Saturday, January 12, 2019

Generalized conformal symmetry, quantum criticality, catastrophe theory, and coupling constant evolution

The notion of quantum criticality allows two realizations: as stationarity of S2 part of the twistor lift of Kähler action and in terms of zeros of zeta are key elements in the explicit proposal for discrete coupling constant evolution reducing to that for cosmological constant.

Quantum criticality from different perspectives

Quantum criticality is however much more general notion, and one must ask how this view relates to the earlier picture.

  1. At the real number side continuous coupling constant evolution makes sense. What does this mean? Can one say that quantum criticality makes possible only adelic physics together with large heff/h0=n as dimension for extension of rationals. This hierarchy is essential for life and cognition.

    Can one conclude that living systems correspond to quantum critical values of S(S2) and therefore αK and in-animate systems correspond to other values of αK? But wouldn't his mean that one gives up the original vision that αK is analogous to critical temperature. The whole point was that this would make physics unique?

    From mathematical view point also continuous αK can make sense. αK can be continuous if it corresponds to a higher-dimensional critical manifold at which two or more preferred extremals associated with the same parameter values co-incide - roots of polynomial P(x,a,b) depending on parameters a,b serves as the canonical example. The degree of quantum criticality would vary and there would be a hierarchy of critical systems characterized by the dimension of the critical manifold. One would have a full analog of statistical physics. For mathematician this is the only convincing interpretation.

    2-D cusp catastrophe serves as a basic example helping to generalize. Cusp corresponds to the roots of dP4/dx=0 of third order polynomial P4(x,a,b), where (a,b) are control variables. The projection of region with 3 real roots to (a,b)-plane is bounded by critical lines forming a roughly V-shaped structure. d2P4/dx2 vanishes at the edges of V, where two roots co-incide and d3P4/dx3 vanishes at the tip of V, where 3 roots co-incide.

  2. A hierarchy of quantum criticalities has been actually assumed. The hierarchy of representations for super-symplectic algebra realizing 4-D analog of super-conformal symmetries allows an infinite hierarchy of representations for which infinite-D sub-algebra isomorphic to a full algebra and its commutator with the full algebra annihilate physical states. Also classical Noether charges vanish. What is new is that conformal weights are non-negative integers. The effective dimensions of these systems are finite - at least in the sense that one one has finite-D Lie algebra (or its quantum counterpart) or corresponding Kac-Moody algebra as symmetries. This realization of quantum criticality generalize the idea that conformal symmetry accompanies 2-D criticality.

    This picture conforms also with the vision about hierarchy of hyper-finite-factors with included hyper-finite factor defining measurement resolution. Hyper-finiteness indeed means finite-dimensionality in excellent approximation.

TGD as catastrophe theory and quantum criticality as prerequisite for the Euclidian signature of WCW metric

It is good to look more precisely how the catastrophe theoretic setting generalizes to TGD.

  1. The value of the twistor lift of Kähler action defining Kähler function very probably corresponds to a maximum of Kähler function since otherwise metric defined by the second derivatives could have non-Euclidian signature. One cannot however exclude the possibility that in complex WCW coordinates the (1,1) restriction of the matrix defined by the second derivatives of Kähler function could be positive definite also for other than minima.

    It would seem that one cannot accept several roots for given zero modes since one cannot have maximum of Kähler function for all of them. This would allow only the the boundary of catastrophe region in which 2 or more roots co-incide. Positive definiteness of WCW metric would force quantum criticality.

    For given values of zero modes there would be single minimum and together with the cancellation of Gaussian and metric determinants this makes perturbation theory extremely simple since exponents of vacuum functional would cancel.

  2. There is an infinite number of zero modes playing the role of control variables since the value of the induce Kähler form is symplectic invariant and there are also other symplectic invariants associated with the M4 degrees of freedom (carrying also the analog of Kähler form for the twistor lift of TGD and giving rise to CP breaking). One would have catastrophe theory with infinite number of control variables so that the number of catastrophes would be infinite so that standard catastrophe theory does not as such apply.

  3. Therefore TGD would not be only a personal professional catastrophe but a catastrophe in much deeper sense. WCW would be a catastrophe surface for the functional gradient of the action defining Kähler function. WCW would consists of regions in which given zero modes would correspond to several minima. The region of zero mode space at which some roots identifiable as space-time surfaces co-incide would be analogous to the V-shaped cusp catastrophe and its higher-D generalizations. The question is whether one allows the entire catastrophe surface or whether one demands quantum criticality in the sense that only the union of singular sets at which roots co-incide is included.

  4. For WCW as catastrophe surface the analog of V in the space of zero modes would correspond to a hierarchy of sub-WCWs consisting of preferred extremals satisfying the gauge conditions associated with a sub-algebra of supersymplectic algebra isomorphic to the full algebra. The sub-WCWs in the hierarchy of sub-WCWs within sub-WCWs would satisfy increasingly stronger gauge conditions and having decreasing dimension just like in the case of ordinary catastrophe. The lower the effective dimension, the higher the quantum criticality.

  5. In ordinary catastrophe theory the effective number of behavior variables for given catastrophe can be reduced to some minimum number. In TGD framework this would correspond to the reduction of super-symplectic algebra to a finite-D Lie algebra or corresponding Kac-Moody (half-)algebra as modes of supersymplectic algebra with generators labelled by non-negative integer n modulo given integer m are eliminated as dynamical degrees of freedom by the gauge conditions: this would effectively leave only the modes smaller than m. The fractal hierarchy of these supersymplectic algebras would correspond to the decomposition of WCW as a catastrophe surface to pieces with varying dimension. The reduction of the effective dimension as two sheets of the catastrophe surface co-incide would mean transformation of some modes contributing to metric to zero modes.

RG invariance implies physical analogy with thermodynamics and gauge theories

One can consider coupling constant evolution and RG invariance from a new perspective based on the minimal surface property.

  1. The critical values of Kähler coupling strength would correspond to quantum criticality of the S2 part S(S2) of 6-D dimensionally reduced Kähler action for fixed values of zero modes. The relative S2 rotation would serve as behavior variable. For its critical values the dimension of the critical manifold would be reduced, and keeping zero modes fixed a critical value of αK would be selected from 1-D continuum.

    Quantum criticality condition might be fundamental since it implies the constancy of the value of the twistor lift of Kähler action for the space-time surfaces contributing to the scattering amplitudes. This would be crucial for number theoretical vision since the continuation of exponential to p-adic sectors is not possible in the generic case. One should however develop stronger arguments to exclude the continuous evolution of Kähler coupling strength in S2 degrees of freedom for the real sector of the theory.

  2. The extremals of twistor lift contain dependence on the rotation parameter for S2 and this must be taken into account in coupling constant evolution along curve of S2 connecting zeros of zeta since Kähler and volume term change with it. This can give an additional non-local term to the evolution equations coming from the dependence of the imbedding space coordinates of the preferred extremal on the evolution parameter. The derivative of the 6-D Kähler action is sum of two terms. The first term involves derivatives of αK and of S(S2). Second term is sum of terms involving derivations of Kähler action and volume with respect to the evolution parameter. This is by chain rule proportional to the functional derivatives of total action with respect to imbedding space coordinates, and vanishes by field equations. It does not matter whether there is coupling between Kähler action and volume term.

Could one find interpretation for the miminal surface property which implies that field equations are separately satisfied for Kähler action and volume term?
  1. Quantum TGD can be seen as a "complex" square root of thermodynamics. In thermodynamics one can define several thermodynamical functions. In particular, one can add to energy E as term pV to get enthalpy H= E+pV, which remains constant when entropy and pressures are kept constant. Could one do the same now?

    In TGD V replaced with volume action and p would be a coupling parameter analogous to pressure. The simplest replacement would give Kähler action as outcome. The replacement would allow RG invariance of the modified action only at critical points so that replacement would be possible only there. Furthermore, field equations must hold true separately for Kähler action and volume term everywhere.

