical conservation laws are lost. Einstein's equations are formulated in terms of energy momentum tensor but Newton's equations (F=ma) expressing the conservation of momentum and energy cannot be formulated in a general coordinate invariant way since the notions of energy and momentum fluxes are lost. No F=ma!

The TGD view of the problem of time inspired Lawrence B. Crowell to ask about the TGD counterpart of $F=ma$. This question can be abstracted to the question about 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.

A detailed consideration of the question of Crowell led to a considerable clarification of the previous views. 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 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 but a self at some level of the hierarchy dies! Thinking is dangerous in the TGD Universe!

The 3 problems related to the notion of time

It is good to beging with my first comment to the posting of Lawrence Crowell.

1. In the materialistic ontology subjective and geometric time are identified and this leads to deep problems.

   In TGD zero energy ontology (see this and this) allows both times and solves both the measurement problem and the problem of free will. Subjective time corresponds to a sequence of "small" state function reductions (SSFRs) replacing the Zeno effect, in which nothing happens, with the notion of self.

   Zero energy ontology replaces space-time surfaces as analogs of Bohr orbits for 3-surfaces having an interpretation as a geometric representation of particles. The classical dynamics is slightly non-deterministic although field equations are satisfied. This has crucial implications for the description of fundamental interactions (see this) and this). This non-determinism also makes possible the description of physical correlates of cognition.

2. The second problem relates to the geometric time. General coordinate invariance allows an endless number of identifications of the time coordinate. In TGD, space-times are 4-surfaces in H=M⁴× CP₂ and M⁴ provides linear Minkowskian time or light-cone proper time (cosmic time) as a preferred time coordinate for the space-time surfaces.
3. The loss of Poincare invariance in General Relativity is the third problem and led to TGD. In TGD one obtains classical conservation laws due to the Poincare invariance of M⁴ factor of H.

What does F= ma mean in TGD?

Lawrence Crowell asked about how the counterpart of F= ma emerges in TGD. At the general level the answer is as follows.

1. F= ma states momentum conservation for a particle plus its environment by characterizing the momentum is exchanged between the particle and environment. In TGD, momentum conservation generalizes to field equations for the space-time surfaces as analogs of Bohr orbits of particles identified as 3-surfaces. The field equations state the conservation of Poincare and color charges classically.

   Newton's equations are not given up as in General Relativity and their generalization defines the dynamics of space-time surfaces. Formally TGD is therefore like hydrodynamics. Einstein's equations follow naturally at the QFT limit as a remnant of Poincare invariance when the sheets of the many-sheeted space-time are replaced with a slightly curved region of M⁴ carrying the sum of induced gauge fields and gravitational fields defined as deviation from M⁴ metric.

2. This can be made more precise holography = holomorphy (H-H) hypothesis ( (see this, (see this, and this) reduces the field equations to local algebraic equations in terms of generalized holomorphy irrespective of action as long as it general coordinate invariant and expressible in terms of the induced geometry. This generalizes the role of holomorphy in string models.

   In conformal field theories holomorphy is a correlate for criticality. In TGD it would be a correlate for quantum criticality in the 4-D sense. This principle is extremely powerful since various dynamical parameters are analogous to a critical temperature.

   Space-time surfaces as minimal surfaces become analogs of Bohr orbits. Minimal surface equations generalize massless field equations and the TGD counterparts of field equations of gauge theories follow automatically.

3. Holomorphy is violated as 3-D surfaces which are analog for the singularities of analytic functions. This can be seen as a generalization of the fact that analytic functions can be expressed in terms of the holographic data given at poles and cuts.
4. What is crucial is that there is a light failure of determinism (but not of field equations). This occurs also for soap films, modellable as 2-D minimal surfaces: the frames do not uniquely determine the soap film. In TGD, the identification of this non-determinism as a p-adic non-determinism is attractive and leads to a generalization of the notion of p-adic number field to a function field (this and this ).

   H-H vision leads to a long-sought-for understanding of the origin of p-adic length scales hypothesis which for 30 years ago led to a surprisingly successful particle mass calculations based on p-adic thermodynamics (see this, this and this). The most recent article is about the application to the calculation of the mass spectrum of quarks and hadrons this). The p-adic non-determinism and p-adic length scale hypothesis would have origin in the iterations of polynomials defining dynamical symmetries in H-H vision and also giving a connection to the Mandelbrot fractals and Julia sets becomes possible.

Geometric and fermionic counterparts of F= ma in TGD

The next question concerns the counterpart of F= ma at geometric and fermionic levels respectively.

F= ma is a simple model for interactions. How are the interactions of two space-time surfaces A and B as analogs of Bohr orbits described geometrically?

1. Geometric vision suggests that a generalization of a contact interaction is in question. The intersection A and B defines the contact points. Without additional assumptions the intersection of A and B would be a discrete set of points. One can argue that this is not enough.
2. The intuitive idea is that there must exist additional prerequisites for the formation of a quantum coherent structure, at least in the interaction region. The proposal is that A and B share a common generalized complex structure, which I call Hamilton-Jacobi structure (see this) so that the conformal moduli defining the H-J structure would identical.

   The common H-J coordinates involve hypercomplex coordinate pair u,v with light-like coordinate curves, common complex M⁴ coordinate w and common complex CP₂ coordinates. The analytic functions defining A and B as their root must be generalized analytic functions of the same H-J coordinates.

3. The solution of field equations in Minkowskian space-time regions implies that either u or v is a passive coordinate since it cannot appear in the generalized analytic functions (the real hypercomplex coordinates u and v are analogous to z and z). The 2-D surfaces at which u and v vary, are generalizations of straight strings of M⁴ and dynamically very simple. Vibrational string degrees of freedom are frozen but the string ends at the partonic orbits are dynamical and can carry fermion numbers.

   In this case, the intersection of A and B consists of 2-D string world sheets connecting light-like partonic orbits. This gives a connection with string model type description.

4. Self-interactions of the space-time surface correspond to self-intersections consisting of string world sheets. For instance, the description of the internal dynamics of hadrons (see this and this) is realized in terms of self-intersections.

In the fermionic sector modified/induced Dirac equation at the space-time level holds true for the induced spinor fields and can be solved exactly by the holomorphy just as in the case of string models. At the level of scattering amplitudes the dynamics reduces to the fermionic N-point functions.

Propagators are free propagators in H and the hard problem is to understand how fermion pair creation is possible when fermions are free in H. The notion of exotic smooth structure, possible only for 4-D space-time surfaces, solves the problem.

How to translate F=ma to a view about the transfer of isometry charges between initial and final state particles?

Let us return to the original questions. How can one understand the generalization of F= ma in terms of a transfer of isometry charges of A (momenta color charges) from the initial state particles A and B to the final state particles? The classical field equations state the local conservation of isometry currents. How can this give rise to a transfer of total charges?

1. In the interaction region the Hamilton-Jacobi structures for A and B must be identical. Intersection consists of string world sheets. The interacting state therefore differs from the non-interacting state. Intuitively it is clear that the incoming states in the distant geometric past approach disjoint Bohr orbits. This is true also in the remote future except that the scattering need not be elastic and the particles identifiable bremsstrahlung can be emitted in the interactions. The interaction can also induce the decay of A and B. What happens in hadronic reactions gives a good idea of what happens.
2. The key notion is the mild failure of classical determinism for the Bohr orbits, which also characterizes criticality. The minimal surfaces describing the space-time surfaces have 3-D loci of non-determinism at which the classical determinism fails. These loci are analogous to the 1-D frames spanning 2-D soap films, which are also slightly non-deterministic minimal surfaces. There are several soap films spanned by the same collection of frames. The non-determinism gives rise to a sequence of small state function reductions (SFRs) generalizing the Zeno effect of standard quantum mechanics.

The description of the scattering in space-time degrees of freedom

Consider first the situation for a single particle as a 4-D Bohr orbit.

