Thursday, December 08, 2016

Space-time engineering from space-time legos


TGD predicts shocking simplicity of both quantal and classical dynamics at space-time level. Could one imagine a construction of more complex geometric objects from basic building bricks - space-time legos?

Let us list the basic ideas.

  1. Physical objects correspond to space-time surfaces of finite size - we see directly the non-trivial topology of space-time in everyday length scales.

  2. There is also a fractal scale hierarchy: 3-surfaces are topologically summed to larger surfaces by connecting them with wormhole contact, which can be also carry monopole magnetic flux in which one obtains particles as pairs of these: these contacts are stable and are ideal for nailing together pieces of the structure stably.

  3. In long length scales in which space-time surface tend to have 4-D M4 projection this gives rise to what I have called many-sheeted spacetime. Sheets are deformations of canonically imbedded M4 extremely near to each other (the maximal distance is determined by CP2 size scale about 104 Planck lengths. The sheets touch each other at topological sum contacts, which can be also identified as building bricks of elementary particles if they carry monopole flux and are thus stable. In D=2 it is easy to visualize this hierarchy.
Simplest legos

What could be the simplest surfaces of this kind - legos?

  1. Assume twistor lift so that action contain volume term besides Kähler action: preferred extremals can be seen as non-linear massless fields coupling to self-gravitation. They also simultaneously extremals of Kähler action. Also hydrodynamical interpretation makes sense in the sense that field equations are conservation laws. What is remarkable is that the solutions have no dependence on coupling parameters: this is crucial for realizing number theoretical universality. Boundary conditions however bring in the dependence on the values of coupling parameters having discrete spectrum by quantum criticality.

  2. The simplest solutions corresponds to Lagrangian sub-manifolds of CP2: induced Kähler form vanishes identically and one has just minimal surfaces. The energy density defined by scale dependent cosmological constant is small in cosmological scales - so that only a template of physical system is in question. In shorter scales the situation changes if the cosmological constant is proportional the inverse of p-adic prime.

    The simplest minimal surfaces are constructed from pieces of geodesic manifolds for which not only the trace of second fundamental form but the form itself vanishes. Geodesic sub-manifolds correspond to points, pieces of lines, planes, and 3-D volumes in E3. In CP2 one has points, circles, geodesic spheres, and CP2 itself.

  3. CP2 type extremals defining a model for wormhole contacts, which can be used to glue basic building bricks at different scales together stably: stability follows from magnetic monopole flux going through the throat so that it cannot be split like homologically trivial contact. Elementary particles are identified as pairs of wormhole contacts and would allow to nail the legos together to from stable structures.

Amazingly, what emerges is the elementary geometry. My apologies for those who hated school geometry.

Geodesic minimal surfaces with vanishing induced gauge fields

Consider first static objects with 1-D CP2 projection having thus vanishing induced gauge fields. These objects are of form M1× X3, X3⊂ E3× CP2. M1 corresponds to time-like or possible light-like geodesic (for CP2 type extremals). I will consider mostly Minkowskian space-time regions in the following.

  1. Quite generally, the simplest legos consist of 3-D geodesic sub-manifolds of E3× CP2. For E3 their dimensions are D=1,2,3 and for CP2, D=0,1,2. CP2 allows both homologically non-trivial resp. trivial geodesic sphere S2I resp. S2II. The geodesic sub-manifolds cen be products G3 =GD1× GD2, D2=3-D1 of geodesic manifolds GD1, D1=1,2,3 for E3 and GD2, D2=0,1,2 for CP2.

  2. It is also possible to have twisted geodesic sub-manifolds G3 having geodesic circle S1 as CP2 projection corresponding to the geodesic lines of S1⊂ CP2, whose projections to E3 and CP2 are geodesic line and geodesic circle respectively. The geodesic is characterized by S1 wave vector. One can have this kind of geodesic lines even in M1× E3× S1 so that the solution is characterized also by frequency and is not static in CP2 degrees of freedom anymore.

    These parameters define a four-D wave vector characterizing the warping of the space-time surface: the space-time surface remains flat but is warped. This effect distinguishes TGD from GRT. For instance, warping in time direction reduces the effective light-velocity in the sense that the time used to travel from A to B increases. One cannot exclude the possibility that the observed freezing of light in condensed matter could have this warping as space-time correlate in TGD framework.

    For instance, one can start from 3-D minimal surfaces X2× D as local structures (thin layer in E3). One can perform twisting by replacing D with twisted closed geodesics in D× S1: this gives valued map from D to S1 (subset CP2) representing geodesic line of D× S1. This geodesic sub-manifold is trivially a minimal surface and defines a two-sheeted cover of X2× D. Wormhole contact pairs (elementary particles) between the sheets can be used to stabilize this structure.

  3. Structures of form D2× S1, where D2 is polygon, are perhaps the simplest building bricks for more complex structures. There are continuity conditions at vertices and edges at which polygons D2i meet and one could think of assigning magnetic flux tubes with edes in the spirit of homology: edges as magnetic flux tubes, faces as 2-D geodesic sub-manifolds and interiors as 3-D geodesic sub-manifolds.

    Platonic solids as 2-D surfaces can be build are one example of this and are abundant in biology and molecular physics. An attractive idea is that molecular physics utilizes this kind of simple basic structures. Various lattices appearing in condensed matter physics represent more complex structures but could also have geodesic minimal 3-surfaces as building bricks. In cosmology the honeycomb structures having large voids as basic building bricks could serve as cosmic legos.

  4. This lego construction very probably generalizes to cosmology, where Euclidian 3-space is replaced with 3-D hyperbolic space SO(3,1)/SO(3). Also now one has pieces of lines, planes and 3-D volumes associated with an arbitrarily chosen point of hyperbolic space. Hyperbolic space allows infinite number of tesselations serving as analogs of 3-D lattices and the characteristic feature is quantization of redshift along line of sight for which empirical evidence is found.

  5. These basic building bricks can glued together by wormhole contact pairs defining elementary particles so that matter emerges as stabilizer of the geometry: they are the nails allowing to fix planks together, one might say.

Geodesic minimal surfaces with non-vanishing gauge fields

What about minimal surfaces and geodesic sub-manifolds carrying non-vanishing gauge fields - in particular em field (Kähler form identifiable as U(1) gauge field for weak hypercharge vanishes and thus also its contribution to em field)? Now one must use 2-D geodesic spheres of CP2 combined with 1-D geodesic lines of E2. Actually both homologically non-trivial resp. trivial geodesic spheres S2I resp. S2II can be used so that also non-vanishing Kähler forms are obtained.

The basic legos are now D× S2i, i=I,II and they can be combined with the basic legos constructed above. These legos correspond to two kinds of magnetic flux tubes in the ideal infinitely thin limit. There are good reasons to expected that these infinitely thin flux tubes can be thickened by deforming them in E3 directions orthogonal to D. These structures could be used as basic building bricks assignable to the edges of the tensor networks in TGD.

Static minimal surfaces, which are not geodesic sub-manifolds

One can consider also more complex static basic building bricks by allowing bricks which are not anymore geodesic sub-manifolds. The simplest static minimal surfaces are form M1× X2× S1, S1 ⊂ CP2 a geodesic line and X2 minimal surface in E3.

Could these structures represent higher level of self-organization emerging in living systems? Could the flexible network formed by living cells correspond to a structure involving more general minimal surfaces - also non-static ones - as basic building bricks? The Wikipedia article about minimal surfaces in E3 suggests the role of minimal surface for instance in bio-chemistry (see this).

The surfaces with constant positive curvature do not allow imbedding as minimal surfaces in E3. Does this mean that the proposal fails? This need not be the case since in TGD one has minimal surface in E3× S1 rather than E3.

Could one lift the immersions of H and S to E3 to minimal surfaces in E3× S1? The constancy of scalar curvature, which is now quadratic in the second fundamental form would pose one additional condition to non-linear Laplace equations expressing the minimal surface property. The analyticity of the minimal surface should make possible to check whether the hypothesis can make sense.

Dynamical minimal surfaces: how space-time manages to engineer itself?

At even higher level of self-organization emerge dynamical minimal surfaces. Here string world sheets as minimal surfaces represent basic example about a building block of type X2× S2i. As a matter fact, S2 can be replaced with complex sub-manifold of CP2.

One can also ask about how to perform this building process. Also massless extremals (MEs) representing TGD view about topologically quantized classical radiation fields are minimal surfaces but now the induced Kähler form is non-vanishing. MEs can be also Lagrangian surfaces and seem to play fundamental role in morphogenesis and morphostasis as a generalization of Chladni mechanism. One might say that they represent the tools to assign material and magnetic flux tube structures at the nodal surfaces of MEs. MEs are the tools of space-time engineering. Here many-sheetedness is essential for having the TGD counterparts of standing waves.

For background see the chapter TGD and M-theory of "TGD and Fringe Physics".

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

Articles and other material related to TGD.

Monday, December 05, 2016

Induced spinor structure and SUSY mystery

This piece of text was already included in previous posting about Occam's razor and TGD. The discussion of induced spinor structure led however to a modification of an earlier idea (one of the many) about how SUSY could be realized in TGD in such a manner that experiments at LHC energies could not discover it and one should perform experiments at the other end of energy spectrum at energies which correspond to the thermal energy about .025 eV at room temperature. I think that this observation could be of crucial importance for understanding of SUSY and therefore deserves republishing.

The notion of induced spinor field deserves a more detailed discussion. Consider first induced spinor structures.

  1. Induced spinor field are spinors of M4× CP2 for which modes are characterized by chirality (quark or lepton like) and em charge and weak isospin.