  2. The coupling between Kähler action and volume term could be non-trivial at singular sub-manifolds, where a transfer of conserved quantities between the two degrees of freedom would take place. The transfer would be proportional to the divergence of the canonical momentum current Dα(gαββhk) assignable to the minimal surface and is conserved outside the singular sub-manifolds.

    Minimal surfaces provide a non-linear generalization of massless wave-equation for which the gradient of the field equals to conserved current. Therefore the interpretation could be that these singular manifolds are sources of the analogs of fields defined by M4 and CP2 coordinates.

    In electrodynamics these singular manifolds would represented by charged particles. The simplest interpretation would be in terms of point like charges so that one would have line singularity. The natural identification of world line singularities would be as boundaries of string world sheets at the 3-D light-like partonic orbits between Minkowskian and Euclidian regions having induced 4-metric degenerating to 3-D metric would be a natural identification. These world lines indeed appear in twistor diagrams. Also string world sheets must be assumed and they are are natural candidates for the singular manifolds serving as sources of charges in 4-D context. Induced spinor fields would serve as a representation for these sources. These strings would generalize the notion of point like particle. Particles as 3-surfaces would be connected by flux tubes to a tensor network and string world sheets would connected fermion lines at the partonic 2-surfaces to an analogous network. This would be new from the standard model perspective.

    Singularities could also correspond to a discrete set of points having an interpretation as cognitive representation for the loci of initial and final states fermions at opposite boundaries of CD and at vertices represented topologically by partonic 2-surfaces at which partonic orbits meet. This interpretation makes sense if one interprets the imbedding space coordinates as analogs of propagators having delta singularities at these points. It is quite possible that also these contributions are present: one would have a hierarchy of delta function singularities associated with string worlds sheets, their boundaries and the ends of the boundaries at boundaries of CD, where string world sheet has edges.

  3. There is also an interpretation of singularities suggested by the generalization of conformal invariance. String world sheets would be co-dimension 2 singularites analogous to poles of analytic function of two complex coordinates in 4-D complex space. String world sheets would be co-dimension 2 singularities analogous to poles at light-like 3-surfaces. The ends of the world lines could be analogous of poles of analytic function at partonic 2-surfaces.

    These singularities could provide to evolution equations what might be called matter contribution. This brings in mind evolution equations for n-point functions in QFT. The resolution of the overall singularity would decompose to 2-D, 1-D and 0-D parts just like cusp catastrophe. One can ask whether the singularities might allow interpretation as catastrophes.

  4. The proposal for the analogs of thermodynamical functions suggests the following physical picture. More general thermodynamical functions are possible only at critical points and only if the extremals are miminal surfaces. The singularities should correspond to physical particles, fermions. Suppose that one considers entire scattering amplitude involving action exponential plus possible analog of pV term plus the terms associated with the fermions assigned with the singularities. Suppose that the coupling constant evolution from 6-D Kähler action is calculated without including the contribution of the singularities.

    The derivative of n-particle amplitude with respect to the evolution parameter contains a term coming from the action exponential receiving contributions only from the singularities and a term coming from the operators at singularities. RG invariance of the scattering amplitude would require that the two terms sum up to zero. In the thermodynamical picture the presence of particles in many particle scattering amplitude would force to add the analog of pressure term to the Kähler function: it would be determined by the zero energy state.

    One can of course ask how general terms can be added by requiring minimal surface property. Minimal surface property reduces to holomorphy, and can be true also for other kinds of actions such as the TGD analogs of electroweak and color actions that I considered originally as possible action candidates.

    This would have interpretation as an analog for YM equations in gauge theories. Space-time singularities as local failure of minimal surface property would correspond to sources for H coordinates as analogs of Maxwell's fields and sources currents would correspond to fermions currents.

See the article Does coupling constant evolution reduce to that of cosmological constant?.

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

Articles and other material related to TGD.

Monday, January 07, 2019

Cosmological Axis of Evil as a memory from primordial cosmology

Axis of evil is very interesting CMB anomaly (thanks for Sky Darmos for mentioning it in FB discussion). It has been even proposed that it forces Earth-centeredness. According to the Wikipedia article :

"The motion of the solar system, and the orientation of the plane of the ecliptic are aligned with features of the microwave sky, which on conventional thinking are caused by structure at the edge of the observable universe. Specifically, with respect to the ecliptic plane the "top half" of the CMB is slightly cooler than the "bottom half"; furthermore, the quadrupole and octupole axes are only a few degrees apart, and these axes are aligned with the top/bottom divide."

This is indeed really strange looking finding. To my view it does not however bring pre-Keplerian world view back but is related to the possibility of quantum coherence even in cosmological scales predicted by TGD. It would also reflect the situation during very early cosmology, which in TGD framework is cosmic string dominated.

  1. The hierarchy of Planck constants heff=n×h0 implies the existence of space-time sheets with arbitrary large size serving as quantum coherent regions. heff=hgr assignable to flux tubes mediating gravitational interaction the value of heff can be gigantic. hgr= GMm/v 0, where M and m are masses such that M can be solar mass or even larger mass.

  2. Cosmic strings dominated the very early TGD inspired cosmology. They have 2-D projections to M^4 and CP_2 so that GRT is not able to describe them. During the analog of inflationary period the dimension of M^4 projection became D=4 and cosmic strings became magnetic flux tubes. Ordinary GRT space-time emerged and GRT started to be a reasonable approximation as QFT limit of TGD.

  3. Quantum coherence make possible long range correlations. One correlation of this kind could be occurrene of cosmic strings which are nearly parallel in even cosmic scales or more precisely nearly parallel at the time when the TGD counterpart of inflation occurred and the ordinary space-time emerged and cosmic strings thickened to magnetic flux tubes - a process directly corresponding to cosmic expansion. This time corresponds in standard cosmology the end of inflationary period.

    The volume that we observe via CMB now would correspond to a rather small volume at the end of the period when ordinary GRT space-time emerged and it is not too difficult to imagine that in this volume the cosmic strings would have formed a bundle nearly parallel cosmic strings. This property would have been preserved in good approximation during expansion. For instance, angular momentum conservation would have taken care of this if the galaxies along long cosmic strings had angular momenta in parallel: there is indeed evidence for this. Turning of cosmic string to a different direction would require a lot of angular momentum since also the galaxies should be turned at the same time.

  4. Cosmic strings thicknened to flux tubes would contain galaxies - pearls in necklace is good metaphor. Galaxies would be local tangles of flux tubes with topology of dipole type magnetic field in reasonable approximation. Also stars and planets would have formed in the similar manner. This leads to a rather detailed model for galaxy formation. See for instance this.

See the chapter More about TGD and Cosmology or the article Breaking of CP, P, and T in cosmological scales in TGD Universe.

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

Articles and other material related to TGD.

Wednesday, January 02, 2019

Solution of renormalization group equation for flux tubes having minimum string tension and RG evolution in terms of Riemann zeta

The great surprise of the last year was that twistor induction allows large number of induced twistor structures. SO(3) acts as moduli space for the dimensional reductions of the 6-D Kähler action defining the twistor space of space-time surface as a 6-D surface in 12-D twistor space assignable to M4× CP2. This 6-D surface has space-time surface as base and sphere S2 as fiber. The area of the twistor sphere in induced twistor structure defines running cosmological constant and one can understand the mysterious smallness of cosmological constant.

This in turn led to the understanding of coupling constant evolution in terms of the flow changing the value of
cosmological constant defined by the area of the twistor sphere of space-time surface for induced twistor structure.

dlog(αK)/ds = -[S(S2)/(SK(X4)+S(S2)] dlog(S(S2))/ds .