1. The non-determinism gives rise to internal interactions assignable to the self intersection as string world sheets. In the TGD inspired theory of consciousness, they can be identified in terms of geometric correlates of cognition.
2. Thinking is however dangerous also at the elementary particle level! The non-determinism is associated with quantum criticality and can lead to the decay of a partonic orbit to two or even more pieces. It can also change the topology of the partonic 2-surface characterized by genus g (CKM mixing). The partonic decay can in turn induce the decay of the space-time surface itself. The outcome would be a particle decay.

   This also leads to an emission of virtual particles as Bohr orbits, which appear as exchanges in 2-particle interactions. Massless extremals/topological light rays (see this) as counterparts of massless modes of gauge fields can be emitted. Closed 2-sheeted monopole flux tubes as geometric particles can be created by a splitting of a single monopole flux pair by a reconnection: this would be involved with a particle decay and emission of a virtual particle.

3. The scattering of two interacting particles A and B reduces to self interaction in the interaction region behaving like a single particle. The slight non-determinism makes possible a geometric generalization of the Feynman diagram type description. Now however all would be discrete and finite. There would be no path integral and therefore no divergences.

   The outcome would be a classical description and the generalization of F= ma would code for the transfers of isometry charges from A and B to the final state particles generated in the scattering. The slight classical non-determinism would make this possible.

The description of the scattering in fermionic degrees of freedom

The description of the scattering in fermionic degrees of freedom involves highly non-trivial aspects.

1. In the fermionic degrees of freedom, the fermionic propagators between points of the singular 3-surfaces defining the interaction vertices as ends of string world sheets of the intersection would describe the situation.
2. The crucial point is the possibility of fermion pair creation only for 4-D space-time surfaces due to the existence of the exotic smooth structures (see this, this). In other space-time dimensions the fermions would be free.
3. Fermion pair creation corresponds intuitively to the turning of a fermion line in time direction. At the 3-D holomorphic singularities X³ (analogous to cuts of analytic functions) the minimal surface equations fail and the additional pieces of the classical action, in particular 4-volume as the analog of cosmological constant term, become relevant. The twistor lift of TGD (see this and this) implies that the action is sum of K\"ahler action and volume term.
4. X³ represents a defect of the standard smooth structure and the turning of a fermion line at X³ at which standard smoothness fails corresponds to the transformation of u-type coordinate curve to a v-type coordinate curve takes place in the pair creations. u and v are associated with the parallel Minkowskian space-time sheets of the 2-sheeted space-time region. The creation of fermion occurs at the boundaries of two string world sheets at different monopole flux tubes so that a decay of monopole flux tube to a pair of them occurs.

   The pair creation would take place in the interaction regions and lead to the generation of final state fermions as the decay to 3-surfaces takes place. Closed 2-sheeted monopole flux tubes carrying fermion lines at their ends defined by Euclidean wormhole contacts connecting two sheets are generated.

5. At the 3-D defects minimal surface property fails and the trace of the second fundamental form, call it H^k, which vanishes almost everywhere, has a delta function singularity. By its group theoretical properties H^k has an interpretation as a generalized Higgs field. What is new is its M⁴ part, which has an interpretation as a local acceleration for a 4-D Bohr orbit. The same interpretation applies to the TGD counterpart of the ordinary Higgs.
6. The vertices at 3-D singularities are analogous to points at which the direction of the motion for a Brownian particle changes. Conformal invariance suggests that the 8-D Higgs vector H^k is light-like so that one has H_kH^k=0. Higgs has the dimension of ℏ/length and its vanishing gives rise to the analog of 8-D massless fixing M⁴ mass squared in terms of CP₂ mass squared. A reasonable guess is that the square of M⁴ part of H^k is proportional to particle mass squared. This would give quantum-classical correspondence.

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.

The surprise of the year: a Nobel prize for discovering macrosopic quantum tunnelling!

I must confess  that the work of Nobel prize winners John Clarke, Michel H. Devoret, and John M. Martinis "for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit" (see this) came as a total surprise for me.

Macroscopic quantum coherence is what makes possible quantum tunnelling in macroscopic scales but the value of Planck constant h is too small to make it plausible.

I have been talking about macroscopic quantum coherence for decades as a basic prediction of Topological Geometrodynamics (TGD). TGD forces us to generalize the standard quantum theory. One prediction is the spectrum h_eff=nh₀ of effective Planck constants as multiples of the minimal value h₀ of Planck constant which is smaller than h. It however seems that the multiples h_eff=nh are the most  important ones. Quantum coherence becomes possible in even astrophysical scales and would play a central role in the TGD inspired quantum biology.    

In the work of Nobel laureates, the quantization of energy and and macroscpic tunnelling were discovered in Josephson junctions.  An interesting question is whether the macroscopic quantum coherence observed in the quantum tunnelling can be really  explained in terms of ordinary quantum mechanics or whether TGD is required. One can indeed  argue that the extremely low temperatures presumably use in the experiments make it possible to have macroscopic quantum coherence in superconducting systems even in the framework of standard quantum mechanics.

The basic mystery of biological systems is their coherence. Could it be induced by macroscopic quantum coherence?  The quantum coherence at room  temperature is  definitely in conflict with standard quantum theory assuming a single value of Planck constant.  Macroscopic quantum tunnelling in high temperature superconductors would  obviously challenge the standard quantum mechanics.

TGD  could explain the quantum coherence at room temperature.  The new view of space-time leads to the notion of a field body, having  magnetic, electric and gravitational field bodies as special cases. These field bodies  carry  phases of ordinary matter with large h_eff. The quantum coherence at the level of  the field body, serving as a controller of the biological body,  would induce the macroscopic coherence (not quantum-) of  the ordinary biomatter.  

For instance, EEG would   relate  to the communications to and the  control by  the field body, which can have layers with the size of the Earth and even larger. In TGD quantum coherence at room  temperature superconductivity would make possible cell membranes as Josephson junctions. They would  play a central role in TGD inspired  quantum biology and neuroscience. The model of nerve pulse and EEG (see this) is one example.  

See for instance https://tgdtheory.fi/public_html/articles/TGD2024I.pdf and https://tgdtheory.fi/public_html/articles/TGD2024II.pdf .

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.

A refined view of the phenomenology of hadron physics and p-adic mass calculations

In the recent article with title "A refined view of the phenomenology of hadron physics and p-adic mass calculations" (see this) the implications of the updated vision of standard model physics and hadron physics are considered. The goal is to develop a phenomenological picture of hadrons based on the general mathematical framework of TGD and on the interpretation of strong and weak interactions as different aspects of color interaction.

The additivity of the mass squared values identified as conformal weights at the level of the embedding space $H$ is a crucial assumption made also in the p-adic mass calculations. One must check whether this assumption is physically sensical and how it relates to the additivity of masses assumed in the constituent quark model and understand the relation between the notions of current quark mass and constituent quark mass. One should also identify various contributions to the hadron mass squared in the new picture and understand the hadronic mass splittings.

The results of the simple calculations deducing the p-adic mass scales of hadrons and quarks mean a breakthrough in the quantitative understanding of the hadronic mass spectrum. In particular, the identification of color interactions in fermionic isospin degrees of freedom as weak interactions with a p-adically scaled up range explains the mass splittings due to isospin. The smallness of the Weinberg angle for scaled up weak interactions can explain how the interactions become strong and why the parity violation for strong interactions is small.

A refined view of the phenomenology of hadron physics and p-adic mass calculations 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.

Analog with Higgs mechanism and 3-D singular surfaces as analogs of soap bubbles

The vertices for the fermion pair creation are located 3-D singular surfaces X³ at which the conformal invariance fails. Can one say anything interesting about these 3-surfaces or even find a possible analogy with the existing physics? The idea that the trace of the second fundamental form which becomes singular at X³ relates closely to Higgs has been around from the beginning of TGD. In the following I want to show that this idea has finally found a precise form.