  2. Induced spinor spinor structure involves the projection of gamma matrices defining induced gamma matrices. This gives rise to superconformal symmetry if the action contains only volume term.

    When Kähler action is present, superconformal symmetry requires that the modified gamma matrices are contractions of canonical momentum currents with imbedding space gamma matrices. Modified gammas appear in the modified Dirac equation and action, whose solution at string world sheets trivializes by super-conformal invariance to same procedure as in the case of string models.

  3. Induced spinor fields correspond to two chiralities carrying quark number and lepton number. Quark chirality does not carry color as spin-like quantum number but it corresponds to a color partial wave in CP2 degrees of freedom: color is analogous to angular momentum. This reduces to spinor harmonics of CP2 describing the ground states of the representations of super-symplectic algebra.

    The harmonics do not satisfy correct correlation between color and electroweak quantum numbers although the triality t=0 for leptonic waves and t=1 for quark waves. There are two manners to solve the problem.

    1. Super-symplectic generators applied to the ground state to get vanishing ground states weight instead of the tachyonic one carry color and would give for the physical states correct correlation: leptons/quarks correspond to the same triality zero(one partial wave irrespective of charge state. This option is assumed in p-adic mass calculations.

    2. Since in TGD elementary particles correspond to pairs of wormhole contacts with weak isospin vanishing for the entire pair, one must have pair of left and right-handed neutrinos at the second wormhole throat. It is possible that the anomalous color quantum numbers for the entire state vanish and one obtains the experimental correlation between color and weak quantum numbers. This option is less plausible since the cancellation of anomalous color is not local as assume in p-adic mass calculations.


The understanding of the details of the fermionic and actually also geometric dynamics has taken a long time. Super-conformal symmetry assigning to the geometric action of an object with given dimension an analog of Dirac action allows however to fix the dynamics uniquely and there is indeed dimensional hierarchy resembling brane hierarchy.

  1. The basic observation was following. The condition that the spinor modes have well-defined em charge implies that they are localized to 2-D string world sheets with vanishing W boson gauge fields which would mix different charge states. At string boundaries classical induced W boson gauge potentials guarantee this. Super-conformal symmetry requires that this 2-surface gives rise to 2-D action which is area term plus topological term defined by the flux of Kähler form.

  2. The most plausible assumption is that induced spinor fields have also interior component but that the contribution from these 2-surfaces gives additional delta function like contribution: this would be analogous to the situation for branes. Fermionic action would be accompanied by an area term by supersymmetry fixing modified Dirac action completely once the bosonic actions for geometric object is known. This is nothing but super-conformal symmetry.

    One would actually have the analog of brane-hierarchy consisting of surfaces with dimension D= 4,3,2,1 carrying induced spinor fields which can be regarded as independent dynamical variables and characterized by geometric action which is D-dimensional analog of the action for Kähler charged point particle. This fermionic hierarchy would accompany the hierarchy of geometric objects with these dimensions and the modified Dirac action would be uniquely determined by the corresponding geometric action principle (Kähler charged point like particle, string world sheet with area term plus Kähler flux, light-like 3-surface with Chern-Simons term, 4-D space-time surface with Kähler action).

  3. This hierarchy of dynamics is consistent with SH only if the dynamics for higher dimensional objects is induced from that for lower dimensional objects - string world sheets or maybe even their boundaries orbits of point like fermions. Number theoretic vision suggests that this induction relies algebraic continuation for preferred extremals. Note that quaternion analyticity means that quaternion analytic function is determined by its values at 1-D curves.

  4. Quantum-classical correspondences (QCI) requires that the classical Noether charges are equal to the eigenvalues of the fermionic charges for surfaces of dimension D=0,1,2,3 at the ends of the CDs. These charges would not be separately conserved. Charges could flow between objects of dimension D+1 and D - from interior to boundary and vice versa. Four-momenta and also other charges would be complex as in twistor approach: could complex values relate somehow to the finite life-time of the state?

    If quantum theory is square root of thermodynamics as ZEO suggests, the idea that particle state would carry information also about its life-time or the time scale of CD to which is associated could make sense. For complex values of αK there would be also flow of canonical and super-canonical momentum currents between Euclidian and Minkowskian regions crucial for understand gravitational interaction as momentum exchange at imbedding space level.

  5. What could be the physical interpretation of the bosonic and fermionic charges associated with objects of given dimension? Condensed matter physicists assign routinely physical states to objects of various dimensions: is this assignment much more than a practical approximation or could condensed matter physics already be probing many-sheeted physics?

  6. Could the addition of fermions to a given state defined in terms of fermionic charges at the fermion lines defined by the boundaries of string worlds sheets at light-like orbits of partonic 2-surfaces be interpreted as supersymmetry? The smallness of cosmological constant implies that the contribution to the four-momentum from interior should be rather small so that an interpretation in terms of broken SUSY might make sense. There would be mass m∼ .03 eV per volume with size defined by the Compton scale hbar/m. Note however that cosmological constant has spectrum coming as inverse powers of prime so that also higher mass scales are possible.

    This interpretation might allow to understand the failure to find SUSY at LHC. Sparticles could be obtained by adding interior right-handed neutrinos and antineutrinos to the particle state. They could be also associated with the magnetic body of the particle. Since they do not have color and weak interactions, SUSY is not badly broken. If the mass difference between particle and sparticle is of order m=.03 eV characterizing ρvac, particle and sparticle could not be distinguished in higher energy physics at LHC since it probes much shorter scales and sees only the particle. I have already earlier proposed a variant of this mechanism but without SUSY breaking.

    To discover SUSY one should do very low energy physics in the energy range m∼ .03 eV having same order of magnitude as thermal energy kT= 2.6× 10-2 eV at room temperature 25 oC. One should be able to demonstrate experimentally the existence of sparticle with mass differing by about m∼ .03 eV from the mass of the particle (one cannot of course exclude higher mass values if Λ has spectrum). An interesting question is whether the sfermions associated with standard fermions could give rise to Bose-Einstein condensates whose existence in the length scale of large neutron is strongly suggested by TGD view about living matter.

See the chapter SUSY in TGD Universe.

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

Articles and other material related to TGD.

Can one apply Occam's razor as a general purpose debunking argument to TGD?

Occam's razor argument is one the standard general purpose arguments used in debunking: the debunked theory is claimed to be hopelessly complicated. This argument is more refined that mere "You are a crackpot!" but is highly subjective and usually the arguments pro or con are not given. Combined with the claim that the theory does not predict anything Occam's razor is very powerful argument unless the audience includes people who have bothered to study the debunked theory.

Let us take a closer look on this argument and compare TGD superstring models and seriously ask which of these theories is simple.

In superstring models one has strings as basic dynamical objects. They live in target space M10, which in some mysterious manner (something "non-perturbative" it is) spontaneously compactifies to M4 × C, C is Calabi-Yau space. The number of them is something like 10500 or probably infinite: depends on the counting criterion. And this estimate leaves their metric open. This leads to landscape and multiverse catastrophe: theory cannot predict anything. As a matter fact M4× C:s must be allowed to deform still in Kaluza-Klein paradigm in which space-time has Calabi-Yau as small additional dimensions. An alternative manner to obtain space-time is as 3-brane. One obtains also higher-D objects. Again by some "non-perturbative" mechanisms. One does not even know what space-time is! Situation looks to me a totally hopeless mess. Reader can conclude whether to regard this as simple and elegant.

I will consider TGD at three levels. At the level of "world of classical worlds" (WCW), at space-time level, and at the level of imbedding space. I hope that I can convince the reader about the simplicity of the approach. The simplicity is actually shocking and certainly an embarrassing experience for the unhappy super string theorists meandering around in the landscape and multiverse. Behind this simplicity are however principles: something, which colleagues usually regard as unpractical philosophizing: "shut-up-and-calculate!"!

1. WCW level: a generalization of Einstein's geometrization program to entire quantum physics

I hope that the reader would read the following arguments keeping in mind the question "Is this really hopelessly complicated?".

  1. Einstein's geometrization program for gravitation has been extremely successful but has failed for other classical fields, which do not have natural geometrization in the case of abstract four-manifolds with metric. One should understand standard model quantum numbers and also family replication for fermions.

    However, if space-time can be regarded surface in H=M4× CP2 also the classical fields find a natural geometrization as induced fields obtained basically by projecting. Also spinor structure can be induced and one avoids the problems due the fact that generic space-time as abstract 4-manifold does not allow spinor structure. The dynamics of space-time surfaces incredibly simple: only 4 field-like variables corresponding to four imbedding space coordinates and induced that of classical geometric fields. Nowadays one would speak of emergence. The complexity emerges from the topology of space-time surfaces giving rise to many-sheeted space-time.


  2. Even this view about geometrization is generalized in TGD. Einstein's geometrization program is applied to the entire quantum physics in terms of the geometry of WCW consisting of 3-D surfaces of H. More precisely, in zero energy ontology (ZEO) it consists of pairs of 3-surfaces at opposite boundaries of causal diamond (CD) connected by a preferred extremals of a variational principle to be discussed.

    Quantum states of the Universe would correspond to the modes of formally classical WCW spinor field satisfying the analog of Dirac equation. No quantization. Just the construction of WCW geometry and spinor structure. The only genuinely quantal element of quantum theory would be state function reduction and in ZEO its description leads to a quantum theory of consciousness.

To me this sounds not only simple but shockingly simple.

1.1. WCW geometry

Consider first the generalization of Einsteins program of at the level of WCW geometry.