Renormalization group equation for flux tubes having minimum string tension

It came as a further pleasant surprise that for a very important special case defined by the minima of the dimensionally reduce action consisting of Kähler magnetic part and volume term one can solve the renormalization group equations explicitly. For magnetic flux tubes for which one has SK(X4)∝ 1/S and Svol∝ S in good approximation, one has SK(X4) =Svol at minimum (say for the flux tubes with radius about 1 mm for the cosmological constant in cosmological scales). One can write

dlog(αK)/ds = -1/2 dlog(S(S2))/ds ,

and solve the equation explicitly:

αK,0K = [S(S2)/S(S2)0]x , x=1/2 .

A more general situation would correspond to a model with x≠ 1/2: the deviation from x=1/2 could be interpreted as anomalous dimension. This allows to deduce numerically a formula for the value spectrum of αK,0K apart from the initial values.

The following considerations strongly suggest that this formula is not quite correct but applies only the real part of Kähler coupling strength. The following argument allows to deduce the imaginary part.

Could the critical values of αK correspond to the zeros of Riemann Zeta?

Number theoretical intuitions strongly suggests that the critical values of 1/αK could somehow correspond to zeros of Riemann Zeta. Riemann zeta is indeed known to be involved with critical systems.

The naivest ad hoc hypothesis is that the values of 1/αK are actually proportional to the non-trivial zeros s=1/2+iy of zeta . A hypothesis more in line with QFT thinking is that they correspond to the imaginary parts of the roots of zeta. In TGD framework however complex values of αK are possible and highly suggestive. In any case, one can test the hypothesis that the values of 1/αK are proportional to the zeros of ζ at critical line. Problems indeed emerge.

  1. The complexity of the zeros and the non-constancy of their phase implies that the RG equation can hold only for the imaginary part of s=1/2+it and therefore only for the imaginary part of the action. This suggests that 1/αK is proportional to y. If 1/αK is complex, RG equation implies that its phase RG invariant since the real and imaginary parts would obey the same RG equation.

  2. The second - and much deeper - problem is that one has no reason for why dlog(αK)/ds should vanish at zeros: one should have dy/ds=0 at zeros but since one can choose instead of parameter s any coordinate as evolution parameter, one can choose s=y so that one has dy/ds=1 and criticality condition cannot hold true. Hence it seems that this proposal is unrealistic although it worked qualitatively at numerical level.

It seems that it is better to proceed in a playful spirit by asking whether one could realize quantum criticality in terms of zeros of zeta.
  1. The very fact that zero of zeta is in question should somehow guarantee quantum criticality. Zeros of ζ define the critical points of the complex analytic function defined by the integral

    X(s0,s)= a∫Cs0→ s ζ (s)ds ,

    where Cs0→ s is any curve connecting zeros of ζ, a is complex valued constant. Here s does not refer to s= sin(ε) introduced above but to complex coordinate s of Riemann sphere.

    By analyticity the integral does not depend on the curve C connecting the initial and final points and the derivative dSc/ds= ζ(s) vanishes at the endpoints if they correspond to zeros of ζ so that would have criticality. The value of the integral for a closed contour containing the pole s=1 of ζ is non-vanishing so that the integral has two values depending on which side of the pole C goes.

  2. The first guess is that one can define Sc as complex analytic function F(X) having interpretation as analytic continuation of the S2 part of action identified as Re(Sc):

    Sc(S2)= F(X(s,s0)) , & X(s,s0)= ∫Cs0→ s ζ (s)ds ,

    S(S2)= Re(Sc)= Re(F(X)) ,

    ζ(s)=0 , & Re(s0)=1/2 .

    Sc(S2)=F(X) would be a complexified version of the Kähler action for S2. s0 must be at critical line but it is not quite clear whether one should require ζ(s0)=0.

    The real valued function S(S2) would be thus extended to an analytic function Sc=F(X) such that the S(S2)=Re(Sc) would depend only on the end points of the integration path Cs0→ s. This is geometrically natural. Different integration paths at Riemann sphere would correspond to paths in the moduli space SO(3), whose action defines paths in S2 and are indeed allowed as most general deformations. Therefore the twistor sphere could be identified Riemann sphere at which Riemann zeta is defined. The critical line and real axis would correspond to particular one parameter sub-groups of SO(3) or to more general one parameter subgroups.

    One would have

    αK,0K= (Sc/S0)1/2 .

    The imaginary part of 1/αK (and in some sense also of the action Sc(S2)) would determined by analyticity somewhat like the real parts of the scattering amplitudes are determined by the discontinuities of their imaginary parts.

  3. What constraints can one pose on F? F must be such that the value range for F(X) is in the value range of S(S2). The lower limit for S(S2) is S(S2)=0 corresponding to J→ 0.

    The upper limit corresponds to the maximum of S(S2). If the one Kähler forms of M4 and S2 have same sign, the maximum is 2× A, where A= 4π is the area of unit sphere. This is however not the physical case.

    If the Kähler forms of M4 and S2 have opposite signs or if one has RP option, the maximum, call it Smax, is smaller. Symmetry considerations strongly suggest that the upper limit corresponds to a rotation of 2π in say (y,z) plane (s=sin(ε)= 1 using the previous notation).

    For s→ s0 the value of Sc approaches zero: this limit must correspond to S(S2)=0 and J→ 0. For Im(s)→ +/- ∞ along the critical line, the behavior of Re(ζ) (see this) strongly suggests that | X|→ ∞ . This requires that F is an analytic function, which approaches to a finite value at the limit |X| → ∞. Perhaps the simplest elementary function satisfying the saturation constraints is

    F(X) = Smaxtanh(-iX) .

    One has tanh(x+iy)→ +/- 1 for y→ +/- ∞ implying F(X)→ +/- Smax at these limits. More explicitly , one has tanh(-i/2-y)= [-1+exp(-4y)-2exp(-2y)(cos(1)-1)]/[1+exp(-4y)-2exp(-2y)(cos(1)-1)]. Since one has tanh(-i/2+0)= 1-1/cos(1)<0 and tanh(-i/2+∞)=1, one must have some finite value y=y0>0 for which one has

    tanh(-i/2+y0)=0 .

    The smallest possible lower bound s0 for the integral defining X would naturally to s0=1/2-iy0 and would be below the real axis.

  4. The interpretation of S(S2) as a positive definite action requires that the sign of S(S2)=Re(F) for a given choice of s0= 1/2+iy0 and for a propertly sign of y-y0 at critical line should remain positive. One should show that the sign of S= a∫ Re(ζ)(s=1/2+it)dt is same for all zeros of ζ. The graph representing the real and imaginary parts of Riemann zeta along critical line s= 1/2+it (see this) shows that both the real and imaginary part oscillate and increase in amplitude. For the first zeros real part stays in good approximation positive but the the amplitude for the negative part increase be gradually. This suggests that S identified as integral of real part oscillates but preserves its sign and gradually increases as required.

A priori there is no reason to exclude the trivial zeros of ζ at s= -2n, n=1,2,....
  1. The natural guess is that the function F(X) is same as for the critical line. The integral defining X would be along real axis and therefore real as also 1/αK provided the sign of Sc is positive: for negative sign for Sc not allowed by the geometric interpretation the square root would give imaginary unit. The graph of the Riemann Zeta at real axis (real) is given in MathWorld Wolfram (see this).

  2. The functional equation

    ζ(1-s)= ζ(s)Γ(s/2)/Γ((1-s)/2)

    allows to deduce information about the behavior of ζ at negative real axis. Γ((1-s)/2) is negative along negative real axis (for Re(s)≤ 1 actually) and poles at n+1/2. Its negative maxima approach to zero for large negative values of Re(s) (see this) whereas ζ(s) approaches value one for large positive values of s (see this). A cautious guess is that the sign of ζ(s) for s≤ 1 remains negative. If the integral defining the area is defined as integral contour directed from s<0 to a point s0 near origin, Sc has positive sign and has a geometric interpretation.