1. The trace of the 8-D second fundamental form defines a generalized local acceleration orthogonal to the space-time surface X⁴, which vanishes almost everywhere by the minimal surface property. It is non-vanishing only at the 3-D singularities X³ representing edges of X⁴. The vertices for fermion pair creation as edges of fermion lines are assigned to intersections of string world sheets with X³ in the intersection of intersecting space-time surfaces with the same Hamilton-Jacobi structure.
2. The second fundamental form is analogous to generalized Higgs, call it H, with the CP₂ part being group theoretically like the ordinary Higgs field and indeed causing a violation of the conservation of M⁴ chirality. The M⁴ part is identifiable as ordinary local acceleration. The generalized acceleration has the dimension of inverse length, that is the dimension of mass divided by Planck constant. Higgs vacuum expectation corresponds to the fermion mass in the standard model. Is this true also in TGD?
3. By both Dirac equation in H and Dirac equation with M⁴ Kähler form for CD the fermions are massless in 8-D sense. If the additivity of M⁴ mass squared, identified as a conformal weight, is assumed, all many-fermion states have a vanishing mass squared in 8-D sense so that the total M⁴ mass squared equals to CP₂ mass squared proportional to color Casimir. It vanishes for color singlets but has a CP₂ mass scale as a natural unit for colored states.
4. If M⁴- and CP₂ parts of the generalized Higgs have magnitude equal to the mass squared of the particle, quantum-classical correspondence is realized. p-Adic thermodynamics would predict M⁴ mass squared (see this). At X³, the condition a_M⁴ = m/h_eff for the M⁴ acceleration, where m the mass of the particle, would be satisfied. Conformal invariance would fail X³ but the 8-D masslessness would remain true. Local mass value depends on the point of X³ unless the magnitudes of a_M⁴ and a_CP2 are constant. The direction of 8-D acceleration is orthogonal to X⁴ and also X³.
5. What could be the physical interpretation for the possible constant magnitude of M⁴ and CP₂ accelerations? Isometrically embedded 3-sphere in E⁴ represents a basic example of this kind of surface. Also a soap bubble is an example of a surface with constant value of local acceleration. The surface tension corresponds to the local acceleration and is proportional to the pressure difference. This suggests that the 3-D singularities are analogous to the surfaces of 3-D soap bubbles.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD 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.

Explicit formulas for the vertices in TGD

It is now intuitively clear that the vertices at the fundamental level should be just the standard model vertices assignable to the 3-D singularities of the divergence of the fermionic current. Also the idea that the vertices should have an interpretation as defects of standard smooth structures to which exotic smooth structure (see this, this, and this) can be assigned (see this, this, this). The difficult challenge (to me at least) is to deduce the vertices in a convincing way. The option discussed below seems to be the most promising of the options considered hitherto.

Are the vertices due to the non-conservation of fermion current associated with the induced/modified Dirac action

One can start from the standard model view of vertices as an intuitive guide line.

1. The singularities should give the emission vertices for Higgs and electroweak gauge bosons. What is new is that electroweak gauge bosons have an interpretation as gluons with the weak gauge group identified as the holonomy group U(2) identifiable as a subgroup of color group SU(3). Strong interactions correspond to the isometries of SU(3) and electroweak interactions to the holonomies assignable to the CP₂ spinor degrees of freedom. Generalized Higgs corresponds to the trace of the second fundamental form having a 3-D singularity at the vertex having interpretation as 8-D local acceleration. This means that the classical action has no role as far as vertices are considered.
2. The interaction vertices emerge from the induced/modified Dirac action. By the modified Dirac equation, this action vanishes almost everywhere. The Dirac action reduces to a divergence of the fermion current and this suggests that at the singularity this divergence is non-vanishing. This conforms with the view that a fermion pair is created and fermion line terms backwards in time. At the 3-D singularity the divergence of the fermion current should have a delta function divergence making possible non-vanishing various vertices.
3. The vertex for the generalized Higgs is not a problem. The trace of the quantity D_μ(Γ^μg₄^1/2) is proportional to the trace of the seocnd fundamental form and gives 3-D delta function for the vertex of the annihilation of Higgs to fermion-antifermion pair.
4. How to obtain electroweak vertices and the possible vertex related to the M⁴ Kähler gauge potential? The electroweak vertices should come from a 3-D delta function singularity X³ of the Dirac action density

   Ψ(-D^←_μ Γ^μ -Γ^μD_μ)Ψg₄^1/2).

   The problem is that the components of the induced spinor connection A have only a step function like discontinuity rather than the desired delta function singularity. The desired singularity should be equal to the difference A₊-A_- of the gauge potentials at the two sides of the singularity, which is invariant under gauge transformations if their action is the same at the two sides. Vertex would be defined by this difference rather than vector potential as in perturbative gauge theories.

5. This can be achieved if the spinor fields have a discontinuity at X³, which gives rise to the difference A₊-A_- under the action of derivatives to the spinor field at X³. This is achieved if the gauge potentials A₊ and A_- are related by a gauge transformation g in the holonomy group. This gives A₊= A_- +dgg^-1 giving dg= (A₊-A_-)g. The spinor fields are discontinuous at the singularity and related by Ψ₊= gΨ_-. The derivative dΨ₊ is given by dΨ₊ = d(gΨ_-)= dgΨ_- + gdΨ_- = (A₊-A_-)gΨ_-+ gdΨ_-. The difference of gauge potentials at the singularity gives rise to the desired vertex.
6. For this option, the vertices are universal and do not depend on classical action for the induced Dirac equation. Also for the modified Dirac equation the electroweak vertices are determined by a gauge transformation in the holonomy group of CP₂. The conservation of the isometry currents for the classical action implies that the Higgs vertex as the divergence of the induced/modified Gamma matrices are expressible in terms of current assignable to the remaining parts of the action. If the classical action is a mere volume action, the conservation of classical isometry currents does not allow singularities. Therefore Kähler action plus volume term strongly suggested by the twistor lift is the minimal option.

The relation to the exotic smooth structures

The vertices should be non-trivial for the 3-D singularities at which the minimal surface property of the space-time surface fails and which corresponds to the defects for the standard smooth structure, which transform it to exotic smooth structure (see this, this, and this). What does this really mean, is far from clear. I have discussed this problem already earlier (see this, this, this) but I am not satisfied with the view.

The edge of the fermion line at the singularity means the breaking of standard smooth structure at which the light-like hypercomplex coordinate changes from u to its hypercomplex conjugate v. The derivatives of the embedding space coordinates as functions of u resp. v at the singularity are infinite for the standard smooth structure. Also the induced Dirac spinors are discontinuous and related by a gauge transformation at the two sides of the singularity if the above argument is correct.

For the exotic smooth structure, the derivatives are continuous at the singularity. Also the vertices should remain the same in the exotic smooth structure. The only reasonable identification of the vertices is as regions at which the exotic smooth structure fails to reduce to the standard smooth structure. Could one introduce a 3-D term to the Dirac action additional term localized to the singular surfaces of the standard smooth structure to guarantee that the non-vanishing divergence of the ordinary Dirac action is compensated by this additional term giving rise to the standard model vertices for the Dirac action.

I have proposed the assignment of Chern-Simons-Kähler action and its fermionic counterpart to the 3-D light-like partonic orbits and a similar term can be considered also now. The modified Dirac action for the Kähler Chern-Simons term would contain the standard model couplings to spinors.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD 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 magnetosphere of Jupiter as a seat of plasma life and its moon Europa as a seat of chemical life?

The FM signals  in radio frequency range 12-40 MHz from Jupiter's moon Ganymede have been reported 4 years ago. The claimed FM signals from the moon Europa have received a lot of attention.  In human  radio wave communications in the frequency range  87.5-  108.0 MHz frequency modulation is used to code  information. This  has raised  speculations about intelligent life  under the ice cover of  Europe and raised the question whether  the radiation could code for information  and even represent   a response  to the signals from the Earth.  

This finding is especially interesting from the TGD point of view since frequency modulation is a basic vay to code information in TGD inspired quantum biology. Also the phenomenological notion of magnetic flux tube is central in the description of the magnetic field of Jupiter: in the TGD framework this notion is not phenomenological and is the basic notion in  practically all applications of TGD based on the notion of field body and the hierarchy of phases of ordinary matter labelled by effective Planck constant $h_{eff}$. Gravitational and electric Planck constants associated with long range classical gravitational and electric fields are of special importance.  Frequency modulation is the key mechanism of communications and control in TGD based quantum biology.