  1. Since complex conjugation must be geometrized, WCW must allow a geometric representation of imaginary unit as an antisymmetric tensor, which is essentially square root of the negative of the metric tensor and thus allow Kähler structure coded by Kähler function. One must have 4-D general coordinate invariance (GCI) but basic objects are 3-D surfaces. Therefore the definition of Kähler function must assign to 3-surface a unique 4-surface.

    Kähler function should have physical meaning and the natural assumption is that it is Kähler action plus possibly also volume term (twistor lift implies it). Space-time surface would be a preferred extremal of this action. The interpretation is also as an analog of Bohr orbit so that Bohr orbitology would correspond exact rather than only approximate part of quantum theory in TGD framework. One could speak also of quantum classical correspondence.

  2. The action principle involves coupling parameters analogous to thermodynamical parameters. Their value spectrum is fixed by the conditions that TGD is quantum critical. For instance Kähler couplings strength is analogous to critical temperature. Different values correspond to different phases. Coupling constant evolution correspond to phase transitions between these phases and loops vanish as in free field theory for N=4 SYM.

  3. The infinite-dimensionality of WCW is a crucial element of simplicity. Already in the case of loop spaces the geometry is essentially unique: loop space is analogous to a symmetric space points of the loop space being geometrically equivalent. For loop spaces Riemann connection exists only of the metric has maximal isometries defined by Kac-Moody algebra.

    The generalization to 3-D case is compelling. In TGD Kac-Moody algebra is replaced by super-symplectic algebra, which is much larger but has same basic structure (conformal weights of two kinds) and a fractal hierarchy of isomorphic sub-algebas with conformal weights coming as multiples of those for the entire algebra is crucial. Physics is unique because of its mathematical existence. WCW decompose to a union of sectors, which are infinite-D variants of symmetric spaces labelled by zero modes whose differentials do not appear in the line element of WCW.

All this sounds to me shockingly simple.

1.2. WCW spinor structure

One must construct also spinor structure for WCW.

  1. The modes of WCW spinor fields would correspond to the solutions of WCW Dirac equation and would define the quantum states of the Universe. WCW spinors (assignable to given 3-surface) would correspond to fermionic Fock states created by fermionic creation operators. In ZEO 3-surfaces are pairs of 3-surfaces assignable to the opposite boundaries of WCW connected by preferred extremal.

    The fermionic states are superpositions of pairs of fermion states with opposite net quantum numbers at the opposite ends of space-time surface at boundaries of CD. The entanglement coefficients define the analogs of S-matrix elements. The analog of Dirac equation is analog for super-Virasoro conditions in string models but assignable to the infinite-D supersymplectic algebra of WCW defining its isometries.

  2. The construction of the geometry of WCW requires that the anticommuting gamma matrices of WCW are expressible in terms of fermionic oscillator operators assignable to the induced spinor fields at space-time surface. Fermionic anti-commutativity at space-time level is not assumed but is forced by the anticommutativity of gamma matrices to metric. Fermi statistics is geometrized.

  3. The gamma matrices of WCW in the coordinates assignable to isometry generators can be regarded as generators of superconformal symmetries. They correspond to classical charges assignable to the preferred extremals and to fermionic generators. The fermionic isometry generators are fermionic bilinears and super-generators are obtained from them by replacing the second second quantized spinor field with its mode. Quantum classical correspondence between fermionic dynamics and classical dynamics (SH) requires that the eigenvalues of the fermionic Cartan charges are equal to corresponding bosonic Noether charges.

  4. The outcome is that quantum TGD reduces to a theory of formally classical spinor fields at the level of WCW and by infinite symmetries the construction of quantum states reduces to the construction of representations of super-symplectic algebra which generalizes to Yangian algebra as twistorial picture suggests. In ZEO everything would reduce to group theory, even the construction of scattering amplitudes! In ZEO the construction of zero energy states and thus scattering amplitudes would reduce to that for the representations of Yangian variant of super-symplectic algebra. Personally I find it hard to imagine anything simpler!

  5. One can go to the extreme and wonder whether the scattering amplitudes as entanglement coefficients for Yangian states are just constant scalars for given values of zero modes as group invariant for isometries. This would leave only integration over zero modes and if number theoretical universality is assumed this integral reduces to sum over points with algebraic coordinates in the preferred coordinates made possible by the symmetric space property.

2. Space-time level: many-sheeted space-time and emergence of classical fields and GRT space-time

At space-time level one must consider dynamics of space-time surface and spinorial dynamics.

2.1 Dynamics of space-time surfaces

Consider first simplicity at space-time level.

  1. Space-time is identified as 4-D surface in certain imbedding space required to have symmetries of special relativity - Poincare invariance. This resolves the energy problem and many other problems of GRT.

    This allows also to see TGD as generalization of string models obtained by replacing strings with 3-surfaces and 2-D string world sheets with 4-D space-time surfaces. Small space-time surfaces are particles, large space-time surfaces the background space-time in which these particles "live". There are only 4 dynamical field like variables for 8-D M4× CP2 since GCI eliminates 4 imbedding space coordinates (they can be taken as space-tme coordinates). This should be compared with the myriads of classical fields for 10-D Einstein's theory coupled to matter fields (do not forget landscape and multiverse!)

  2. Classical fields are induced at the level of single space-time sheet from their geometric counterparts in imbedding space. A more fashionable way to say the same is that they emerge. Classical gravitational field correspond to the induced metric, electroweak gauge potentials to induced spinor connection of CP2 and color gauge potentials to projections of Killing vector fields for CP2.

  3. In TGD the space-time of GRT is replaced by many-sheeted space-time constructed from basic building bricks, which are preferred extremals of Kähler action + volume term. This action emerges in twistor lift of TGD existing only for H=M4× CP2: TGD is completely unique since only M4 and CP2 allows twistor space with Kähler structure. This also predicts Planck length as radius of twistor sphere associated with M4. Cosmological constant appears as the coefficient of the volume term and obeys p-adic length scale evolution predicting automatically correct order of magnitude in the scale of recent cosmos. Besides this one has CP2 size which is of same order of magnitude as GUT scale, and Kähler coupling strength. By quantum criticality the various parameters are quantized.

    Quantum criticality is basic dynamical principle and discretizes coupling constant evolution: only coupling constants corresponding to quantum criticality are realized and discretized coupling constant evolution corresponds to phase transitions between these values of coupling constants. All radiative corrections vanish so that only tree diagram contribute.

  4. Preferred extremals realize strong form of holography (SH) implied by strong form of GCI (SGCI) emerging naturally in TGD framework. That GCI implies SH meaning an enormous simplification at the conceptual level.

    One has two choices for fundamental 3-D objects. They could be light-like boundaries between regions of Minkowskian and Euclidian signatures of the induced metric or they could be pairs of space-time 3-surfaces at the ends of space-time surface at opposite boundaries of causal diamond (CD) (CDs for a scale hierarchy). Both options should be correct so that the intersections of these 3-surfaces consisting of partonic 2-surfaces at which light-like partonic orbits and space-like 3-surfaces intersect should carry the data making possible holography. Also data about normal space of partonic 2-surface is involved.

    SH generalizes AdS/CFT correspondence by replacing holography with what is very much like the familiar holography. String world, sheets, which are minimal surfaces carrying fermion fields and partonic 2-surfaces intersecting string world sheets at discrete points determine by SH the entire 4-D dynamics. The boundaries of string world sheets are world lines with fermion number coupling to classical Kähler force. In the interior Kähler force vanishes so that one has "dynamics of avoidance" required also by number theoretic universality satisfied if the coupling constants do not appear in the field equations at all: they are however seen in the boundary values stating vanishing of the classical super-symplectic charges (Noether's theorem) so that one obtains dependence of coupling constants via boundary conditions and coupling constant evolutions makes it manifest also classically. Hence the preferred extremals from which the space-time surfaces are engineered are extremely simple objects.

  5. In twistor formulation the assumption that the inverse of Kähler coupling strength has zeros of Riemann zeta as the spectrum of its quantum critical values gives excellent prediction for the coupling constant of U(1) coupling constant of electroweak interactions. Complexity means that extremals are extremals of both Kähler action and volume term: minimal surfaces extremals of Kähler action. This would be part of preferred extremal property.

    The conditions state that sub-algebra of super-symplectic algebra isomorphic to itself and its commutator with the entire algebra annihilate the physical states (classical Noether charges vanish). The condition could follow from minimal surface extremality or provide additional conditions reducing the degrees of freedom. In any case, 3-surfaces would be almost 2-D objects.


  6. GRT space-time emerges from many-sheeted space-time as one replaces the sheets of many-sheeted space-time (4-D M4 projection) to single slightly curved region of M4 defining GRT space-time. Since test particle regarded as 3-surface touching the space-time sheets of many-sheeted spacetime, test particle experiences the sum of forces associated with the classical fields at the space-time sheets. Hence the classical fields of GRT space-time are sums of these fields. Disjoint union for space-time sheets maps to the sum of the induced fields. This gives standard model and GRT as long range scale limit of TGD.

Induced spinor structure

The notion of induced spinor field deserves a more detailed discussion. Consider first induced spinor structures.

  1. Induced spinor field are spinors of M4× CP2 for which modes are characterized by chirality (quark or lepton like) and em charge and weak isospin.

  2. Induced spinor spinor structure involves the projection of gamma matrices defining induced gamma matrices. This gives rise to superconformal symmetry if the action contains only volume term.

    When Kähler action is present, superconformal symmetry requires that the modified gamma matrices are contractions of canonical momentum currents with imbedding space gamma matrices. Modified gammas appear in the modified Dirac equation and action, whose solution at string world sheets trivializes by super-conformal invariance to same procedure as in the case of string models.