  3. The formula for 1/αK would read as αK,0K(s=-2n) = (Sc/S0)1/2 so that αK would remain real. This integration path could be interpreted as a rotation around z-axis leaving invariant the Kähler form J of S2(X4) and therefore also S=Re(Sc). Im(Sc)=0 indeed holds true. For the non-trivial zeros this is not the case and S=Re(Sc) is not invariant.

  4. One can wonder whether one could distinguish between Minkowskian and Euclidian and regions in the sense that in Minkowskian regions 1/αK correspond to the non-trivial zeros and in Euclidian regions to trivial zeros along negative real axis. The interpretation as different kind of phases might be appropriate.

What is nice that the hypothesis about equivalence of the geometry based and number theoretic approaches can be killed by just calculating the integral S as function of parameter s. The identification of the parameter s appearing in the RG equations is no unique. The identification of the Riemann sphere and twistor sphere could even allow identify the parameter t as imaginary coordinate in complex coordinates in SO(3) rotations around z-axis act as phase multiplication and in which metric has the standard form.

See the article TGD View about Coupling Constant Evolutionor the chapter with the same title.

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

Articles and other material related to TGD.

Tuesday, January 01, 2019

Reduction of coupling constant evolution to that for cosmological constant

One of the chronic problems of TGD has been the understanding of what coupling constant evolution could be defined in TGD.

  1. The notion of quantum criticality is certainly central. The continuous coupling constant evolution having no counterpart in the p-adic sectors of adele would contain as a sub-evolution discrete p-adic coupling constant evolution such that the discrete values of coupling constants allowing interpretation also in p-adic number fields are fixed points of coupling constant evolution.

    Quantum criticality is realized also in terms of zero modes, which by definition do not contribute to WCW metric. Zero modes are like control parameters of a potential function in catastrophe theory. Potential function is extremum with respect to behavior variables replaced now by WCW degrees of freedom. The graph for preferred extremals as surface in the space of zero modes is like the surface describing the catastrophe. For given zero modes there are several preferred extremals and the catastrophe corresponds to the regions of zero mode space, where some branches of co-incide. The degeneration of roots of polynomials is a concrete realization for this.

    Quantum criticality would also mean that coupling parameters effectively disappear from field equations. For minimal surfaces (generalization of massless field equation allowing conformal invariance characterizing criticality) this happens since they are separately extremals of Kähler action and of volume term.

    Quantum criticality is accompanied by conformal invariance in the case of 2-D systems and in TGD this symmetry extends to its 4-D analog acting as isometries of WCW.

  2. In the case of 4-D Kähler action the natural hypothesis was that coupling constant evolution should reduce to that of Kähler coupling strength 1/αK inducing the evolution of other coupling parameters. Also in the case of the twistor lift 1/αK could have similar role. One can however ask whether the value of the 6-D Kähler action for the twistor sphere S2(X4) defining cosmological constant could define additional parameter replacing cutoff length scale as the evolution parameter of renormalization group.

  3. The hierarchy of adeles should define a hierarchy of values of coupling strengths so that the discrete coupling constant evolution could reduce to the hierarchy of extensions of rationals and be expressible in terms of parameters characterizing them.

  4. I have also considered number theoretical existence conditions as a possible manner to fix the values of coupling parameters. The condition that the exponent of Kähler function should exist also for the p-adic sectors of the adele is what comes in mind as a constraint but it seems that this condition is quite too strong.

    If the functional integral is given by perturbations around single maximum of Kähler function, the exponent vanishes from the expression for the scattering amplitudes due to the presence of normalization factor. There indeed should exist only single maximum by the Euclidian signature of the WCW Kähler metric for given values of zero modes (several extrema would mean extrema with non-trivial signature) and the parameters fixing the topology of 3-surfaces at the ends of preferred extremal inside CD. This formulation as counterpart also in terms of the analog of micro-canonical ensemble (allowing only states with the same energy) allowing only discrete sum over extremals with the same Kähler action.

  5. I have also considered more or less ad hoc guesses for the evolution of Kähler coupling strength such as reduction of the discrete values of 1/αK to the spectrum of zeros of Riemann zeta or actually of its fermionic counterpart. These proposals are however highly ad hoc.

As I started once again to consider coupling constant evolution I realized that the basic problem has been the lack of explicit formula defining what coupling constant evolution really is.

  1. In quantum field theories (QFTs) the presence of infinities forces the introduction of momentum cutoff. The hypothesis that scattering amplitudes do not depend on momentum cutoff forces the evolution of coupling constants. TGD is not plagued by the divergence problems of QFTs. This is fine but implies that there has been no obvious manner to define what coupling constant evolution as a continuous process making sense in the real sector of adelic physics could mean!

  2. Cosmological constant is usually experienced as a terrible head ache but it could provide the helping hand now. Could the cutoff length scale be replaced with the value of the length scale defined by the cosmological constant defined by the S2 part of 6-D Kähler action? This parameter would depend on the details of the induced twistor structure. It was shown above that if the moduli space for induced twistor structures corresponds to rotations of S2 possibly combined with the reflection, the parameter for coupling constant restricted to that to SO(2) subgroup of SO(3) could be taken to be taken s= sin(ε).

  3. RG invariance would state that the 6-D Kähler action is stationary with respect to variations with respect to s. The variation with respect to s would involve several contributions. Besides the variation of 1/αK(s) and the variation of the S(2) part of 6-D Kähler action defining the cosmological constant, there would be variation coming from the variations of 4-D Kähler action plus 4-D volume term . This variation vanishes by field equations. As matter of fact, the variations of 4-D Kähler action and volume term vanish separately except at discrete set of singular points at which there is energy transfer between these terms. This condition is one manner to state quantum criticality stating that field equations involved no coupling parameters.

    One obtains explicit RG equation for αK and Λ having the standard form involving logarithmic derivatives. The form of the equation would be

    dlog(αK)/ds = -S(S2)/SK(X4)+S(S2) dlog(S(S2))/ds .

    The equation contains the ratio S(S2)/(SK(X4)+S(S2)) of actions as a parameter. This does not conform with idea of micro-locality. One can however argue that this conforms with the generalization of point like particle to 3-D surface. For preferred extremal the action is indeed determined by the 3 surfaces at its ends at the boundaries of CD. This implies that the construction of quantum theory requires the solution of classical theory.

    In particular, the 4-D classical theory is necessary for the construction of scattering amplitudes. and one cannot reduce TGD to string theory although strong form of holography states that the data about quantum states can be assigned with 2-D surfaces. Even more: M8-H correspondence implies that the data determining quantum states can be assigned with discrete set of points defining cognitive representations for given adel This set of points depends on the preferred extremal!

  4. How to identify quantum critical values of αK? At these points one should have dlog(αK)/ds=0. This implies dlog(S(S2)/ds=0, which in turn implies dlog(αK)/ds=0 unless one has SK(X4)+S(S2)=0. This condition would make exponent of 6-D Kähler action trivial and the continuation to the p-adic sectors of adele would be trivial. I have considered also this possibility.

    The critical values of coupling constant evolution would correspond to the critical values of S and therefore of cosmological constant. The basic nuisance of theoretical physics would determine the coupling constant evolution completely! Critical values are in principle possible. Both the numerator J2 and the numerator 1/(det(g))1/2 increase with ε. If the rate for the variation of these quantities with s vary it is possible to have a situation in which the one has

    dlog(J2)/ds =-dlog((det(g))1/2)/ds .

  5. One can test the hypothesis that the values of 1/αK are proportional to the zeros of ζ at critical line. The complexity of the zeros and the non-constancy of their phase implies that the RG equation can hold only for the imaginary part of s=1/2+iy and therefore only for the imaginary part of the action. One can also consider the possibily that 1/αK is proportional to y If the equation holds for entire 1/αK, its phase must be RG invariant since the real and imaginary parts would obey the same RG equation.