This motivates the  development of the TGD based models for the magnetospheres of Jupiter and its moons and   also an analog for the maser cyclotron instability. The ensuing model for Jupiter's auroras is consistent with the empirical facts. Also the possibility of plasma life at the field bodies associated with Jupiter as well as primitive life in the interior of Europa can be considered.

See the article The magnetosphere of Jupiter as a seat of plasma life and its moon Europa as a seat of chemical life? or the chapter Quantum gravitation and quantum biology in TGD Universe

The description of E and B modes of CMB in the TGD framework

There are two key differences between inflation theory and TGD. In TGD, the almost constant value of the CMB temperature is due to quantum coherence in arbitrarily long scales rather than exponential expansion which does not look plausible. There is however expansion in the transition from the primordial cosmic string dominated phase in which space-time surfaces have 2-D string world sheets as M^4 projection, to monopole flux tubes liberating energy and leading to a radiation dominated cosmology. An entire sequence of phase transitions leading to the thickening of the monopole flux tubes is predicted, and interpreted as transitions between copies of standard model physics labelled by different p-adic mass scales predicted by TGD. If there is an exponential expansion, it is associated with this sequence.

So called B modes are the key prediction of the inflation theory. They are generated already in the inflationary period in the exponential expansion amplifying quantum fluctuations to cosmic scales. The primordial B modes are caused by gravitational waves and leave an imprint of primordial quantum fluctuation in cosmic scales. Their observation would be a victory of inflationary cosmology but their observation is extremely difficult due to the fact that also gravitational lensing transforms E modes to B modes.

The massless extremals (MEs) as counterparts of classical radiation fields provide a TGD based model for E and B modes. The prediction of the holography = holomorphy principle is that these modes are interchangeable locally. The local polarization vector for MEs is a holomorphic vector for which curl and divergence vanish apart from singularities, where the holomorphy fails. E and B modes differ only globally: for the B modes the coordinate lines of the polarization vector are closed curves around singularities. For E they connect singularities. The detected intensity vanishes outside the singular points,where it has a delta function type singularity. A natural interpretation as a vertex for photon emission/absorption.

See the article The description of E and B modes of CMB in the TGD framework or the chapter TGD and cosmology .

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 compositions of the Earth and Moon are identical as predicted by TGD!

TGD based view of the formation of planets is as mini Big Bangs, that is explosions throwing out a layer of Sun suffering gravitational condensation to a planet. This proposal generalizes: also the Moon could have been formed in an explosion throwing out a surface layer of the Earth with the mass of the Moon. Same could apply also to Martian moons (see this).

The basic prediction of the model is that the compositions of the Earth and Moon are the same. The model of formation based on the collision of a Mars sized object with the Earth does not predict this. Quite recently, Taylor Reed Ramsey informed me that this seems to be the case. The article titled "Composition, structure, and origin of the Moon" by Sossia et al (see this) and this) provides the details.

See the article What makes the mini Big Bangs energetically possible? or the chapter A HREF="https://tgdtheory.fi/pdfpool/magnbubble1.pdf">Magnetic Bubbles in TGD Universe: Part I).

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.

Direct support for the TGD based model of star from supernova explosion

There is support for a solid surface of the Sun (see this) and this was one of the many solar anomalies leading to the TGD based proposal for the model of the Sun (see this), in which the stellar surface would produce and contain elements. I didn't however expect that any other support for the proposal would emerge during my lifetime.

However, the recent news about strange findings about supernova SN2021yfj changed the situation (see the Nature article, popular article and the popular article in finnish.

The explosion of supernova SN2021yfj ejected shells rich in silicon, sulphur and argon. These elements should exist in the core of the star, not at its surface if we believe in the standard model of nuclear fusion. Therefore the discovery came as a total surprise.

Here is the abstract of the article titled "Extremely stripped supernova reveals a silicon and sulfur formation site". Stars are initially powered by the fusion of hydrogen to helium. These ashes serve as fuel in a series of stages transforming massive stars into a structure of shells. These are composed of natal hydrogen on the outside and consecutively heavier compositions inside, predicted to be dominated by He, C/O, O/Ne/Mg and O/Si/S. Silicon and sulfur are fused into iron, leading to the collapse of the core and either a supernova explosion or the formation of a black hole. Stripped stars, in which the outer hydrogen layer has been removed and the internal He-rich or even the C/O layer below it is exposed, provide evidence for this shell structure and the cosmic element production mechanism it reflects. The supernova types that arise from stripped stars embedded in shells of circumstellar material (CSM) confirm this scenario. However, direct evidence for the most interior shells, which are responsible for producing elements heavier than oxygen, is lacking. Here we report the discovery of the supernova SN2021yfj resulting from a star stripped to its O/Si/S-rich layer.

We directly observe a thick, massive Si/S-rich shell, expelled by the progenitor shortly before the supernova explosion. Exposing such an inner stellar layer is theoretically challenging and probably requires a rarely observed mass-loss mechanism. This rare supernova event reveals advanced stages of stellar evolution, forming heavier elements, including silicon, sulfur and argon, than those detected on the surface of any known class of massive stars.

The phrase "extremely stripped" explains why the discovery was so unexpected. The article interprets SN2021yfj as a very rare case having already lost its outer layers by some mechanism, perhaps by an explosion throwing out the outer layers.

Could one understand these findings in the TGD framework?

1. In the TGD based model (see this), the transformation of dark M₈₉ nucleons to ordinary nucleons occurs at the surface layer of thickness, which is roughly the Compton length of M₈₉ nucleons scaled up by ℏ_gr,Sun/h and about Earth radius, of the star. This produces solar wind and radiation energy. The dark M₈₉ nucleons at the surface layer would decay to ordinary nucleons, radiation and perhaps also heavier elements by a process that I call p-adic cooling (see this).
2. The consumption of M₈₉ hadrons at the surface layer of the Sun requires a compensating a feed of M₈₉ hadrons as the analog of metabolic energy feed along monopole flux tubes, most naturally connecting the Sun to the galactic nucleus or blackhole.

   The Sun might be seen as a cell-like system and the interior of the Sun could be very different from what it is believed to be, maybe even analogous to a cell nucleus so that the Sun could be a conscious, intelligent macroscopic quantum system. The thermodynamic model for the core would be simply wrong.

3. The nucleons would suffer dark fusion as the TGD counterpart of "cold fusion" to form heavier elements. The distribution of the elements produced would closely resemble the distribution assumed to be produced in ordinary fusion. This could explain the evidence for the solid surface of the Sun (see this) containing even elements as heavy as iron.
4. What could happen to the elements generated by the dark fusion? A good guess is that they sink to the lower heights in the gravitational field of the Sun so that they have a layered structure, having ordering similar to that assumed in the standard model of the solar core. However, the layered structure would be at the surface of the Sun rather than in the core! In the TGD based model, it would be much easier to explain the findings about SN2021yfj and also the findings of Moshina (see this).
5. TGD also predicts that planets were formed in the explosions throwing out a shell of dark matter at the surface of the star, later suffering a gravitational condensation to a planet (see this). SN2021yfj could have experienced this kind of explosion, mini Big Bangs throwing out surface layers.

   This would predict that the nearer the planet is to the Sun, the heavier the elements forming it are and the smaller its distance from the Sun is. This conforms with the fact that inner planets are rocky planets and outer giant planets contain mostly light elements. Also SN2021yfj could have planets consisting of elements lighter than those detected.

The fractality of the TGD Universe in both spatial and temporal sense suggest what might be regarded as a generalization of the "ontogeny recapitulates phylogeny" principle (ORP) of biology stating that the evolution of an individual reflects the evolution of the species. The evolution of the astrophysical system by mini Big Bangs could be identified as a fractally scaled down version for the evolution of the cosmos by Big Bang.