  3. Induced spinor fields correspond to two chiralities carrying quark number and lepton number. Quark chirality does not carry color as spin-like quantum number but it corresponds to a color partial wave in CP2 degrees of freedom: color is analogous to angular momentum. This reduces to spinor harmonics of CP2 describing the ground states of the representations of super-symplectic algebra.

    The harmonics do not satisfy correct correlation between color and electroweak quantum numbers although the triality t=0 for leptonic waves and t=1 for quark waves. There are two manners to solve the problem.

    1. Super-symplectic generators applied to the ground state to get vanishing ground states weight instead of the tachyonic one carry color and would give for the physical states correct correlation: leptons/quarks correspond to the same triality zero(one partial wave irrespective of charge state. This option is assumed in p-adic mass calculations.

    2. Since in TGD elementary particles correspond to pairs of wormhole contacts with weak isospin vanishing for the entire pair, one must have pair of left and right-handed neutrinos at the second wormhole throat. It is possible that the anomalous color quantum numbers for the entire state vanish and one obtains the experimental correlation between color and weak quantum numbers. This option is less plausible since the cancellation of anomalous color is not local as assume in p-adic mass calculations.


The understanding of the details of the fermionic and actually also geometric dynamics has taken a long time. Super-conformal symmetry assigning to the geometric action of an object with given dimension an analog of Dirac action allows however to fix the dynamics uniquely and there is indeed dimensional hierarchy resembling brane hierarchy.

  1. The basic observation was following. The condition that the spinor modes have well-defined em charge implies that they are localized to 2-D string world sheets with vanishing W boson gauge fields which would mix different charge states. At string boundaries classical induced W boson gauge potentials guarantee this. Super-conformal symmetry requires that this 2-surface gives rise to 2-D action which is area term plus topological term defined by the flux of Kähler form.

  2. The most plausible assumption is that induced spinor fields have also interior component but that the contribution from these 2-surfaces gives additional delta function like contribution: this would be analogous to the situation for branes. Fermionic action would be accompanied by an area term by supersymmetry fixing modified Dirac action completely once the bosonic actions for geometric object is known. This is nothing but super-conformal symmetry.

    One would actually have the analog of brane-hierarchy consisting of surfaces with dimension D= 4,3,2,1 carrying induced spinor fields which can be regarded as independent dynamical variables and characterized by geometric action which is D-dimensional analog of the action for Kähler charged point particle. This fermionic hierarchy would accompany the hierarchy of geometric objects with these dimensions and the modified Dirac action would be uniquely determined by the corresponding geometric action principle (Kähler charged point like particle, string world sheet with area term plus Kähler flux, light-like 3-surface with Chern-Simons term, 4-D space-time surface with Kähler action).

  3. This hierarchy of dynamics is consistent with SH only if the dynamics for higher dimensional objects is induced from that for lower dimensional objects - string world sheets or maybe even their boundaries orbits of point like fermions. Number theoretic vision suggests that this induction relies algebraic continuation for preferred extremals. Note that quaternion analyticity means that quaternion analytic function is determined by its values at 1-D curves.

  4. Quantum-classical correspondences (QCI) requires that the classical Noether charges are equal to the eigenvalues of the fermionic charges for surfaces of dimension D=0,1,2,3 at the ends of the CDs. These charges would not be separately conserved. Charges could flow between objects of dimension D+1 and D - from interior to boundary and vice versa. Four-momenta and also other charges would be complex as in twistor approach: could complex values relate somehow to the finite life-time of the state?

    If quantum theory is square root of thermodynamics as ZEO suggests, the idea that particle state would carry information also about its life-time or the time scale of CD to which is associated could make sense. For complex values of αK there would be also flow of canonical and super-canonical momentum currents between Euclidian and Minkowskian regions crucial for understand gravitational interaction as momentum exchange at imbedding space level.

  5. What could be the physical interpretation of the bosonic and fermionic charges associated with objects of given dimension? Condensed matter physicists assign routinely physical states to objects of various dimensions: is this assignment much more than a practical approximation or could condensed matter physics already be probing many-sheeted physics?

  6. Could the addition of fermions to a given state defined in terms of fermionic charges at the fermion lines defined by the boundaries of string worlds sheets at light-like orbits of partonic 2-surfaces be interpreted as supersymmetry? The smallness of cosmological constant implies that the contribution to the four-momentum from interior should be rather small so that an interpretation in terms of broken SUSY might make sense. There would be mass m≈ .03 eV per volume with size defined by the Compton scale hbar/m.

    This interpretation might allow to understand the failure to find SUSY at LHC. Sparticles could be obtained by adding interior right-handed neutrinos and antineutrinos to the particle state. They could be also associated with the magnetic body of the particle. Since they do not have color and weak interactions, SUSY is not badly broken. If the mass difference between particle and sparticle is of order m=.03 eV characterizing ρvac, particle and sparticle could not be distinguished in higher energy physics at LHC since it probes much shorter scales and sees only the particle. I have already earlier proposed a variant of this mechanism but without SUSY breaking.

    To discover SUSY one should do very low energy physics in the energy range m≈ .03 eV having same order of magnitude as thermal energy kT= 2.6× 10-2 eV at room temperature 25 oC. One should be able to demonstrate experimentally the existence of sparticle with mass differing by about m≈ .03 eV from the mass of the particle. An interesting question is whether the sfermions associated with standard fermions could give rise to Bose-Einstein condensates whose existence in the length scale of large neutron is strongly suggested by TGD view about living matter.

3. Imbedding space level

In GRT the description of gravitation involve only space-time and gravitational force is eliminated. In TGD also imbedding space level is involved with the description.

  1. The incoming and outgoing states of particle reaction are labelled by the quantum numbers associated with the isometries of the imbedding space and by the contributions of super-symplectic generators and isometry generators to the quantum numbers. This follows from the fact that the ground states of super-symplectic representations correspond to the modes of imbedding space spinors fields. These quantum numbers appear in the S-matrix of QFT limit too. In particular, color quantum numbers as angular momentum like quantum numbers at fundamental level are transformed to spin-like quantum numbers at QFT limit.

  2. In GRT the applications rely on Post-Newtonian approximation (PNA). This means that the notion of gravitational force is brought to the theory although it has been eliminated from the basic GRT. This is not simple. One could argue that there is genuine physics behind this PNA and TGD suggests what this physics is.

    At the level of space-time surfaces particles move along geodesic lines and in TGD minimal surface equation states the generalization of the geodesic line property for 3-D particles. At the imbedding space level gravitational interaction involves exchanges of four-momentum and in principle of color quantum numbers too. Indeed, there is an exchange of classical charges through the light-like 3-surfaces defining the boundaries of Euclidian regions defining Euclidian regions as "lines" of generalized scattering diagrams. This however requires that Kähler coupling strength is allowed to be complex (say correspond to zero of Riemann Zeta). Hence in TGD also Newtonian view would be correct and needed.

See the chapter TGD and M-theory of "Overall View about TGD" or the article Can one apply Occam's razor as a general purpose debunking argument to TGD?

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

Articles and other material related to TGD.

Saturday, December 03, 2016

Basic course in misunderstanding publicly what TGD is

I have had interesting debate with person X in Facebook about TGD. The following is not a personal attack against X or anyone. I have enjoyed the discussions. TGD is for me not much about my ego but implications of a marvellous idea that for some reason happened to become aware of decades ago. My apologies for all colleagues for producing so much green colored suffering: this idea just came to my head. I feel that it is appropriate to summarize the essence of what I have learned from these discussions.

During years I have learned a lot about the scientific arrogance - this arrogance is not a personal sin but cruelly forced by the social pressures in science community - basically the deep fear to lose membership of the community as a sanction for using own brain and making un-cautious remarks about the clothing of the Emperor.

This leads to the crackpot hunter syndrome very similar to what young nazis are suffering also at the streets of finnish cities nowadays. This syndrome plagues almost all researchers and only retired scientists sometimes manage to get rid of it and realize that nothing prevents them from thinking with their own brains. Those who do this too early, are mercilessly kicked out from the community. Science is today what church was at medieval times. This is just sociology. Being outsider is not however fatal at all for a thinker who does not need expensive laboratory equipment - just the contrary since it gives the precious freedom.

1. Did you see the gorilla?

How to achieve a complete misunderstanding about some new idea? In email discussion about this I was told about "Did you see the gorilla" effect. If you totally direct your attention to something almost anything can happen and you fail to perceive it. For instance, gorilla can walk through the scene repeatedly and you do not notice it.

Gorilla effect explains why it is almost hopeless to discuss with a person - call him X - who identifies himself as "serious scientist" about something, which involves new thinking.

The basic attitude of X is that person Y with the new theory is a crackpot. X directs his attention to single task: to find a fatal mistake in the arguments of Y instead of trying to understand what is the new idea - the gorilla - is. X is convinced that Y as crackpot building his "theory" by picking up pieces from the "real" theories and combining them in some silly fashion.

And indeed: X finds that this is the case! Gorilla can stare X at face, tap X on shoulder, kick X on knee, and X does not notice anything! X concludes that Y is indeed a complete crackpot as he actually new before hand - these randomly picked pieces simply do not form any coherent whole. X is fitting left shoe to the right leg and when this does not work he accuses the right hand leg or being a crackpot leg.

2. How to achieve a complete misunderstanding of TGD?

A concrete application helps to understand the secrets of successful debunking. I try to formulate my experiences about being debunked as a recipe for achieving complete misunderstanding about what TGD is.

  1. Take care that you are young and arrogant enough. Arrogance is necessary since it implies that you regard all scientists without academic position crackpots irrespective of what they say. Do not care about such minor details like
    3 published books and 17 online books and numerous articles. All this only tells that this crackpot is really tragic case: spend 40 years writing all this nonsense!