  6. One should demonstrate that the critical values of s are such that the continuation to p-adic sectors of the adele makes sense. For preferred extremals cosmological constant appears as a parameter in field equations but does not affect the field equations expect at the singular points. Singular points play the same role as the poles of analytic function or point charges in electrodynamics inducing long range correlations. Therefore the extremals depend on parameter s and the dependence should be such that the continuation to the p-adic sectors is possible.

    A naive guess is that the values of s are rational numbers. Above the proposal s= 2-k/2 motivated by p-adic length scale hypothesis was considered but also s= p-k/2 can be considered. These guesses might be however wrong, the most important point is that there is that one can indeed calculate αK(s) and identify its critical values.

  7. What about scattering amplitudes and evolution of various coupling parameters? If the exponent of action disappears from scattering amplitudes, the continuation of scattering amplitudes is simple. This seems to be the only reasonable option. In the adelic approach amplitudes are determined by data at a discrete set of points of space-time surface (defining what I call cognitive representation) for which the points have M8 coordinates belong to the extension of rationals defining the adele.

    Each point of S2(X4) corresponds to a slightly different X4 so that the singular points depend on the parameter s, which induces dependence of scattering amplitudes on s. Since coupling constants are identified in terms of scattering amplitudes, this induces coupling constant evolution having discrete coupling constant evolution as sub-evolution.

The following argument suggests a connection between p-adic length scale hypothesis and evolution of cosmological constant but must be taken as an ad hoc guess: the above formula is enough to predict the evolution.
  1. p-Adicization is possible only under very special conditions, and suggests that anomalous dimension involving logarithms should vanish for s= 2-k/2 corresponding to preferred p-adic length scales associated with p≈ 2k. Quantum criticality in turn requires that discrete p-adic coupling constant evolution allows the values of coupling parameters, which are fixed points of RG group so that radiative corrections should vanish for them. Also anomalous dimensions Δ k should vanish.

  2. Could one have Δ kn,a=0 for s=2-k/2, perhaps for even values k=2k1? If so, the ratio c/s would satisfy c/s= 2k1-1 at these points and Mersenne primes as values of c/s would be obtained as a special case. Could the preferred p-adic primes correspond to a prime near to but not larger than c/s=2k1-1 as p-adic length scale hypothesis states? This suggest that we are on correct track but the hypothesis could be too strong.

  3. The condition Δ d=0 should correspond to the vanishing of dS/ds. Geometrically this would mean that S(s) curve is above (below) S(s)=xs2 and touches it at points s= x2-k, which would be minima (maxima). Intermediate extrema above or below S=xs2 would be maxima (minima).

See the chapter TGD View about Coupling Constant Evolution or the article with the same title.

Friday, December 28, 2018

What bio-teleportation could mean?

Below is a comment from a discussion about teleportation. How to make teleportation a more realistic notion? What bio-teleportation could mean?

Teleportation uses all information needed to code the quantum state of the system to be teleported and then transfers this information to distant target where it is used to rebuild the system from basic building bricks existing there. The amount of information is huge.

Quantum entanglement increases this information exponentially from what it would be classically: recently this has been proposed as an argument against practical realization of quantum computation.

How could one transform teleportation ideas to something more realistic?

  1. One can argue that in living matter quantum entanglement is not at all free. TGD leads to the notion of negentropic entanglement: entanglement coefficients are in extension of rationals (algebraic numbers ). This allows to speak about p-adic entanglement entropy. The p-adic entropies can be non-positive telling that entanglement carries information - about the relationship of the entangled systems. One identification for conscious experienced associated with this kind of entangled relationship is as experience of love.

    Could the condition that entanglement is negentropic in this sense, reduce the number of possible entangled configurations to a more reasonable number?

  2. One can of course challenge the idea that one should transfer all the information needed to construct the state. One could provide just the needed prerequisites for the system to do it it itself: that is to self-organise and evolve to the state. In biology genes seems to be this prerequisite.

Transferring all information is not realistic. What can one transfer?. Could one just transfer just the property of being living in the sense that we understand it? Or perhaps transfer some constraints to the outcome of the spontaneously occurring evolution generated by the signal.
  1. Metabolic energy feed is certainly one prerequisite. It is needed to create state with larger value of heff carrying able to build rather stable negentropic entanglement carrying conscious information. This problem disappears if the target receives energy in some form, say from star near it. The signal sending the needed information could have large value of heff (consist of dark photons) and provide the needed energy and do it with precisely desired manner so that the induced evolution might be much faster.

  2. The transfer of biological life seems hopelessly complicated task. Biomolecules are extremely complex. TGD however leads to a proposal that so called dark genetic code with proton triplets providing representations for DNA and RNA codons, amino-acids, tRNA, is universal: dark proton sequences are dark nuclei with reduced binding energy. What is highly non-trivial that the model predicts correctly the vertebrate genetic code. Model has also strong empirical basis based on on findings of Pollack.

    Dark nuclei realize genetic code and define the dramatically simpler dynamics - dark variant of nuclear physics - behind extremely complex shadow dynamics of biochemistry. Dark nuclear physics would serve as the template for bio-chemistry and all basic processes like replication, transcription, and translation would have very simple templates at the level of dark nuclear physics. One should reconstruct the dark variants of basic biomolecules using genetic information and the system at the second end would do the rest.

    Something like this could indeed happen in the experiments of Montagnier et al and Gariaev discussed from TGD point of view here.

  3. How could one communicate the needed information over long distances? Radiation would be needed and it should be highly negentropic - dark photons - to provide metabolic energy at the same time. I have proposed what I call bio-harmony - it turns out to provide a realization of genetic code (something highly non-trivial as also the dark realization of genetic code) - allowing to assign to dark codons 3-chords consisting of light (or even sound).

    This would allow coding of DNA to 3-chords of dark photons allowing the transfer of genetic information along long distances to receiver, which could be water: could this induce generation of dark proton sequences by Pollack effect, creating dark copies of the original dark genes. These in turn could eventually lead to a generation of life as we know as biochemistry would develop around them. One might be however forced to wait for some billion years! If the dark proton sequences can be constructed as precise copies of original this process could become must faster.

  4. How to translate the pattern of dark photons 3-chords back to a sequence dark proton triplets?

    An antenna, which can send, can also receive. The reception would be time reversal of the process of sending and generate the desired dark proton sequence but only in ZEO allowing time reversals of topological quantum computations inducing processes at the level of ordinary matter as shadow processes (bio-chemistry would be shadow dynamics induced by the much simpler dynamics of dark proton sequences realizing dark variants of basic biomolecules and realizing genetic code).

    Could this work? I have considered here the ZEO based idea that motor actions in very general senses including also DNA transcription etc.. are realized using the time reversal of the reverse of motor action as a template realized at magnetic body and inducing the motor action at the level of ordinary matter. These time reversals would be realized as braiding patterns for magnetic flux tubes, topological quantum computer programs. State function reduction changing the arrow of clock time would be essential and would be possible in ZEO but not in standard quantum theory. The essential point is that one does not send 3-D pattern, but entire 4-D pattern, process. ZEO makes this possible.

    This picture is possible only in TGD framework ( the notion of magnetic body implied by many-sheeted space-time, dark matter as a hierarchy of heff=n× h0 phases, and ZEO).

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

Articles and other material related to TGD.

Friday, December 21, 2018

Motor actions as TQC programs written by Nature itself

I wrote a long email explaining the basic terms used in the model of motor actions as topological quantum computer programs. It might be useful to add it also as a blog post.

ZEO based view about consciousness

What is state function reduction? What is self? What is death? What is re-incarnation?

  1. What ZEO is? Zero energy states are pairs of states with opposite total quantum numbers. Members of state are associated with opposite boundaries of causal diamond (CD). CD is geometric correlate for self. CD has size. CD has active and passive boundary: see below.