1. If taken seriously, this principle could make possible educated guesses about the cosmic evolution, for instance what happened in the formation of galaxies and stars as done in (see this this). For instance, the lower bound for the temperature of sunspots is 3000 K which is the temperature at which the decoupling of radiation from matter would have occurred in the standard cosmology. The order of magnitude for the temperature of the photosphere is about 5000 K, was this the cosmic temperature at which the stars were formed?
2. The standard cosmology requires much lower temperature and this could explain the findings of JWST in conflict with the standard cosmology. The Universe would remain transparent since the radiation could propagate along monopole flux tubes connecting astrophysical objects.

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 and 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.

Two big news: interstellar space has "EEG" and stellar energy production could occur at its surface

Today I learned of two highly interesting findigs, which might mean a revolution in the world view.

The first news (see this) was that Voyager 1 has detected strange hum in interstellar space. Plasma waves are in question. The google search with the prompt "frequency range of the cosmic hum detected by Voyager 1" gives a short summary informing that the hum is in the frequency range 20-100 Hz. This frequency range is contained in EEG, whose frequencies are in the range 1-100 Hz. 20 Hz represents the lower limit for the frequencies heard by humans. It would not be terribly surprising if this hum would relate to consciousness and quantum biology.

It took one day for the skeptic inside me to get worried and to warn that the claimed frequency range might be a quirk of the language model involved, just a wrong association. From the article Persistent plasma waves in interstellar space detected by Voyager 1 of Ocker et al, published in Nature Astronomy already 2021, one learns that the actual actual frequency is around 3 kHz. Google informs that the plasma frequency of electrons in ionosphere is also few kHz so that electron densities are roughly the same.

It would correspond to the plasma frequency of electron equal to (n_ee²/_e)^1/2, where n_e is the number density of electrons and m_e is the mass of electron. 20 Hz frequency would correspond to an electron density, which is by a factor about .5× 10^-4 lower. For protons, having m^p∼ 2×10³m_e, the frequency for the same number density suggested by plasma neutrality would be around 190 Hz.

However, the brain has neuronal synchrony at a frequency around 1 kHz, which in TGD would originate from quantum coherence, so that the finding might have something to do with consciousness. TGD inspired theory of consciouness and quantum biology indeed predict that plasmoids are predecessors of biological life. They exist in plasma phase. NASA has detected evidence for plasmoids in ionosophere and also the interplanetary and interstellar space can contain them (see for instance this).

Plasma oscillations would make possible coherent long scale oscillations at the level of plasma induced by the quantum coherence at the field body of the system. The frequency modulation of the signal from the field body generating plasma waves by resonance could generate non-propagating analogos of nerve pulse patterns and define analogs of non-propagating nerve pulse patterns. TGD suggests an analogous mechanism for the communication from and control of the neural system to the field body. Also non-propagating sequences of Sine-Gordon solitons are possible (see for instance this).

There also a second fascinating news (see this and the Nature article). There is also a popular article in finnish (see this). The explosion of supernova SN 2021yfj ejected shells rich in silicon, sulphur and argon. These elements should exist in the core of star, not at its surface if we believe in the standard model of nuclear fusion.

How does this relate to TGD? Last year it became clear that TGD leads to a model of the star that even deviates drastically from the standard model. The production of radiation energy and solar wind would occur on the surface of the star by a process in which the new physics predicted by TGD plays a central role (see this). In other words, there need be no nuclear fusion in the core of the star. The story about the mechanism of energy production in the star could be completely wrong.

I didn't think that confirmation of this prediction would come in my lifetime. It did! It hadn't occurred to me that a supernova explosion could verify the model.

One consequence is that the attempt to reproduce the conditions of the solar core in the laboratory to achieve nuclear fusion might be a failure. This might explain why fusion has not succeeded despite attempts for who knows how long. TGD also predicts an alternative energy production process as the counterpart of "cold fusion" (see this).

Could life have emerged when the universe was at room temperature?

The following considerations were inspired by the popular article " Ask Ethan: Did life begin when the Universe was room temperature? of Ethan Siegel (see this).

One can consider this question in both standard cosmology and in the TGD inspired cosmology. For both options, if one identifies life as chemical life, the building brick atoms of various important biomolecules should have been present at this stage of cosmological evolution.

Cosmic microwave background (CMB) was decoupled from matter at temperature 3,000 K, below which only light neutral atoms, but no molecules, were present. After that CMB temperatures decreased and at some moment it was equal to T∼ 300 K. The identification of the temperature T for the emergence of life as temperature of the cosmic microwave background (CMB) is excluded since no basic bio-molecules were present at that time, only simplest atoms were present. Therefore the temperature T∼ 300 K for matter should have emerged during the gravitational heating.

If the heating led to the ordinary nuclear fusion, it is difficult to understand how the biomolecules could have survived. In the standard cosmology this does not look plausible. Therefore the answer to the question is negative.

In TGD inspired cosmology, the temperature T would naturally correspond to the quantum critical temperature T_P ∼ 300 K for the Pollack effect (see this). In TGD it would be involved with the transformation of protons to their dark counterparts at magnetic flux tubes (see this, this, this, this and this). Dark nuclei would have transformed to ordinary nuclei liberating almost all nuclear binding energy. The temperature T_P would have been reached by gravitational heating and Pollack effect would make possible the generation of nuclei by dark fusion (see this, this, this and this) in turn forming the needed biomolecules.

One can argue that the liberated energy heats the matter to even higher temperatures and the ordinary fusion is ignited. However, the infinite number of degrees of freedom for the monopole flux tubes implies that there is a limiting temperature T_H (see this and this), analogous to the Hagedorn temperature (see this) discovered in string models and nuclei could be generated solely by "cold fusion" without not ignition of ordinary fusion. Note that there is an entire hierarchy of Hagedorn temperatures corresponding to preferred p-adic length scales characterizing the flux tubes.

The biomolecules would have survived if T_P was slightly below the Hagedorn temperature T_H for the monopole flux tubes serving as an upper bound for the temperature of flux tubes and therefore of the temperature of matter. Dark fusion could have generated planets (see this) and perhaps even part of the matter of the Sun (see this), the physics of which could be dramatically different from that in the standard model. If so, the ordinary nuclear fusion could be replaced with dark fusion in TGD. Life could have emerged much earlier than in the standard cosmology.

See the article Could life have emerged when the universe was at room temperature? or the chapter Quantum gravitation and quantum biology in TGD Universe.

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.

What the mysterious shortening of the day by 1.6 ms could mean?

I encountered an interesting posting in the Deep in Space group. I also found a popular article about the effect (this). There are many effects causing variation of the length of the day but this particular finding has not found any convincing explanation in terms of the known physics.

Here is the copy of the posting of the Deep in Space group:

On multiple days this summer including July 22 and August 5 Earth spun faster than usual, making the day shorter by up to 1.6 milliseconds. Even July 11 was confirmed by atomic clocks as the shortest day of 2025 so far. This isn t just a one-off quirk. The unusual speed-up was first noticed in 2020 and has continued into 2025, baffling researchers. While our planet's rotation naturally wobbles and shifts, this sustained acceleration is unprecedented.

Scientists have theories: shifting ocean currents, atmospheric patterns, movements in Earth's molten core, even the Moon's changing position relative to the equator. But here's the twist: none of these fully explain what's happening.

Nobody expected this, says Leonid Zotov of Moscow State University. And that is the unsettling part: we don't know why our days are shrinking. Could it be a natural cycle we don t yet understand? Or is there something deeper, hidden in the rhythms of our planet? For now, the mystery continues and the clock is quite literally ticking faster.

The finding of a standard physics based model for the finding has turned out to be very difficult. There are two basic options according to whether there is external angular momentum feed or not.

External angular momentum feed seems to be needed

There is no convicing standard physics explanation for the shortening of the day. As an example, one can consider one particular attempt, which starts from natural question whether angular momentum conservation and perhaps even energy conservation could be used to model the effect. One can perform a quantitative estimate demonstrating that this is not possible.

1. Assume that the rotation velocity of an object, which is some part of the Earth, most naturally the entire Earth since the increased rotation rate is observed at the surface of the Earth. Also outer core, inner core, or innermost core can be considered.