  2. Spill first out the standard generic accusations carefully avoiding to say anyhing about contents. You can tell that the logic is circular, that Y just picks up this and and that from "real" science and puts them together to build an a meaningless world salad - his "theory". Tell that Y has no source criticism. Tell that he has mis-understood all principles of science. Tell that the work of Y fails to satisfy all imaginable requirements to be posed on scientific work.

    These generic accusations are standard bad rhetorices and it would be easy to program a chatbot producing them with slight variations: it is already now possible to write poems composed of sentences from existing poems as also ironic statements. Kind of database for generic academic hate speech would be needed.

    Layman usually does not notice this rhetoric trick. In the unfortunate case that this happens publicly X is forced to read something from Y or patientely listen to him. Professional of course realizes the trick but are silent and certainly the victim Y understands what you are trying.

  3. If you do not manage to put Y down with general purpose rant you are forced to discuss with him or even read something written by him. This is irritating but you must do it if you are in public forum. You can start by throwing some random claims about the work of Y and see how Y reacts to them and demonstrate that he is a crackpot and make a theatrical exit telling that you have got enough.

If you are forced to say something about contents, you can attack on two fronts. The core of the argument that crackpots are in war against "serious" science and that Y is in war against serious science. Audience can make its own conclusions. I continue with the same example in which Y is theoretical physicist.
  1. Argue that Y is in war with general relativity.

  2. Argue that Y is also in war against quantum theory and understands nothing about quantum theory and tries to mimic quantum theory by picking some pieces and trying to put them together.

2.1. Y is in war against special and general relativities
  1. Tell that Y loses Poincare invariance in his theory.

    Y however tells that it is general relativity i(GRT) in which Poincare in invariance is lost. This is true but do not comment: in the audience very few understand this delicacy.

    Y tells that the very starting point of his theory was just the acceptance of Poincare invariance as an exact symmetry of Nature. He is only fusing special and general theories of relativity so that relativity principle (RP) is consistent with Equivalence Principle (EP) and General Coordinate Invariance (GCI) and that already Einstein might have discovered this but did not.

    Y claims of having discovered something that Einstein did not!!!: god grief - a clear sympton of crackpotness: Haha! Do not listen [laugh from audience].

    Y tells that the whole idea is to lift Poincare invariance to the imbedding space M4× CP2: symmetries do not shift point of space-time surface along space-time surface (they would be general coordinate transformations in this case) but rotate or translate entire 3-surface which is like rigid body. Do not listen.

  2. Tell that Y loses GCI by introducing some special coordinates but formulate it so that it is impossible to understand what you mean (neither do you understand but this does not matter since also audience fails to understand).

    Y tells that his theory relies on GCI and this implies in his framework holography. Even strong form of GCI is highly motivated and implies what he calls strong form of holography: construction of quantum theory needs only data at string world sheets and partonic 2-surcaces (or possibly also at their light-like orbits). Do not listen.

    Then Y makes a fatal mistake. Y tells also that the extension of physics to adelic physics involving introduction of p-adic physics as correlates for cognition brings in description of cognition. The worlds in which theoretician uses spherical coordinates resp. linear coordinates are indeed a little bit different since the discretization of the symmetry groups implies tiny effects assignable to cognition. No need to say anything. Y has finally crucified himself as pseudo-scientists by talking about consciousness and cognition. Congratulate yourself.

You can also make questions about blackholes. All popularizers talk about blackhole interiors as scientifically proven concept and typical theoretician believes this. And of course ordinary laymen: what else they could do?

Y tells that experimentally one does not know anything about blackhole interiors and that they are a source of myriads of problems since at blackhole horizon GRT begins to fail.

Now Y makes a second fatal mistake. He tells that in this theory blackhole interiors are replaced by regions of space-time surface with Euclidian signature of metric so that time and space are in completely symmetric position unlike for blackholes for which the roles of radial coordinate and time coordinate are changed below horizon.

Y also tells that any physical object is accompanied by this kind of space-time sheet containing smaller space-time sheets glued to it and talks about fractals. Now Y has finally demontrated his crackpot character! Tell that all respectable theoreticians believe in blackhole interiors [laugh from audience].

Y does not give up. He tells that these respectable theoreticians also routinely use a calculational trick replacing Minkowskian metric with Euclidian. Could it be that the presence of these Euclidian regions could make functional integral replacing path integral in this theory convergent and mathematically well-defined. Could it be that behind the trick there is a reality? Do not listen.

Y might also tell about the notions of field body and magnetic body as basic distinctions between TGD and ordinary classical field theory.This becomes really bad. Y must have lost his mind. Do not listen.

2.2. Y is also in war against quantum theory

This is the second theme.

  1. Tell that the theory of Y is inconsistent with basic quantum mechanics.

    Y says "No!" and tells that he accepts linear superposition, tensor products, quantum entanglement, Born rules: actually the entire calculational apparatus of quantum theory. Only quantum measurement theory, which is the black sheep of quantum theory is replaced by its modification based on what he calls zero energy ontology and that this modification leads to a theory of consciousness with a lot of non-trivial predictions. Y also tells that physics is essentially the study of regularities of conscious experience.

    Take a fatherly attitude and tell that quantum measurement theory is completely understood and that talking about consciousness as something interesting in some sense is medieval nonsense. Perform a theatrical loss of temper and leave the stage: Nooo-noooo-noooo!! Why am I discussing with this miserable crackpot?!

  2. Tell that Y tries to reduce quantum theory to classical space-time dynamics (not true but it does not matter).

    Y tells that classical dynamics of preferred extremals is exact part of quantum theory in this theory. He does not try to reduce quantum theory to a classical theory: this would be idiotic. Do not listen.

    Y tells that his preferred extremals are not an outcome of stationary phase approximation or Bohr rules. Y tells that the preferred extremal property - or Bohr orbitology - is necessary to realize GCI for the geometry of WCW. The definition of metric - Kähler function - must assign to 3-surfaces a unique space-time surface. Y compares this approach to what happens in integrable theories, where path integral reduces to sum over extremals of action. Do not listen.

  3. Tell that the theory of Y does not even involve quantization and is therefore total trash.

    Y tells that he does not perform quantization since it is not needed and that quantization is a childhood disease of quantum theory! How arrogant! [Laugh from audience].

    Y claims that 80 per cent of quantum theory is group theory and the enormous symmetries of his theory reduce quantization to the study of representations of his funny infinite-D symmetry algebra (he calls it super-symplectic algebra: do not waste time to look what it might mean).

    Do not take Y seriously and say that Y does not understand quantum theory at all. Say that only crackpot can claim that quantization is not needed.

    To this Y says that geometrization of quantum theory as generalization of Einstein's program for classical physics in terms of infinite-dimensional geometry of WCW

    • requires only that WCW (space or 3-surfaces roughly) has Kähler geometry in order to geometrize hermitian conjugation and that this geometry boils down to an identification of Kähler function,

    • that its definition must assign to a given 3-surface a unique space-time surface,

    • and that this is achieved if Kähler function is defined by action for a space-time surface identified as preferred extremal of certain action consisting of Kähler action and volume term having interpretation in terms of cosmological constant and emerging from the twistor lift of his theory possible only for M4× CP2 so that TGD is also mathematically unique and not only implied by standard model symmetries.

    Do not listen.

    Y also tells that quantum states of Universe are classical spinor fields in WCW: entire quantum theory is classical apart from state function reduction and that its proper description leads to consciousness theory. Now it is time to get emotional: Y is claiming that quantum theory is classical theory [laugh from the audience].

    Tell that Y should quantize since all serious scientists quantize. Tell that Y must perform at least geometric quantization to make his theory physical. Give a friendly advice: the least Y could do is to replace his WCW with its phase space bringing in canonical momenta (or densities) and forcing to select somehow the configuration space. Hope that Y admits this. Then you could tell that geometric quantization is not unique since there is an infinite number of manners to select the configuration space as sub-manifold with vanishing induced Kahler form (symplectic form). Haha!!: the whole thing is highly non-unique and Y is utterly wrong in his dreams.

    Irritatingly, Y says that this no need for geometric quantization or any kind quantization apart from second quantization of induced spinor fields at space-time level forced by the anticommutation relations of WCW gamma matrices expressible as linear combinations of fermionic oscillator operators so that also Fermi statistics is geometrized. Do not listen.

    Y gives even an example. In CP2 one can construct spinor harmonics without any need for selecting Lagrangian sub-manifold. Same for WCW. The infinite-D symmetries of WCW reduce quantization to group theory very much analogous to but generaling that needed in the construction of representations of super-conformal algebras. Do not listen.

  4. Y also tells that his theory introduces also some new elements to quantum theory.

    • The identification of quantum states as spinor fields of world of classical worlds (WCW),

    • zero energy ontology (ZEO),

    • hierachy of phases of matter with non-standard value of (effective) Planck constant,

    • hyper-finite factors of type II1 and their inclusions as correlate for finite measurement resolution.
    No need to comment. Planck constant is known with several decimals and all serious scientists believe that dark matter is some exotic particle or few of them: they are not yet found but will be found [laugh from audience].


Thursday, December 01, 2016

About minimal surface extremals of Kähler action

If the spectrum for the critical value of Kähler coupling strength is complex - say given by the complex zeros of zeta - the preferred extremals of Kähler action are minimal surfaces. This means that they satisfy simultaneously the field equations associated with two variational principles.

Conservation laws for the minimal surface extremals of Kähler action

Consider first the basic conservation laws.