  2. What is state function reduction in ZEO? There are small and big state function reductions.

  3. Small state function reduction.

    1. In small reduction - weak measurement - following unitary evolution, the passive boundary of CD is unaffected as also members of state pairs (defining zero energy states) at it. Passive boundary corresponds to unchanging part of consciousness.

    2. The members of state pairs at active boundary of CD change in small reduction which is much like classical measurement, not dramatic changes. This corresponds to the sensory input and thoughts etc induced by it - the changing part of consciousness, Maya might some-one say. Also the location of the active boundary boundary changes - its distance from fixed boundary of CD increases in statistical sense - unavoidably. This corresponds to the increase of clock time assignable to the sequence of small reductions.

      Arrow of time corresponds to direction to which the active boundary of CD shifts.

  4. Big state function reduction. The roles of passive and active boundary change. The arrow of time changes. CD begins to increase in opposite direction of geometric time. Previous self dies and new is born and lives in opposite direction of time.

Motor actions and sensory percepts correspond to mental images -sub-selves- sub-CDs of CD. Motor action is sensory percept in opposite arrow of time. It seems that it cannot be conscious to self with opposite arrow of time. The definition of these notions is extremely general. For instance, DNA transcription corresponds to a motor action.

Magnetic body, biological body, tensor network, braiding, TQC program

  1. Magnetic body (MB) and biological body (BB) are key notions. MB controls BB and receives sensory data. Braiding generated by motion of parts of BB corresponds to sensory input to MB (not the only sensory input).

    Behaviours are essentially motor actions controlled by BB.

  2. Tensor network formed by magnetic flux tubes of MB and space-time sheets representing BB. When one has MB -magnetic flux tubes as space-time sheets parallel to space-time sheets representing matter in M4×CP2 (overlapping M4 projections) - they have 3-D contacts and interaction.

    Flux tubes of MB connect space-time sheets representing particles of ordinary bio-matter. This is tensor network.

  3. Topological quantum computer program as braiding: dance metaphor.

    When these particles of BB move flux tubes of MB get braided and when flux tubes de-braid, matter is forced to move: this is motor action.

    Dance metaphor helps: dancers with feet connected to wall by threads. Dance as dynamical pattern forces the threads to get braided: this defines memory of dance as topological quantum computer program realizes as space-time topology, topology of flux tube structure.

Motor action induces TQC program and TQC program in reversed time direction induces motor action
  1. Assume that BB lives in standard time direction but MB can change its time direction by big state function reduction.

  2. Consider motor action for BB living in standard direction of time but assume that one has time reversal of motor action otherwise. From end to the beginning. The motion of parts of BB gives rise to a braiding of flux tubes defining TQC program.

    This TQC program is recorded automatically - this is the big thing. There is no need for a nerd to write the code. Nature does it automatically. This is like learning from model. Here connections to Sheldrake's ideas are rather obvious.
    Nature learns all the time: habits/ behaviors/ functions/ motor actions - as you wish.

  3. Perform now big quantum jump to the MB. Arrow of time changes and the time reversal of braiding takes place. Since braiding for MB represents time reversal of motor action for BB, its time reversal forces motor action in the desired time direction for BB. Note that BB has standard time direction.

  4. When BB and MB have same time direction: MB gets sensory data by braiding. When MB has time direction opposite to that of BB, MB induces a motor action of BB.

See the chapter Sensory Perception and Motor Action as Time Reversals of Each Other: a Royal Road to the Understanding of Other Minds? 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.

Monday, December 17, 2018

How could the TQC programs representing basic bio-reactions emerge?

The basic bio-chemical processes such as replication, transcription, translation have remained mysteries in standard biology. My conviction is that a lot of new physics is needed. Bio-chemistry is not enough, even QFT is not enough. Even standard views about space-time and classical fields, QM, and basic ontology are not enough.

TGD approach indeed brings in several new physics elements.

  1. The notion of magnetic body (MB). MB carrying dark matter identified as dark variants of charged particles having non-standard value heff= n×h0 of Planck constant is central in TGD inspired quantum biology. MB is the intentional agent receiving sensory input from biological body and controlling it. The interactions at the level of ordinary bio-matter would be governed by the MBs of molecules, and bio-chemistry would be a shadow of this much simpler dynamics.

    MB of water entrains to the cyclotron frequencies of the MBs of the basic biomolecules by varying flux tube thickness. This makes possible water memory (see this) and implies homeopathy like mechanisms serving as basic quantal building bricks in the functioning of the immune system. Dark variants of DNA, etc.. realized as dark proton sequences would be one aspect of this representation.

  2. The braiding of the magnetic flux tubes makes possible realization of topological quantum computer (TQC) programs. Biological functions should correspond to TQC programs and the challenge is to understand how they emerge naturally. A possible answer to this question will be proposed in the sequel.

  3. There are also other central notions such as zero energy ontology (ZEO) predicting that the arrow of time is not fixed. The following arguments suggests that ZEO is absolutely essential for the understanding of the miracles of bio-chemistry. TQC programs running backwards in time would generate as output various biological functions such as DNA transcription and other basic processes.

What are the big problems?

It is best to start from the problems that one should solve. At bio-molecular level the basic problem is to understand how complex temporal sequences of bio-chemical reactions involving bio-catalysts are possible as highly deterministic sequences.

  1. How the reacting molecules - including catalysts - are able to find each other in the molecular soup?

    TGD answer: Contraction of flux tubes connecting molecules very selectively as heff is reduced brings molecules together. Connections between molecules are generated by reconnection of U-shaped flux tubes scanning enviroment and producing pair of flux tubes connecting the two systems provided they have the same cyclotron frequency. Resonant em coupling by dark photons is in question.

  2. How the attached molecules are able to attach to just the correct spot and orient just in the correct manner?

    TGD answer: the contraction mechanism for flux tubes automatically guarantees also this.

  3. How the rate of reaction can exceed the expected rate by so huge factor?

    TGD answer: Reactants are connected by flux tubes so that the probability that they find each other is much higher and depends on the occurrence of heff reducing transition which occurs spontaneously. The energy liberated in the contraction of flux tube allows to overcome potential wall in the reaction and exponential increase in the rate is achieve.

  4. How bio-catalysis can proceed in time ordered manner like deterministic computer program so that very many initial states can lead to the same outcome?

    Here the initial states would correspond to positions orientations, etc of input molecules. Huge number of initial states lead to the same outcome.

    I think that this is the really difficult question. I am highly skeptic about the possibility to understand this in QFT framework. In the following I propose TGD inspired solution of this problem requiring ZEO, which means a revolutionary modification of basic ontology and of views about time.

How bio-catalysis can proceed in time ordered manner like deterministic computer program so that very many initial states can lead to the same outcome?

Apparently a breaking of second law is involved. Very many initial states lead to the same outcome rather than vice versa. As if the process would be controlled by the time reversal of the original process and entropy would increase but in opposite time direction as usually but at the control level! The notion of syntropy introduced by Fantappie comes in mind!

TGD answer would involve at least the following pieces.

  1. Dark DNA and dark variant associated with enzyme should be part of the story. Large heff brings in conscious information realized as algebraic complexity and large scale quantum coherence.

  2. ZEO allowing time reversed processes should be essential. ZEO predicts both directions of time and motor actions are postulated to correspond to sensory perception in opposite arrow of time (see this). What this precisely means is not however clear.

  3. Magnetic body (MB) should be the boss controlling dynamics. This dynamics should be very simple. Biochemistry should be shadow dynamics and apparently extremely complex.

  4. Topological quantum computational aspect(TQC) is also central but I have not been able to articulate what TQC programs emerge: the following ZEO arguments suggests an astonishingly simple mechanism for this.

    The complex reaction sequences like transcription should correspond to a running of topological quantum computer (TQC) program coded by the braiding. I just made a big step of progress in the understanding of sensory memories. Memory recall would be like a quantum computer program running backwards in time and producing sensory experience as output (see this).