   Idealize the rotating object as a solid ball with radius R, having a constant density ρ, which in the first approximation is the average density of Earth. The mass is M(R)= (4\pi/3) ρ R³ and the moment of inertia is I=xMR², x= 2/5 .

   If the rotating object is liquid (outer core is liquid), its inertial momentum is smaller due to the varying velocity field of the liquid. Suppose this gives a correction factor y so that one has

   I= yxMR², x=2/5 .

2. Assume angular momentum conservation in the transition in which the rotation frequency changes. The Earth would be like a skater contracting itself so that its momentum of inertia would be reduced. For a spherical solid body with constant density, the angular momentum is

   L= Iω = yxMR²ω .

   The conservation condition gives

   Δ R/R= -1/2 × (Δ ω/ω) .

   Δ ω/ω is from Δ T= 1.6 ms given by Δ ω/ω ∼ 3.1 × 10^-8. At the surface of the Earth this would give an unrealistically large value of ΔR∼.09 m. This alone excludes the assumption that angular momentum is conserved.

   Obviously a model, which assumes also energy conservation is doomed to fail.

Could external momentum feed from the gravitational body of the Earth and Sun explain the shortening of the day?

It seems that external angular momentum feed must be assumed. It also seems that new physics might be involved.

1. The notion of gravitational magnetic/field body represents new astrophysics predicted by the TGD based view of space-time as a 4-surface in H=M⁴× CP₂ (see this and this).
2. Holography = holomorphy principle (H-H) is an essential part of TGD (see this, this and this) and forces the introduction of what I call zero energy ontology (ZEO) (see this and this). This means that the space-time surface, analogous to Bohr orbit, replaces 3-surface as a fundamental object. This surface turns out to be a minimal surface except at singularities and is slightly non-deterministic as also 2-D minimal surfaces for which a given frame allows several minimal surfaces. This non-determinism forces ZEO, which solves the basic problem of quantum measurement theory.
3. Number theoretical vision predicts a hierarchy of effective Planck constants (see this), involving gravitational and also electric Planck constants (see this and this) assignable to long range classical fields. This predits quantum coherence in astrophysical scales and predicts a large number of numerical miracles in astrophysical scales.

Could one identify the shortening of the day as a quantum transition involving an angular momentum transfer from the gravitational magnetic body of the Sun-Earth system to the Earth where it becomes classical angular momentum?

1. The gravitational Planck constant ℏ_gr introduced originally by Nottale (see this), characterizes the magnetic body of the Sun-Earth system (see this). ℏ_gr is given by

   ℏ_gr= GM_SM_E/β₀, β₀∼ 2^-11 .

   Here the solar mass is given by M_S= .333× 10⁶M_E. This result follows from the Bohr orbit model of the planetary orbits introduced by Nottale.

   The minimal feed of the angular momentum would be ℏ_gr and classically corresponds to Δ L=x M_E R²Δ ω, x= 2/5.

2. Assume that the transferred angular momentum becomes classical angular momentum of the Earth. In the general case the increase of the angular momentum for the Earth is quantized and given by

   Δ L = IΔ ω =(2/5M_E R²Δ ω= nℏ_gr= n(GM_SM_E/β₀ .

   Here n is an integer. This gives the condition

   (2/5) (R_E/cT_s= (GM_S/β₀)= n(r_S(Sun)/R_E)/2β₀ .

   The basic numbers are r_s(Sun)= 3 km and R_E= 6.3734× 10⁶ m giving r_s(Sun)/R_E= .471× 10^-3. T_s= 1.6 ms gives R_E/cT_s = 13.279. The above equation gives 5.31= .471n and is satisfied for n=11.27 ∼ 11. The transition with ΔL= 11 ℏ_gr would give a reasonable result. There are different estimates for the value of T_s varying from 1.2 ms to 1.6 ms so that the value of n are in the range [8,11].

The effect could be interpreted as a transfer of angular momentum from the Sun to the Earth. The effect could serve as a direct evidence for the notion of gravitational magnetic body and the notion of gravitational Planck constant. The quantization of the effect gives hope of testing of the model.

See the article Magnetic Bubbles in TGD Universe: Part I 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.

Comparing the standard view and TGD vision of the formation of astrophysical objects

I learned of a very interesting empirical finding (see this) related to the attempts to understand the process leading to the formation of light molecules H₂ and HD from atoms. According to the standard view, this process precedes the ignition of the nuclear fusion made possible by gravitational condensation. This process is not so well-understood as one might think and the findings challenge the prevailing view.

The gravitational collapse leading to the formation of a star requires low temperature and large enough mass. In the formation of first stars, HeH⁺ molecules act as coolants of the gas cloud. In standard view, this helps to reach gravitational instability inducing a gravitational collapse leading to the formation of a star and initiation of nuclear fusion. The surprise was that the rate for the reactions removing the coolant does not decrease with temperature as expected. This finding challenges the prevailing view about the formation of the first generation stars and inspired the comparison of the standard view of the formation of galaxies, stars and planets with the TGD view.

See the article Comparing the standard view and TGD vision of the formation of astrophysical objects 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 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.

Holography = holomorphy principle (H-H) and CP2 type extremals as a model for wormhole contact

I used a lot of effect in trying to solve what I thought to a technical problem related to the  finding of the roots of (f₁,f₂) appearing in the Euclidean space-time regions. It took time to realizes that this only an ansatz, which is  less general than H-H  and need not work  for wormhole contacts as deformations of CP₂ type extremals (see this).

1. The first problem is that in Minkowskian regions defining the parallel space-time sheets one has two kinds of solutions for which  hypercomplex coordinate u resp.  its conjugate v appears in f_i resp. its conjugate. These should correspond to a single solution and the only way is to consider their  union. The two regions in question have a natural identification as Minkowskian space-time sheets connected by  a wormhole contact with an Euclidean signature of the induced metric.

   At the  surface,  where  the two sheets are glued,   f_i must be invariant under conjugation, which for real coefficients of f_i requires  u=v  and reality of various complex coordinates or at least that the surface in question is invariant under complex conjugation.

2.   In Euclidean regions, the realization of holography = holomorphy principle (H-H), using (f₁,f₂)=(0,0) ansatz assuming that either hypercomplex coordinate   u or v   is a  dynamical variable,  leads to a problem. Either u or v is a complex analytic function f of CP₂ coordinates  and its reality implies  Im(f)=0   so that CP₂ projection is 3-dimensional, which means the failure of the holomorphy with respect to the CP₂ coordinates.  For a moment I thought that Wick rotation might help but this was not the case.
3. This forces to give up (f₁,f₂)=(0,0) ansatz and assume only H-H. The original vision was that the Euclidean region as a wormhole contact corresponds to a deformation of a canonically embedded CP₂ so that it has a light-like coordinate curve  of u or v as M⁴ projection. These space-time surfaces are holomorphic so that field equations are satisfied.

   The gluing condition implies constancy condition  v=v₀ resp. u=u₀   and v resp. u  is replaced with a real CP₂ coordinate s(u) resp. s(v).  M⁴ complex coordinate w can be a function of CP₂ coordinates.

4. The gluing condition for the two sheets requires u₀=v₀ which for u=m⁰+m³ and v= m⁰-m³ gives m⁰ = 2u₀ and m³=0. At the points of this 3-surface) there is an edge at which the coordinate curves for u and v meet: the interpretation could be in terms of an exotic smooth structure (see this, this, and this) as standard smooth structure with a defect to which fermion pair creation or fermion scattering vertex can be assigned. The two sheets are glued together along a 3-surface X³ with 3-D CP₂ projection invariant under complex conjugation. The CP₂ projection X³ must contain a homologically non-trivial 2-surface since the wormhole contact must carry a monopole flux between the space-time sheets.  

This tentative picture would relate several key ideas of TGD: H-H involving hypercomplex numbers, the notion of light-like partonic orbit, the idea that exotic smooth structures make possible non-trivial scattering theory in 4 dimensional space-time. One can compare this picture with the intuitive phenomenological picture.