  1. Complex value of αK means that conserved quantities are complex: this brings strongly in mind twistor approach. The value of cosmological constant is assumed to be real. There are two separate local conservations laws associated with the volume term and Kähler action respectively in both Minkowskian and Euclidian regions. This need not mean separate global conservation laws in Minkowskian and Euclidian regions. If there is non canonical momentum current between Minkowskian (M) and Euclidian (E) space-time regions the real and imaginary parts of conserved quantum numbers correspond schematically to the sums

    l Re(Q)= Re(1/αK)QK(E) + Im(1/αK)QK(M) +ρvac QV(M)

    Im(Q)=Im(1/αK)QK(E) + Re(1/αK)QK(M) .

    Here the subscripts V and K refer to the volume term and Kähler action respectively.

  2. If the canonical momentum current vanishes there both real and imaginary parts decompose to two separately conserved parts.

    Re(Q1)= Re(1/αK)QK(E) ,

    Re(Q2)= Im(1/αK)QK(M) +ρvac QV(M) ,

    Im(Q1)= Im(1/αK)QK(E) ,

    Im(Q2)= Re(1/αK)QK(M) .

    This looks strange and the natural assumption is that canonical momentum currents can flow between the Euclidian and Minkowskian regions and boundary conditions equate the components of normal currents at both sides.

Are minimal surface extremals of Kähler action holomorphic surfaces in some sense?

I have considered several ansätze for the general solutions of the field equations for the preferred extremals. One proposal is that preferred extremals as 4-surfaces of imbedding space with octonionic tangent space structure have quaternionic tangent space or normal space (so called M8-H duality). Second proposal is that preferred extremals can be seen as quaternion analytic surfaces. Third proposal relies on a fusion of complex and hyper-complex structures to what I call Hamilton-Jacobi structure. In Euclidian regions this would correspond to complex structure. Twistor approach suggests that the condition that the twistor lift of the space-time surface to a 6-D surface in the product of twistor spaces of M4 and CP2 equals to the twistor space of CP2. This proposal is highly interesting since twistor lift works only for M4× CP2. The intuitive picture is that the field equations are integrable and all these views might be consistent.

Preferred extremals of Kähler action as minimal surfaces would be a further proposal. Can one make conclusions about general form of solutions assuming that one has minimal surface extremals of Kähler action?

In D=2 case minimal surfaces are holomorphic surfaces or they hyper-complex variants and the imbedding space coordinates can be expressed as complex-analytic functions of complex coordinate or a hypercomplex analog of this. Field equations stating the vanishing of the trace gαβHkαβ if the second fundamental form Hkαβ== Dα&partial;βhk are satisfied because the metric is tensor of type (1,1) and second fundamental form of type (2,0) ⊕ (2,0). Field equations reduce to an algebraic identity and functions involved are otherwise arbitrary functions. The constraint comes from the condition that metric is of form (1,1) as holomorphic tensor.

This raises the question whether this finding generalizes to the level of 4-D space-time surfaces and perhaps allows to solve the field equations exactly in coordinates generalizing the hypercomplex coordinates for string world sheet and complex coordinates for the partonic 2-surface.

The known non-vacuum extremals of Kähler action are actually minimal surfaces. The common feature suggested already earlier to be common for all preferred extremals is the existence of generalization of complex structure.

  1. For Minkowskian regions this structure would correspond to what I have called Hamilton-Jacobi structure. The tangent space of the space-time surface X4 decomposes to local direct sum T(X4)= T(X2)⊕ T(Y2), where the 2-D tangent places T(X2) and T(Y2) define an integrable distribution integrating to a decomposition X4=X2× Y2. The complex structure is generalized to a direct some of hyper-complex structure in X2 meaning that there is a local light-like direction defining light-like coordinate u and its dual v. Y2 has complex complex coordinate (w,wbar). Minkowski space M4 has similar structure. It is still an open question whether metric decomposes to a direct sum of orthogonal metrics assignable to X2 and Y2 or is the most general analog of complex metric in question. guv and gwbar are certainly non-vanishing components of the induced metric. Metric could allow as non-vanishing components also guw and gvbarw. This slicing by pairs of surfaces would correspond to decomposition to a product of string world sheet and partonic 2-surface everywhere.

    In Euclidian regions ne would have 4-D complex structure with two complex coordinates (z,w) and their conjugates and completely analogous decompositions. In CP2 one has similar complex structure and actually Kähler structure extending to quaternionic structure. I have actually proposed that quaternion analyticity could provide the general solution of field equations.

  2. Assuming minimal surface property the field equations for Kähler action reduce to the vanishing of a sum of two terms. The first term comes from the variation with respect to the induced metric and is proportional to the contraction

    A=Jαγ JγβHkαβ .

    Second term comes from the variation with respect to induced Kähler form and is proportional to

    B=jα PksJslαhl .

    Here Pkl is projector to the normal space of space-time surface and jα= Dβ Jαβ is the conserved Kähler current.

    For the known extremals j vanishes or is light-like (for massless extremals) in which case A and B vanish separately.

  3. An attractive manner to satisfy field equations would be by assuming that the situation for 2-D minimal surface generalizes so that minimal surface equations are identically satisfied. Extremal property for Kähler action could be achieved by requiring that energy momentum tensor also for Kähler action is of type (1,1) so that one would have A=0. This implies jααsk=0. This can be true if j vanishes or is light-like as it is for the known extremals and if sk depend only on the light-like coordinate. In Euclidian regions one would have j=0.

  4. The proposed generalization is especially interesting in the case of cosmic string extremals of form X2× Y2, where X2⊂ M4 is minimal surface (string world sheet) and Y2 is complex homologically non-trivial sub-manifold of CP2 carrying Kähler magnetic charge. The generalization would be that the two transversal coordinates (w,wbar) in the plane orthogonal to the string world sheet defining polarization plane depend holomorphically on the complex coordinates of complex surface of CP2. This would transform cosmic string to flux tube.

  5. There are also solutions of form X2× Y2, where Y2 is Lagrangian sub-manifold of CP2 with vanishing Kähler magnetic charge and their deformations with (w,barw) depending on the complex coordinates of Y2 (see the slides of "On Lagrangian minimal surfaces on the complex projective plane" ). In this case Y2 is not complex sub-manifold of CP2 with arbitrary genus and induced Kähler form vanishes. The simplest choice for Y2 would be as homologically trivial geodesic sphere. Because of its 2-dimensionality Y2 has a complex structure defined by its induced metric so that solution ansatz makes sense also now.

See the new chapter How the hierarchy of Planck constants might relate to the almost vacuum degeneracy for twistor lift of TGD? or the article with the same title. See also the article About minimal surface extremals of Kähler action

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

Articles and other material related to TGD.

Wednesday, November 30, 2016

Do you already believe in emergent gravity?

Popular writer Sabine Hossenfelder gave a highly authoritative explanation for what emergent gravity is (see this). Actually, she started by bravely expanding the notion of emergence: not only gravitation but also free will, cell, and brain emerge. You are fundamentally just a lot of fundamental particles. Get over it! I can only admire Bee's intuitive powers: not a single argument for why this would be the case was needed. Only the great (and somewhat aggressive) insight transcending over the boundaries of sciences. But why this strange emotionality about free will, life and consciousness not typical for scientist? As an outsider I can only try to guess the reasons.

The idea of emergence of gravitation is the newest fashion in the long sequence of fashions that has plagued theoretical physics during more than four decades. GUTs, supergravity, loop gravity, super string models, M-theory and its descendents, multiverse, AdS/CFT, reduction of physics to that of blackholes... Now it is fashionable to believe that Einstein was wrong: gravitation has a non-geometric origin: gravity as entropic force, emergence of gravition and 3-space and even space-time.

Verlinde argues that the origin is thermodynamical. That it cannot be became clear already for 6 years ago experimentally. I have written about this in more detail in previous blog posting. Gravitational potential appears in the Schrödinger equation of neutron: it should not if gravitational potential is a thermodynamical quantity: thermodynamical quantities should not appear in quantal equations since they are derived from the statistical predictions of quantum theory. This elementary fact was noticed by Kobakidzhe. For some funny reason, this simple observation has not got through and it is probably too late now: during next years entropic gravity will produce a lot of stuff in archives for the future sociologists of science. We are living post-truth period and theoretical physics has been the forerunner in this respect.

Bee mentions as an example about emergent gravity the model of Xiao-Gang Wen and collaborators. As usual, the model turned out to be a disappointment. Space-time emerges from space-time as it does also in other models in the best tradition of circular logic. One replaces space-time with a lattice keeping the 4-dimensionality: assigns finite-D Hilbert space at points of this 4-D lattice: essentially a discretization of quantum field theory is in question. One constructs Hamiltonian as sum of local Hamiltonians for a symmetric tensor field in such a manner that one obtains Einstein's equations in lowest order as continuum limit. Why I am not happy with this?

One of course should not have any lattice assumed to have structure of 4-D lattice. One should have no tensor fields. One should have only Hilbert space. One however starts from fields in continuous space-time, discretizes, it and makes continuous again! I have always wondered why these naive mathematically primitive tricks familiar already from loop gravity. Superstring theories were not physically correct simple because the dimension of fundamental objects was too small (1 instead of 3) and this actually led to the idea that space-time energes: either by compactication or as 3-brane or as it seems as both;-). String model was however based on refined mathematics. I can only imagine the pains suffered by Witten as he sees this intellectual degeneration of theoretical physics.