    There is a strong temptation to believe that this is completely general aspect of all also motor actions. By fractality also DNA transcription, translation, etc... are analogs of motor actions. Somehow they should be coded to TQC programs realized as braidings of flux tubes of MB.

    The output of the TQC program running backwards with respect to the standard direction of time would be motor action as we observe it. All basic bio-processes involving several steps be coded to braidings. One can imagine a hierarchical structure: programs, subprograms, etc... for the TQC programs. Braidings of braidings of.... This conforms with the hierarchical many-sheeted structure of space-time.

How to realize motor actions as outputs of TQC programs running in non-standard direction of time?
  1. Assume that when some process - such as DNA transcription or its time reversal occurs - it induces braiding of flux tubes - topological quantum computer (TQC) program at the level of MB.

    As this TQC program runs backwards in time, the time reversal of the original process is generated as output at the level of ordinary bio-matter.

  2. For instance, in the case of transcription, one should assume that the time reversal of transcription meaning the decay of mRNA back to its building bricks generates the TQC program as braiding. Running of this TQC problem in the reverse time direction should generate transcription.

  3. What looks strange that the time reversal of the assembly process - essentially a decay process occurring in very manners - would code for the highly deterministic TQC program for the assembly process. But this is actually just what one wants!!

    The decay process is highly unpredictable but its time-reversal is highly predictable! There are very many TQC programs, which give rise to the desired output! The ways from Rome lead to all possible directions but all ways lead to Rome! In ZEO butterfly effect transforms to extreme predictivity in opposite time direction!

  4. How MB and space-time sheets assignable to ordinary matter and having opposite arrows of time - or more generally two levels of heff hierarchy with different values of heff and different arrow of time - could interact? If the arrows of time are opposite, the intersection of space-time sheets should have dimension smaller than D=4. Since the classical dynamics determined by twistor lift breaks T symmetry (the analog of Kähler action in M4 degrees of freedom is the reason), 3-D intersection does not imply that the surfaces co-incide for the space-time surface and its time reversal.

    The interaction should be via common boundary conditions: the space-time sheets with different arrow of time should intersect along 3-D or even lower-dimensional surfaces at the boundaries of CD and perhaps also at the 3-D light-like orbits of partonic 2-surfaces at which the signature of the induced metric changes. Magnetic flux tubes induce braiding, which suggests that magnetic flux tubes of MB as 4-D surfaces should have at most 3-D intersection with the space-time surfaces representing ordinary bio-matter and defining the nodes of tensor network (see this). These 3-D - possibly light-like - intersections would mediate the interaction. For the usual arrow of time for MB interaction would be sensory input to MB and induce braiding. For the opposite arrow of time for MB it would be motor action in which MB would be the controller forcing bio-matter to follow in the un-braiding process.

    In the generic case the intersection of two 4-surfaces in M4× CP2 is discrete. Could the intersection of space-time surfaces with different arrow of time consist of a discrete set of points? Could this be enough for MB to control bio-matter? Note that cognitive representations identified as intersections of real space-time surfaces and their p-adic variants consist of a discrete set of points (see this).

  5. The connection with Sheldrake's vision about morphogenetic fields, in particular the genereration of "habits" even at the level of so called dead matter is rather obvious. TQC programs would indeed code for habits and would be generated by Nature without a need of a programmer writing the code. I have discussed Sheldrake's vision from a slightly different viewpoint here.

There are interesting connections to ancient Indian philosophy and Christianity. ZEO has analog in ancient Indian philosophy as I learned from a discussion with Savyasanchi Ghose while writing this. As notions doer and un-doer are analogous to self and time reversed self. MB would be in the role of supreme observer although it would not be outsider to the Universe. The undoing the time reversal of deed by MB would serve as a template for the dynamics of deed at the level of ordinary matter.

Building braids and opening them are the basic operations in TQC according to ZEO. A visit to web using "undoer" reveals that it appears also in Christianity, Mary the undoer of knots! Knots are now a metaphor for sins and undoing them means mercy. In Christianity God would be the counterpart of MB and we would be 4-D dynamical images of God.

To sum up, this sounds like mystics and brings strongly in my mind a french movie about time that I saw decades ago. It was very poetic and somehow caught at the emotional level something very deep about the mysteries of time, life, and consciousness in a manner not expressible using the vocabulary of scientist. It seems that TGD is providing the language that I did not have at that time and that ZEO is starting to demonstrate its magnificent explanatory power.

See the chapter Sensory Perception and Motor Action as Time Reversals of Each Other: a Royal Road to the Understanding of Other Minds? 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.

Long term sensory memories in TGD framework

There was a highly interesting popular article (see this) inspired by the recent findings about long term memory (see this) in conflict with the standard view about memories. Of course, also the memory feats of so called idiot savants known for decades are in sharp conflict with the standard view about memory.

The discussion of these findings in TGD framework led to a decisive improvement in the understanding of the proposed mechanism of sensory memory recall. Also a connection with the model of topological quantum computation realized axon-microtubule level emerged. Sensory memory would be realized as a topological quantum computer program running in reversed time direction in memory recall and generating the virtual sensory input from brain to sensory organs creating the original sensory experience.

The findings

The following gives a brief summary of the results of the experiment discussed here.

  1. A huge amount of storage capacity is required and it increases as more and more experiences are experienced.

    One can imagine an abstraction as a cure: store only essentials about the input. This is extremely powerful manner to store the relevant information. Picture about grandmother's house with all detail is replaced with world "grandmother's house". What is lost is detail. This storage mechanism is certainly used at higher levels of evolutionary hierarchy. Verbal memories are a good example.

    The experiment mentioned above however demonstrates that the memory storage is at least 1000 times more detailed than it could be, which suggest that a different very detailed storage mechanism usually unconscious to us is involved.

    Indeed, the memory feats of idiot savants show that sensory percepts can be stored in amazing detail. A possible TGD based explanation is that all of us have sensory memories - essentially re-experiences but at a lower level of personal self hierarchy, not as mental images represented as sub-selves but as sub-sub-..-selves not directly conscious to us. Temporal democracy would make it impossible to distinguish between recent and past and make it difficult to survive. Here would be the reason for why these persons are often called idiot savants.

    Sensory memories must be unconscious at our level of self hierarchy to allow the experience about living in definite moment of time and only cognitive (symbolic, verbal) memories involving a lot of abstraction satisfy this condition. If the percept is cognitive, it is about geometric past. If sensory, it is about "Now". Perceptive field effectively reduces from 4-D to 3-D (actually the duration of sensory chronon is about .1 seconds).

    Situation changes when temporal lobes are stimulated electrically as neuroscientists have known for decades but "forgotten". Perhaps animals do not conceptualize and have sensory memories.

  2. Proteins used for the storage in terms of modified synaptic contacts is slow by a factor 1000 slower than required to understand the above experiment. Memorizing would require a repeated stimulation but now the pictures were seen only once or twice.

  3. The lifetime of the proteins in synaptic contacts is only few weeks so that also long term memories would be unstable. Humans can remember for about 50 years, 1000 times longer than expected.

  4. The technical realization of the 3-D storage is also a problem. One should remember also the place, where the memory is stored, not only the memory itself! Here the association mechanism seems the only possibility but would allow only conditionings. In computer language LISP this idea is very concretely realized. Conditionings are however only pseudo-memories.

Wrong views about time andthe notion of memory as the basic problems

To sum up, the standard view about memories suffers from two fatal problems.

  1. The first fatal problem of the standard model of memory is the wrong view about the relationship between experienced and geometric time. The identification of these times forces to the notion of memory storage analogous to that in computer. The information about what happened must be stored again and again. This view has many problems already discussed.

  2. Second fatal problem is the conceptual flaw forced by behaviorism: memories are identified as conditiongs, habits, or behaviors - as you like. Genuine sensory memories are however re-experiences and would however correspond to re-experience to which is associated a synchronously firing neuron group: what neurons fire is not determined by synaptic contacts but by the sensory input mapped topographically to sensory area. This is very delicate and crucial difference.