See the article Holography= holomorphy vision and a more precise view of partonic orbits or the chapter Holography= holomorphy vision: analogues of elliptic curves and partonic orbits.

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.

What are entanglement batteries and quantum batteries?

Quantum information science is a rapidly developing field. My latest surprise was caused by a popular article in Sciencedaily (see this). The article told about the article of Ray Ganardi et al with the title "Second Law of Entanglement Manipulation with Entanglement Battery" (see this). I also learned of quantum batteries as a new extremely fast way to store energy (see this). What do these notions mean and what could be their TGD counterparts?

Entanglement batteries

The key idea of quantum information science leading to these notions is to take thermodynamics as a "role model" for quantum information science by replacing energy with information.

Consider first thermodynamics.

1. In thermodynamics, Carnot's law relates to a thermodynamic system in a heat bath and gives an upper bound for the fraction of heat energy which can be transformed to work, which is ordered energy. A cylinder containing a hot case and expanding is a basic example of this kind of situation.
2. The heat bath serves as a source of thermal energy, which can be partially transformed to work. This operation is the reversal for the dissipation occurring spontaneously by the second law. The presence of the heat bath would be required by the second law. Carnot's law gives an expression for the maximal efficiency in terms of the ratio of the difference of the temperatures of the system and heat bath and the temperature of the heat bath.
3. The heat bath as a source of thermal energy can be replaced with a source of some other kind of energy. Battery is the basic example of this kind of energy source. In biology cell membranes and proteins serve as batteries providing metabolic energy.

In quantum information theory energy is replaced by entanglement to which one can assign information. Assume that entanglement manipulation involves only local operations and classical communications.

1. Is reversible entanglement manipulation by a third system possible? This would be analogous to the manipulation of the system in a heat bath or in presence of a battery so that the system could do work and be returned to its original state reversibly.
2. Reversible entanglement manipulation is not possible for a mere pair of entangled systems. But what happens if one adds a third system as an analog of heat bath or battery but carrying entanglement instead of energy? One can call this system an entanglement battery. Is reversible entanglement manipulation possible now? Does the analog of Carnot law make sense?

   It turns out that in this case the entanglement manipulation can be a reversible process for the pair of entangled systems but the third system loses entanglement and therefore information so that the analog of the second law is true.

TGD counterpart for entanglement battery

If good to start by listing the basic new ideas brought by TGD (see this and this).

TGD involves two complementary views of reality.

1. The view of physics as geometry, combined with the condition that Poincare invariance of the special relativity is not lost, leads to a new view about space-time differing rather dramatically from the Einsteinian view.

   Space-time is a surface in H=M⁴× CP₂ Holography = holomorphy principle (H-H) characterizing its dynamics has deep implications: for instance, classical theory is exactly solvable and the space-time surface are minimal surfaces, analogous to Bohr orbits of particles identified as 3-surfaces, irrespective of the classical action as long as it is general coordinate invariant and depends only on the induced geometry (see this, this, this, and this).

2. The view of physics as number theory leads to a vision about what cognition is but makes also very powerful predictions about ordinary physics. As a matter of fact, most quantitative predictions follow from the number theoretic vision (see this, this, this, this, and this).

The TGD view of quantum physics involves several new elements.

1. The hierarchy of effective Planck constants h_eff=nh₀ with the estimate h= (7!)²h₀, where h₀ is the miminal value of h_eff=nh₀ (see this). This makes possible equantum coherence in arbitrarily long scales. This also leads to p-adic physics as correlate for cognition.
2. Zero energy ontology (ZEO) (see this and this) predicts that the counterpart for a sequence of repeated quantum measurements of the same observables does not change the system unaffected but a flow of consciousness, a conscious entity, self. In these "small" state function reductions (SSFRs), the system's internal state changes. The corresponding observables relate to the classical non-determinism associated with the space-time surfaces if H-H is true and are assigned with cognition. These observables have no counterpart in standard physics.
3. In ZEO, the TGD counterparts of quantum measurements of physical observables correspond to "big" state function reductions (BSFRs). The arrow of geometric time changes in BSFR (see this). The change of the arrow of time can be regarded as death or falling asleep: this in a universal sense. Consciousness is not lost but corresponds to a self with an opposite arrow of geometric time. The classical signals sent during this period do not reach the brain in the future so that we do not remember anything about the deep sleep state.

What implications the TGD view of physics and consciousness might have concerning quantum information science, in particular the notion of entanglement battery?

1. The number theoretic view of TGD brings in the p-adic physics of cognition in which a hierarchy of Planck constants (see this, this, this, this and this) and hierarchy of p-adic length scales are in a central role (see this).

   Recent work (see this, this, and this) has led to a generalization of p-adic number fields to function fields related to p-adic number fields by a morphism. In this view p-adic physics could be seen as a convenient description of the non-determinism of real number based physics rather than a fundamental notion. Prime p corresponds to a prime near power of a small prime defining a degree of a polynomial. This generalization makes it possible to understand the p-adic length scale hypothesis stating that p-adic primes new powers of 2 (and also 3) seem to be physically of special importance.

2. Cognitive information is associated with cognitive entanglement and cognitive state function reductions reduce this entanglement. This kind of entanglement is not possible in standard quantum theory. It relates to the slight non-determinism of the classical time evolution assuming H-H. Space-time surfaces as fundamental objects are like slightly non-deterministic Bohr orbits for particles as 3-surfaces. This non-determinism naturally corresponds to p-adic non-determinism.

   Transfer of cognitive information would mean transfer of mental images. One can say that in the simplest situation the entangled pair of systems would be like a student whereas the entanglement manipulator would be in the role of a teacher, and the entanglement battery would be like a text book. The learning would mean generation of entanglement between the members of the pair (or a more general system) defining the student. Quantum teleportation could make possible the transfer of entanglement for a subsystem.

3. The number theoretical counterpart of the second law is Negentropy Maximization Principle (NMP) (see this) states that the number theoretical complexity of the space-time surfaces is bound to increase. By H-H principle, space-time surfaces are roots for a pair of polynomials of generalized complex coordinates of H and their algebraic complexity unavoidably increases in the sequence of quantum jumps. This gives rise to evolution.
4. One particular measure for the number theoretical complexity is given by the effective Planck constant h_eff, which could correspond to the dimension of an algebraic extension of rationals. The degree of the polynomial defining the extension provides an alternative measure and it is not possible to make strong conclusions at this stage. The larger the value of h_eff, the larger the maximal entanglement entropy and the potential cognitive information content.
5. p-Adic entanglement negentropy can be positive and by NMP tends to be so (see this). Negentropic entanglement serves as a correlate for conscious cognitive information associated with p-adic physics characterizing the classical non-determinism. One can assign to it p-adic entanglement negentropy as a generalization of Shannon entropy. In the number theoretic evolution maximal entanglement negentropy increases. This tendency, coded by NMP, is mathematically analogous to the increase of entropy but states just the opposite. This can be understood: the p-adic negentropy is associated with the entanglement whereas the ordinary entropy is associated with information of a third system about either entangled system.
6. p-Adic entanglement negentropy and real entanglement entropy are closely related but p-adic entanglement negentropy can be larger than the latter and by NMP tends to be so. Jeremy England (see this) has observed that evolution and increase of entropy are closely related. This looks paradoxical. In the TGD framework which can be however understood since the increase of p-adic negentropy in evolution implies the increase of real entropy (see this).
7. The energy scale of a quantum system as a function of h_eff increases. Therefore the increase of h_eff and of maximal cognitive information requires energy feed having an interpretation as metabolic energy. Biosystems need a metabolic energy feed to stay cognitively conscious.

The theorem of Ganardi et al and the TGD view of living systems

The theorem of Ganardi et al allows to have a new perspective on the TGD view of living and conscious systems.