I have tried to explain that discretization occurs naturally due to the finite measurement resolution for both sensory experience and cognition. This however requires that consciousness and cognition are something which does not reduce to dynamics of particles. This leads to a notion of manifold involving naturally both discretization in terms of algebraic extensions of rationals and continuum aspects and also fusion of various number fields so that one can speak about adelic space-time - already Leibniz dreamed about this as he talked about monads. Most importanly, in this framework discretization does not lead to a loss of fundamental space-time symmetries: this is what killed loop gravity. Both the symmetries of special relativity and general coordinate invariance are exact and new infinite-dimensional symmetry algebras - in particular huge extension of conformal symmetries, are predicted.

I have also talked about emergence: very many things emerge in TGD. Elementary bosons and actually also elementary fermions emerge from induced spinor fields and topology of wormhole contact pairs. Standard model and general relativity emerge as approximation to many-sheeted space-time having most important application to biology, neuroscience, and consciousness. These are definitely not emergent for point like particles! Generalizations of the usual positive energy ontology to zero energy ontology and of quantum measurement theory are needed.

Classical gauge fields and gravitational fields at the level of single space-time sheet emerge from the dynamical geometry of space-time as a 4-D surface. The outcome is ridiculously simple: by general coordinate invariance there are only 4 fundamental field like degrees of freedom: for instance CP2 coordinates at macroscopic limit. Gravitational field of GRT and gauge fields of standrad model emerge as the sheets of the many-sheeted space-time are lumped together and the gauge potentials and deviation of metric from Minkowski metric sum up to gauge
potentials and gravitational field of GRT.

Space-time does not however emerge! Only the conscious experience about 3-space - proprioception - emerges through tensor nets formed by magnetic flux tubes meeting at nodes defined by 3-surfaces. How rapid the progress in physics would be if colleagues could finally accept that also the conscious observer must be understood physically.

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

Articles and other material related to TGD.

Tuesday, November 29, 2016

Mersenne integers and brain

I received a link to an interesting the article "Brain Computation Is Organized via Power-of-Two-Based Permutation Logic" by Kun Xie et al in Frontiers in Systems Neuroscience (see this).

The proposed model is about how brain classifies neuronal inputs and suggests that the classification is based on Boolean algebra represents as subsets of n-element set for n inputs. The following represents my attempt to understand the model of the article.

  1. One can consider a situation in which one has n inputs identifiable as bits: bit could correspond to neuron firing or not. The question is however to classify various input combinations. The obvious criterion is how many bits are equal to 1 (corresponding neuron fires). The input combinations in the same class have same number of firing neurons and the number of subsets with k elements is given by the binomial coefficient B(n,k)= n!/k!(n-k)!. There are clearly n-1 different classes in the classification since no neurons firing is not a possible observation. The conceptualization would tell how many neurons fire but would not specify which of them.

  2. To represent these bit combinations one needs 2n-1 neuron groups acting as unit representing one particular firing combination. These subsets with k elements would be mapped to neuron cliques with k firing neutrons. For given input individual firing neurons (k=1) would represent features, lowest level information. The n cliques with k=2 neurons would represent a more general classification of input. One obtains Mn=2n-1 combinations of firing neurons since the situations in which no neurons are firing is not counted as an input.

  3. If all neurons are firing then all the however level cliques are also activated. Set theoretically the subsets of set partially ordered by the number of elements form an inclusion hierarchy, which in Boolean algebra corresponds to the hierarchy of implications in opposite direction. The clique with all neurons firing correspond to the most general statement implying all the lower level statements. At k:th level of hierarchy the statements are inconsistent so that one has B(n,k) disjoint classes.

The Mn=2n-1 (Mersenne number) labelling the algorithm is more than familiar to me.
  1. For instance, electron's p-adic prime corresponds to Mersenne prime M127 =2127-1, the largest not completely super-astrophysical Mersenne prime for which the mass of particle would be extremely small. Hadron physics corresponds to M107 and M89 to weak bosons and possible scaled up variant of hadron physics with mass scale scaled up by a factor 512 (=2(107-89)/2). Also Gaussian Mersennes seem to be physically important: for instance, muon and also nuclear physics corresponds to MG,n= (1+i)n-1, n=113.

  2. In biology the Mersenne prime M7= 27-1 is especially interesting. The number of statements in Boolean algebra of 7 bits is 128 and the number of statements that are consistent with given atomic statement (one bit fixed) is 26= 64. This is the number of genetic codons which suggests that the letters of code represent 2 bits. As a matter of fact, the so called Combinatorial Hierarchy M(n)= MM(n-1) consists of Mersenne primes n=3,7,127, 2127-1 and would have an interpretation as a hierarchy of statements about statements about ... It is now known whether the hierarchy continues beyond M127 and what it means if it does not continue. One can ask whether M127 defines a higher level code - memetic code as I have called it - and realizable in terms of DNA codon sequences of 21 codons (see this).

  3. The Gaussian Mersennes MG,n n=151,157,163,167, can be regarded as a number theoretical miracles since the these primes are so near to each other. They correspond to p-adic length scales varying between cell membrane thickness 10 nm and cell nucleus size 2.5 μm and should be of fundamental importance in biology. I have proposed that p-adically scaled down variants of hadron physics and perhaps also weak interaction physics are associated with them.

I have made attempts to understand why Mersenne primes Mn and more generally primes near powers of 2 seem to be so important physically in TGD Universe.
  1. The states formed from n fermions form a Boolean algebra with 2n elements, but one of the elements is vacuum state and could be argued to be non-realizable. Hence Mersenne number Mn=2n-1. The realization as algebra of subsets contains empty set, which is also physically non-realizable. Mersenne primes are especially interesting as sine the reduction of statements to prime nearest to Mn corresponds to the number Mn-1 of physically representable Boolean
    statements.

  2. Quantum information theory suggests itself as explanation for the importance of Mersenne primes since Mn would correspond the number of physically representable Boolean statements of a Boolean algebra with n-elements. The prime p≤ Mn could represent the number of elements of Boolean algebra representable p-adically (see this).

  3. In TGD Fermion Fock states basis has interpretation as elements of quantum Boolean algebra and fermionic zero energy states in ZEO expressible as superpositions of pairs of states with same net fermion numbers can be interpreted as logical implications. WCW spinor structure would define quantum Boolean logic as "square root of Kähler geometry". This Boolean algebra would be infinite-dimensional and the above classification for the abstractness of concept by the number of elements in subset would correspond to similar classification by fermion number. One could say that bosonic degrees of freedom (the geometry of 3-surfaces) represent sensory world and spinor structure (many-fermion states) represent that logical thought in quantum sense.

  4. Fermion number conservation would seem to represent an obstacle but in ZEO it can circumvented since zero energy states can be superpositions of pair of states with opposite fermion number F at opposite boundaries of causal diamond (CD) in such a manner that F varies. In state function reduction however localization to single value of F is expected to happen usually. If superconductors carry coherent states of Cooper pairs, fermion number for them is ill defined and this makes sense in ZEO but not in standard ontology unless one gives up the super-selection rule that fermion number of quantum states is well-defined.

One can of course ask whether primes n defining Mersenne primes (see this) could define preferred numbers of inputs for subsystems of neurons. This would predict n=2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257,.. define favoured numbers of inputs. n=127 would correspond to memetic code.

See the article Why Mersenne Primes Are So Special? or the chapter Unified Number Theoretical Vision of "Physics as Generalized Number Theory".

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

Articles and other material related to TGD.

Sunday, November 27, 2016

Does the presence of cosmological constant term make Kähler coupling strength a genuine coupling constant classically?

The addition of the volume term to Kähler action has very nice interpretation as a generalization of equations of motion for a world-line extended to a 4-D space-time surface. The field equations generalize in the same manner for 3-D light-like surfaces at which the signature of the induced metric changes from Minkowskian to Euclidian, for 2-D string world sheets, and for their 1-D boundaries defining world lines at the light-like 3-surfaces. For 3-D light-like surfaces the volume term is absent. Either light-like 3-surface is freely choosable in which case one would have Kac-Moody symmetry as gauge symmetry or that the extremal property for Chern-Simons term fixes the gauge.

The known non-vacuum extremals are minimal surface extremals of Kähler action and it might well be that the preferred extremal property realizing SH quite generally demands this. The addition of the volume term could however make Kähler coupling strength a manifest coupling parameter also classically when the phases of Λ and αK are same. Therefore quantum criticality for Λ and αK would have a precise local meaning also classically in the interior of space-time surface. The equations of motion for a world line of U(1) charged particle would generalize to field equations for a "world line" of 3-D extended particle.

This is an attractive idea consistent with standard wisdom but one can invent strong objections against it in TGD framework.

  1. All known non-vacuum extremals of Kähler action are minimal surfaces and the minimal surface vacuum extremals of Kähler action become non-vacuum extremals. This suggest that preferred extremals are minimal surface extremals of Kähler action so that the two dynamics apparently decouple. Minimal surface extremals are analogs for geodesics in the case of point-like particles: one might say that one has only gravitational interaction. This conforms with SH stating that gauge interactions at boundaries (orbits of partonic 2-surfaces and 2-surfaces at the ends of CD) correspond classically to the gravitational dynamics in the space-time interior.

    Note that at the boundaries of the string world sheets at light-like 3-surfaces the situation is different: one has equations of motion for geodesic line coupled to induce Kähler gauge potential and gauge coupling indeed appears classically as one might expect! For string world sheets one has only the topological magnetic flux term and minimal surface equation in string world sheet. Magnetic flux term gives the Kähler coupling at the boundary.

  2. Decoupling would allow to realize number theoretical universality since the field equations would not depend on coupling parameters at all. It is very difficult to imagine how the solutions could be expressible in terms of rational functions with coefficients in algebraic extension of rationals unless αK and Λ have very special relationship. If they have different phases, minimal surface extremals of Kähler action are automatically implied. If the values of αK correspond to complex zeros of Riemann ζ, also Λ should have same complex phase, in order to have genuine classical coupling. This looks somewhat un-natural but cannot be excluded.