TGD view about sensory memories

Could one realize memory as re-experience in TGD framework?

  1. In zero energy ontology (ZEO) of TGD no 3-D memory storage to the "brain now" is required. Memories are ideally where (in 4-D sense) the event occurred but memory recall creates further - usually less detailed and more abstracted copies - of the memory. To remember (in the genuine sense of the word) is to re-experience. Memory in this sense would be in the geometric past. Memory recall would be seeing in time: sending a signal to geometric past, where it is time-reflected back. Each memory recall could generate at least conceptual copy about the memory and in this manner the signal sent to the geometric past would have higher probability to generate the re-experience or at least secondary version of it. Learning, which is not mere conditioning, could rely on the generation of copies of the memory in 4-D perceptive field.

  2. Memories as re-experiences would involve synchronously firing neuron groups associated with quantum coherent units defined by magnetic bodies (MBs) of neurons and representing mental images. To understand this concretely, one needs besides the notion of MB also the hierarchy heff= n× h0, h=6×h0 of Planck constants. The synchronously firing neuron group (involving quantum coherent part of MB) in the geometric past is woken up by the time reversed signal to the geometric past and reflecting from it by providing energy (now negative). ZEO makes this possible.

  3. How the memory recall could realize this synchronous firing in the geometric past? This mechanism should be analogous to the reflection of negative energy signal in time direction from the brain of the geometric past. ZEO allows sending of a negative energy signal travelling to geometric past. It should somehow induce a transition generating the synchronous firing. The signal generating this transition should be very simple. It must induce the transition at correct location in the geometric past. Here the period of the carrier wave of the signal could be essential and large value of heff could make the signal energetic enough despite the period which could be measured in years so that energy for the ordinary value of Planck constant would be extremely small. Signal could also provide metabolic energy for the neurons, which should fire synchronously. Replicas of the memory help to achieve activation at the correct location.

  4. There must be a coding of the sensory input to the physical state of neuronal pathways coded by nerve pulse patterns representing the original sensory input from the sensory organs. If genuine sensory re-experience is required a signal generating the original sensory experience and thus the nerve pulse pattern from sensory organs creating it should be re-generated.

    As if one had in the geometric past a magnetic tape representing somehow the original experience. When played it would generate a signal to the sensory organs in turn generating the signal to the brain (including nerve pulses) giving rise to the original sensory experience. Note that ZEO indeed allows the sensory experience to be in geometric past. It is however communicate cognitive information about it to recent too.

TGD leads to a model for what could happen based on the idea that topological computation is realized in terms of the braiding of magnetic flux tubes connecting two subsystems (see this and this). This model leads to a model of memory representations as a kind of topological quantum computer program giving the original experience as an output while running.

Let us assume that second system is axonal membrane along which the nerve pulse patterns (and whatever else is needed) representing the sensory input flow. Second system would be naturally microtubules inside it.

  1. The flux tubes would connect the lipids of the axonal membrane to the tubulins (or units formed by them). Axonal membrane can be in liquid-crystal state meaning that the lipid are like liquid particles able to move. Nerve pulses would induce a 2-D liquid flow inducing the braiding of the flux tubes having second end fixed to (say) tubulin of the microtubule.

    There would be both time-like and space-like braiding. Dance metaphor is very helpful here. Consider dancers at the parquet with legs connected by threads (flux tubes) to a wall (microtubule). Time-like braiding would correspond to the dynamical dance pattern of lipids in time direction having a representation as a 2-D projection defined by the paths of dancers at the parquet. Time like braiding would be analogous to a running topological quantum computer program.

    Space-like braiding would be the outcome of the dance representing tangle of the flux tubes fixed to the wall and defining topological quantum computer program serving as a representation for the time like braiding and therefore also for the nerve pulse pattern (and whatever the signal involves) and the sensory input. Space-like braiding is analogous to the code representing the topological quantum computer program and should make possible to represent the program.

    If this space-like braiding can generate a signal serving as a virtual sensory input to the sensory organs, the sensory memory could be regenerated. The running of the topological quantum computer program would mean the opening/un-knotting of this braiding and would represent the time reversal of the sensory input, not yet sensory input, which could correspond to nerve pulse pattern from the sensory organs generating the sensory percept. It seems that the opening must generate a signal to sensory organs as virtual sensory input.

  2. Virtual sensory input brain indeed is the basic element of TGD inspired model of sensory perception as construction of artwork. The basic difference to the standard view is that the sensory qualia are at the level of sensory organs rather than in brain. Brain only gives names for the percepts and builds standard sensory mental images by using virtual sensory input from brain. The process is like pattern recognition by driving sensory input to a standard input near to the real input.

    In TGD framework however nerve pulse patterns would not carry the sensory information to the brain but would generate sensory input to MB as Josephson radiation from the cell membrane. The transmitters emitted at the synaptic contacts would generate bridges connecting axonal magnetic flux tubes to longer connected flux tubes and in this manner create the communication channels - kind of wave guides. Along thee dark photons (which can transform to bio-photons) could travel with light velocity.

    This communication mechanism is dramatically faster than the communication by nerve pulses and allows forth-and-back signalling involving virtual sensory input from brain to generate the standard percepts assignable to the synchronously firing neuron groups accompanied by magnetic bodies obtained by connecting neuronal magnetic bodies by flux tubes.

    The standard mental images would contain only the features relevant for survival or otherwise interesting. A still open question is whether the virtual sensory input corresponds to the time reversal of the ordinary sensory input (see this). The following consideration suggests that time reversal is indeed in question.

  3. If the virtual sensory input from brain is in time reversed time direction, one can think of very simple model for memory as re-experience. Big state function could occur meaning that the mental images associated with braiding generated by nerve pulse pattern and dark photon beam die and re-incarnate in opposite time direction. A time-reversed mental image is generated. This mental images is not conscious at our level of hierarchy living in opposite time direction.

    This mental image is not quite exact time reversal of the original and there is non-determinism of state function reduction involved. One can have however statistical determinism possible if large enough number of neurons are involved. Therefore the differences need not be too big. Also standardization comes in rescue: it would take care that the sensory mental is very nearly the counterpart of the original.

    The time-reversed signal from brain to the sensory organ should generate a nerve pulse pattern just as in the case of ordinary perception and the dark photon signal generating the sensory mental image defining the original sensory memory in good approximation.

  4. For the simplest alternative dark photons alone induce the flow of the lipids. Hitherto it has been assumed that the flow is induced by nerve pulse patterns. The most general option is that both are involved in the generation of the flow. One cannot exclude the possibility that the communication of data about nerve pulse pattern to MB generates a control signal which induces the liquid flow. There are many options to consider but the basic idea is clear and involves ZEO and MB in a crucial manner.

  5. An important open question is whether the virtual sensory input using dark photons propagates

    1. to the "sensory organs then" so that only cognitive memories would result as copies. In this case a person, who has lost eyesight during lifetime could have visual memories from time when she could see.

    2. or via the MB to the "sensory organs now" and stimulates sensory experience in "brain now". Person lost eyes during lifetime could not have visual sensory memories in this case.

    For the latter option one can ask whether the sensory experience is
    1. realized by the mere virtual sensory input to sensory organs. No copies of the sensory representation at the microtubule-axon level would be generated. If sensory organs are not intact, sensory memories would not be possible.

    2. or whether also a signal from sensory organs to brain involving nerve pulse pattern is needed to generate the experience. Each memory recall would create an almost exact copy of topological computer program giving rise to a genuine sensory memory while running.

    Various options might be tested by electric stimulation of the temporal lobes known to generate sensory memories.
See the chapter Sensory Perception and Motor Action as Time Reversals of Each Other: a Royal Road to the Understanding of Other Minds? 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.