1. In TGD inspired theory of consciousness and quantum biology, sensory perception and cognition could be seen as construction of standardized mental images (see this) and conscious communications could be seen as a transfer of standardized mental images. TGD inspired biology and neuroscience involve a concrete proposal for the mechanism involved. The theorem of Ganardi et al justifies the intuitive picture concerning conscious information transfer.
2. Entangled subsystem pairs of a biological system, such as the two DNA strands, the brain consisting of two hemispheres, and the magnetic bodies of the left and right hemisphere, define conscious information packets. By the theorem of Ganardi et al, the entanglement can be transferred by quantum teleportation involving local operations and classical communications between two conscious systems. The entangled subsystem pairs would define cognitive mental images so that one could talk about a telepathic transfer of mental images.

   Note that in TGD classical physics dictated by H-H is an exact part of quantum physics so that classical communications are very natural.

3. H-H implies that the basic geometric objects are space-time surfaces analogous to Bohr orbits for particles identified as 3-surfaces and replace 3-surfaces in ZEO as fundamental objects. The Bohr orbits are slightly non-deterministic due to the weak non-determinism associated with classical time evolution. This also implies non-determinism in fermionic degrees of freedom (see this and this): H-H allows to solve exactly also the Dirac equation for the induced spinors to be distinguished from the Dirac equation for in H.
4. The cognitive entanglement could be in discrete degrees of freedom associated with a single space-time surface or between these degrees of freedom associated with separate space-time surfaces. For ordinary 2-D minimal surfaces the seats of non-determinism correspond to frames at which the surface can branch in several ways. In the 4-D case, these degrees of freedom would correspond to 3-surfaces as loci of classical non-determinism. These loci would define memories at the fundamental level (see this). Also the entanglement between two disjoint space-time surfaces can be considered as well as the entanglement between 3-D light-like partonic orbits.

One can pose several questions in this framework.

1. Does the generalized Carnot's law give an upper bound of information transferred from the entanglement battery to the entangled pair of systems in terms of the p-adic temperature as the cognitive analog of temperature having a spectrum quantized as T_p=1/n?

   Does the T_p→ 0 limit correspond to an optimal situation in which the entanglement battery is a pure system and an ideal source of entanglement provided it has a large degeneracy of states.

2. The failure of the strict classical dynamics predicts large degeneracy of states due to the possibility of a large number of non-deterministic time evolutions. This non-determinism would correspond mathematically to the non-determinism of p-adic differential equations. This alone does not give rise to entanglement however.
3. One can however regard the discrete set of loci as subsystems which can have time like-entanglement so that the non-determinism gives rise to a cognitive entanglement battery.

Quantum batteries

Quantum batteries (see this) are highly entangled quantum coherent systems. This makes possible their loading using collective quantum transitions in which the component systems experience quantum transition simultaneously. This can make the loading of quantum batteries extremely fast (see this).

In TGD, this kind of collective quantum transitions, analogous to phase transitions, are a basic element in the model of conscious information transfer and TGD suggests a concrete model for these phase transitions. Genetic code, having a universal realization in TGD, would play a key role in this mechanism.

1. Genetic codons correspond at fundamental level correspond to entangled dark proton triplets and chemical representation is only a secondary representation (see this, this, this, and this). Dark codons in turn entangle further to form dark genes. The communications between dark genes with 3N dark protons occur by sending entangled dark 3N-photons analogous to Bose-Einstein condensates.
2. The communication occurs by 3N-resonance involving simultaneous absorption of 3N-photons changing the state of the dark gene represented by 3N dark protons.
3. The frequencies involved are cyclotron frequencies for dark protons and the modulation of the frequency scale represents the message transformed to a sequence of 3N-pulses. Also partial multi resonance is possible if the modulation is not the same for all dark protons. The communications to the magnetic/field body (such as EEG) and control of biomatter by the field body would be based on this mechanism.

See the article What are entanglement batteries and quantum batteries? or the chapter Are Conscious Computers Possible in TGD Universe?.

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.

New physics in Jupiter?

I heard interesting news about the physics of the solar system. The physics of the Jupiter's magnetosphere is not quite as it should be. There is popular article "Unusual Plasma Waves Above Jupiter s North Pole" (see this). There is also a popular article in finnish (see this).

First some information about Jupiter. Jupiter is a giant planet with 90 moons. A giant storm, the red spot, has been raging for at least the last 350 years. Jupiter has a strong magnetic field, which is 54 times that of Earth (27 Gauss) and auroras are involved with it.

A team of researchers led by the University of Minnesota in the United States has observed new types of plasma waves at Jupiter's north pole that have not been seen before in the solar system. NASA's Juno spacecraft detected this mysterious wave phenomenon. The Juno spacecraft was launched into space in 2011 and reached Jupiter on July 4, 2016. Since then, the spacecraft has been studying the gas giant - including its magnetic field. In the final phase of its operation, Juno observed that Alfven waves in Jupiter's magnetic field plasma were transformed into Langmuir waves. This has not been observed anywhere else before.

Alfven waves and Languir waves are are related to the plasma phase in a magnetic field. Wikipedia gives more information about these waves.

1. Alfven waves can be visualized as transverse oscillations of magnetic flux tubes. They propagate at an almost constant speed like light, but the speed depends slightly on the magnetic field and ion density and approach the speed of light in strong magnetic fields. The speed is proportional to the magnetic field strength and inversely proportional to the square root of the average ion density. (see this).
2. Langmuir waves are electron waves parallel to the magnetic field (i.e. longitudinal) for which the frequency depends very weakly on the wave vector and is inversely proportional to the square root of the electron density. (see this).

   Langmuir waves occur at a frequency at which the dielectric constant vanishes. This means physically that at the plasma frequency an insulator cannot store energy in an electrostatic field. For example, the frequency-dependent capacitance of a capacitor goes to zero at this frequency. The energy propagates as a wave motion at this frequency that has very weak dependence on the wavelength. One could say that the energy of the sm radiation is stored in the plasmonic oscillation of electrons. For smaller frequencies the propagation is not possible and radiation is reflected at the surface.

The transformation of Alfven waves into Langmuir waves was not expected. The frequencies would be the same for these waves, which gives a condition that fixes the wave vector for the Alfven wave.

What would TGD (see this and this) say about the possible new physics.

1. In TGD Alfwen waves could correspond to transverse oscillations of monopole flux tubes (see this and this). Monopole flux tubes, not possible in Maxwell's theory, could be one piece of the conjectured new physics.

   A second piece of the new physics could be that at the monopole flux tubes protons and perhaps also other ions can be "dark", i.e. they are associated with a large effective Planck constant h_eff. They do not interact directly with the ordinary matter and in this sense behave like dark matter.

   The transformation of ordinary matter into dark matter is possible. The large h_eff implies quantum coherence on very long scales and it plays a fundamental role in TGD-based quantum biology and astrophysics.

   This dark matter does not correspond to galactic dark matter. It however explains the mysterious gradual reduction of baryon density in cosmological scales as a transformation of ordinary baryons to dark baryons at the monopole flux tubes associated with cosmic evolution as increase of the number theoretic complexity (see this).

2. The creation of the h_eff>h phase requires energy and, for example, the Pollack effect provides energy when photons are absorbed. The energy of photons is typically at IR, visible and UV wavelengths.

   When positively charged protons/ions are "kicked" by photons onto a magnetic body, they become "dark". The result is a negatively charged region, the exclusion zone (EZ), as Pollack calls it. Charge separation occurs: positive charge on magnetic flux tubes and negative charge in the EZ. This is new physics and is a central part of TGD-based quantum biology.

3. However, dark protons/ions spontaneously transform into ordinary ones when h_eff decreases and releases energy. At the same time, they are "dropped" from the monopole flux tubes and become ordinary. The released energy must go somewhere. Could the energies of the dark protons be stored in the Langmuir waves?
4. But how do Alfven waves relate to this? Could the Alfwen wave relate to dark protons/ions as an oscillation of the flux tube. As ordinary protons are kicked onto the flux tubes by photon absorption, the flux tube receives an impulse in addition to energy and starts to oscillate like a spring that has been pushed. When they drop from the flux tube, the oscillations and therefore also the Alfwen wave would disappear.
5. This mechanism could make possible the transfer of positive proton charge from the surface of the planet to the higher heights and might contribute to the generation of negative charge at the surface of Earth.

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.