    The most natural option is that Λ is real and αK corresponds to zeros of zeta. For trivial zeros the phases are different and decoupling occurs. For trivial zeros Λ and αK differ by imaginary unit so that again decoupling occurs.

  3. One can argue that the decoupling makes it impossible to understand coupling constant evolution. This is not the case. The point is that the classical charges assignable to super-symplectic algebra are sums over contributions from Kähler action and volume term and therefore depend on the coupling parameters. Their vanishing conditions for sub-algebra and its commutator with entire algebra give boundary conditions on preferred extremals so that coupling constant evolution creeps in classically!

    The condition that the eigenvalues of fermionic charge operators are equal to the classical charges brings in the dependence of quantum charges on coupling parameters. Since the elements of scattering matrix are expected to involve as building bricks the matrix elements of super-symplectic algebra and Kac-Moody algebra of isometry charges, one expectes that discrete coupling constant evolution creeps in also quantally via the boundary conditions for preferred extremals.

Although the above arguments seem to kill the idea that the dynamics of Kähler action and volume term could couple in space-time interior, one can compare this view (Option II) with the view based on complete decoupling (Option I).
  1. For Option I the coupling between the two dynamics could be induced just by the condition that the space-time surface becomes an analog of geodesic line by arranging its interior so that the U(1) force vanishes! This would generalize Chladni mechanism! The interaction would be present but be based on going to the nodal surfaces! Also the dynamics of string world sheets is similar: if the string sheets carry vanishing W boson classical fields, em charge is well-defined and conserved. One would also avoid the problems produced by large coupling constant between the two-dynamics present already at the classical level. At quantum level the fixed point property of quantum critical couplings would be the counterparts for decoupling.

  2. For Option II the coupling is of conventional form. When cosmological constant is small as in the scale of the known Universe, the dynamics of Kähler action is perturbed only very slightly by the volume term. The alternative view is that minimal surface equation has a very large perturbation proportional to the inverse of Λ so that the dynamics of Kähler action could serve as a controller of the dynamics defined by the volume term providing a small push or pull now and then. Could this sensitivity relate to quantum criticality and to the view about morphogenesis relying on Chladni mechanism in which field patterns control the dynamics with charged flux tubes ending up to the nodal surfaces of (Kähler) electric field (see this)? Magnetic flux tubes containing dark matter would in turn control and serve as template for the dynamics of ordinary matter.

Could the possible coupling of the two dynamics suggest any ideas about the values of αK and Λ at quantum criticality besides the expectation that cosmological constant is proportional to an inverse of p-adic prime?
  1. Number theoretic vision suggests the existence of preferred extremals represented by rational functions with rational or algebraic coefficients in preferred coordinates. For Option I one has preferred extremals of Kähler action which are minimal surfaces so that there is no coupling and no constraints on the ratio of couplings emerges: even better, both dynamics are independent of the coupling. All known non-vacuum extremals of Kähler action are indeed also minimal surfaces. For Option II the ratio of the coefficients Λ/8π G and 1/4παK should be rational or at most algebraic number. One must be however very cautious here: the minimal option allowed by strong form of holography is that the rational functions of proposed kind emerge only at the level of partonic 2-surfaces and string world sheets.

  2. I have proposed that that the inverse of Kähler coupling strength has spectrum coming as zeros of zeta or their imaginary parts (see this). The phases of complexified 1/αK and Λ/2G must be same in order to avoid the decoupling of Kähler action and minimal surface term implying minimal surface extremals of Kähler action.

    This conjecture is consistent with the rational function property only if αK and vacuum energy density ρvac appearing as the coefficient of volume term are proportional to the same possibly transcendental number with proportionality coefficient being an algebraic or rational number.

    If the phases are not identical (say Λ is real and one allows complex zeros) one has Option I and effective decoupling occurs. The coupling (Option2)) can occur for the trivial zeros of zeta if the volume term has coefficient iΛ/8πG rather than Λ/8π G to guarantee same phase as for 1/4παK. The coefficient iΛ/8πG would give in Minkowskian regions large real exponent of volume and this looks strange. In this case also number theoretical universality might make sense but SH would be broken in the sense that the space-time surfaces would not be analogous to geodesic lines.

  3. At quantum level number theoretical universality requires that the exponent of the total action defining vacuum functional reduces to the product of roots of unity and exponent of integer existing in finite-dimensional extension of p-adic numbers. This would suggest that total action reduces to a number of form q1+iq2π, qi rational number, so that its exponent is of the required form. Whether this can conform with the properties of zeros of zeta and properties of extremals is not clear.

ZEO suggests deep connections with the basic phenomenology of particle physics, quantum consciousness theory, and quantum biology and one can look the situation for both these options.
  1. Option I: Decoupling of the dynamics of Kähler action and volume term in space-time interior for all values of coupling parameters.
  2. Option II: Coupling of dynamics for trivial zeros of zeta and Λ→ iΛ.
Particle physics perspective

Consider a typical particle physics experiment. There are incoming and outgoing free particles moving along geodesics, these particles interact, and emanate as free particles from the interaction volume. This phenomenological picture does not follow from quantum field theory but is put in by hand, in particular the idea about interaction couplings becoming non-zero is involved. Also the role of the observer remains poorly understood.

The motion of incoming and outgoing particles is analogous to free motion along geodesic lines with particles generalized to 3-D extended objects. For both options these would correspond to the preferred extremals in the complement of CD within larger CD representing observer or measurement instrument. Decoupling would take place. In the interaction volume interactions are "coupled on" and particles interact inside the volume characterized by causal diamond (CD). What could be the TGD view translation of this picture?

  1. For Option I one would still have decoupling and the interpretation would be in terms of twistor picture in which
    one always has also in the internal lines on mass shell particles but with complex four-momenta. In TGD framework the momenta would be always complex due to the contribution of Euclidian regions defining the lines of generalized scattering diagrams. As explained coupling constant evolution can be understood also in this case and also classical dynamics depends on coupling parameters via the boundary conditions. The transitory period (control action) leading to the decoupled situation would be replaced by state function reduction, possibly to the opposite boundary.

  2. For Option II the transitory period would correspond to the coupling between the two classical dynamics and would take place inside CD after a phase transition identifiable as "big state function reduction" to time reversed mode. The problem is that in the interacting phase αK would not have a value approximately equal to the U(1) coupling strength of weak interactions (see this) so that the physical picture breaks down.

Quantum measurement theory in ZEO.
  1. For Option I state preparation and state function reduction would be in symmetric role. Also now there would be inherent asymmetry between zero energy states and their time reversals. With respect to observer the time reversed period would be invisible.

  2. For Option II state preparation for CD would correspond to a phase transition to a time reversed phase labelled by a trivial zero of zeta and Λ→ iΛ. In state function reduction to the original boundary of CD a phase transition to a phase labelled by non-trivial zero of zeta would occur and final state of free particles would emerge. The phase transitions would thus mean hopping from the critical line of zeta to the real axis and back and change the values of αK and possibly Λ. There would be strong breaking in time reversal symmetry.

    One cannot of course take this large asymmetry as an adhoc assumption: it should be induced by the presence of larger CD, which could also affect quite generally the values of αK and Λ (having also a spectrum of values).

TGD inspired theory of consciousness

What happens within sub-CD could be fundamental for the understanding of directed attention and sensory-motor cycle.

  1. The target of directed attention would correspond to the volume of CD - call it c - within larger CD - call it C representing the observer - attendee having c as part of its perceptive field. c would serve as a target of directed attention of C and thus define part of the perceptive field of c. c would correspond also to sub-self giving rise to a mental image of C. This would also allow to understand why the attention is directed rather than being completely symmetric with respect to C and c. For both options directed attention would correspond to sub-self c interpreted as mental image. There would be no difference.

  2. Quite generally, the self and time-reversed self could be seen as sensory input and motor response (Libet's findings). Directed attention would define the sensory input and sub-self could react to it by dying and re-incarnating as time-reversed subself. The two selves would correspond to sensory input and motor action following it as a reaction. Motor reaction would be sensory mental image in reversed time direction experienced by time reversed self. Only the description for the reaction would differ for the two options.

    The motor action would be time-reversed sensory perception for Option I. For Option II motor action would correspond
    to a different phase in which Kähler action and volume term couple classically.

TGD inspired quantum biology

The free geodesic line dynamics with vanishing U(1) Kähler force indeed brings in mind the proposed generalization of Chladni mechanism generating nodal surfaces at which charged magnetic flux tubes are driven (see this).

  1. For Option I the interiors of all space-time surfaces would be analogous to nodal surfaces and state function reductions would correspond to transition periods between different nodal surfaces. The decoupling would be dynamics of avoidance and could highly analogous to Chladni mechanism.

  2. For Option II the phase labelled by trivial zeros of zeta would correspond to period during which nodal surfaces are formed. This view about state function reduction and preparation as phase transitions in ZEO would provide classical description for the transition to the phase without direct interactions.

To sum up, it seems that the complete decoupling of the two dynamics (Option I) is favored by both SH, realization of preferred extremal property (perhaps as minimal surface extremals of Kähler action, number theoretical universality, discrete coupling constant evolution, and generalization of Chladni mechanism to a dynamics of avoidance.

For background see the new chapter How the hierarchy of Planck constants might relate to the almost vacuum degeneracy for twistor lift of TGD? of "Towards M-matrix" or the article with the same title.

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

Articles and other material related to TGD.