Sunday, August 18, 2019

A visit to Baden-Baden

I participated a symposium held in Baden-Baden (31st International Conference on Systems Research, Informatics and Cybernetics – InterSymp 2019: Symposium on Causal and Anticipative Systems in Living Science, Biophysics, Quantum Mechanics, Relativity). The visit was pleasant: Baden-Baden is small town which has preserved its personal warm character.

I wrote a slightly extended version of the related article mentioning the recent experimental finding of Minev et al supporting zero energy ontology crucial for the approach. The following is the abstract of the article.

Topological Geometro-Dynamics (TGD) proposes a unification of fundamental interactions by identifying space-times as 4-surfaces in 8-D space H=M4× CP2, whose geometry codes for standard model symmetries and geometrizes known fields. Point-like particle is replaced with 3-surface (3-space). One ends up with the notions of many-sheeted space-time and magnetic body (MB) central in TGD inspired quantum biology. p-Adic and adelic physics follows from the extension of physics to describe also the correlates of cognition and imagination. Adelic physics predicts a hierarchy of Planck constants labelling phases of ordinary matter interpreted as dark matter: the predicted quantum coherence in arbitrarily long scales is crucial for quantum biology. Quantum TGD replaces standard ontology with "zero energy ontology" (ZEO) replacing quantum state as time=constant snapshot with zero energy state (ZES) identified as a superposition of deterministic classical time evolutions - kind of quantum program.

See the article TGD inspired theory of consciousness and living systems.

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

Articles and other material related to TGD.

Saturday, August 17, 2019

Could metaplectic group have some role in TGD framework?

Metaplectic group appears as a covering group of linear symplectic group Sp(2n,F) for any number field and its representations can be regarded as analogs of spinor representations of the rotation group. Since infinite-D symplectic group of δ M4+× CP2, where δ M4+ is light-cone boundary, appears as an excellent candidate for the isometries of the "world of classical worlds" in zero energy ontology (ZEO), one can ask whether and how the notion of metaplectic group could generalize to TGD framework.

The condition for the existence of metaplectic structure is same as of the spinor structure and not met in the case of CP2. One however expects that also the modified metaplectic structure exists if one couples spinors to an odd integer multiple of Kähler gauge potential. For triality 1 representation assignable to quarks one has n=1. The fact that the center of SU(3) is Z3 suggests that metaplectic group for CP2 is 3- or 6-fold covering of symplectic group instead of 2-fold covering.

Besides the ordinary representations of SL(2,C) also the possibly existing analogs of metaplectic representations of SL(2,C) = Sp(2,C) acting on wave functions in hyperbolic space H3 represented as a2=t2-r2 hyperbololoid of M4+ are cosmologically interesting since the many-sheeted space-time in number theoretic vision allows quantum coherence in even cosmological scales and there are indications for periodic redshift suggests tesselations of H3 analogous to lattices in E3 and defined by discrete subgroup of Sl(2,C). In this case one could require that only the subgroup SU(2) is represented projectively so that one would have an analogy with modular functions for discrete subgroup of SL(2,Z) would be represented in this manner.

See the chapter Recent View about K\"ahler Geometry and Spin Structure of WCW.

Wednesday, August 07, 2019

Phase transitions generating dark phases and sensory perception

The TGD based model for biological self-organization relies on the hierarchy heff=nh0 of effective Planck constants labelling dark phases of ordinary particles residing at magnetic flux quanta. This model generalizes and suggests the replacement of non-equilibrium thermodynamics as basis of self-organization with its quantum variant based on dark matter hierarchy. The challenge is to formulate basic thermodynamical notions like work in terms TGD based quantum theory relying on zero energy ontology (ZEO).

The basic mechanism would be a phase transition creating dark matter phase as a Bose-Einstein condensate like state with particles having identical conserved quantum numbers. Conservation laws would force the ordinary matter to have opposite total charges. For instance, in the case of work one has momentum or angular momentum as a conserved charge. In the case of charge separation and high Tc superconductivity it would be em charge. Even color charges can correspond to conserved charges in TGD framework allowing scaled variants of strong interaction physics.

Basic biological functions involving the notion of work and also the formation of sensory percepts would rely on this mechanism. Also the ZEO based theory of consciousness predicting the change the arrow of time in ordinary state function reduction plays a central role and a model of nerve pulse is discussed as an example.

Sensory perception (time reversal of motor action could involve generation of coherent phases of dark matter carrying collective quantum numbers in 1-1 corresponds with the sensory qualia. This would represent a general charge separation process.

Consider first sensory capacitor model for color qualia.

  1. The notion of QCD color as analog of ordinary visual colors was originally introduced as a joke since the algebra of color summation resembles that for the summation of QCD colors in tensor product. In TGD however the dark hierarchy (heff) and p-adic length scale hierarchy predict that scaled variants of QCD type physics are possible for arbitrarily large length scales. In cellular scales scaled up QCDs are predicted. In the length scale range between cell membrane thickness and nucleus size there are as many as 4 Gaussian Mersennes, which is a number theoretical miracle. They could label copies of QCDs with size scale for the analogs of hadrons given by the corresponding p-adic length scales. QCD type colors could correspond to perceived colors.

  2. Gluons or quarks labelled by color charge characterizing particular color quale would flow between the plates of "capacitor" associated with the sensory receptor. The amount of particular color charge increases at the other plate giving rise to sensation of this particular color quale and its complement at the other plate - by color confinement also the same plate could also contain regions with complementary colors. This would explain why we see around a region of particular color a narrow boundary with complementary color.

  3. The model for sensory perception as sequences of analogs of weak measurements suggest that the flow of color charges could induce color qualia. The prediction emerging from the structure of SU(3) color algebra would be four pairs of basic color and complement color: 3 ordinary pairs and white-black pair. They could correspond to particular changes of color quantum numbers and color quantum numbers of gluons. Also color mixing could be understood.

  4. Photons are not coloured but gluons (and also quarks) are, and the latter and could be responsible for color sensation. How photon flux can generate a flow of color quantum numbers? The notion of induced gauge field -classical color gauge potentials would be projections of SU(3) Killing vectors - explains this.

    In TGD classical em field is sum of two terms induced Kähler form and neutral vectorial component of spinor curvature. Classical gluon field has components proportional to classical color Hamiltonian (function in CP2 which can be said to have quantum numbers of gluon) and induced Kähler form. In general case any classical em field is accompanied by a classical color field.

    Photons are accompanied by classical em fields and therefore also by classical gluon fields at the fundamental level: this correspondence disappears at QFT limit unable to describe biology and sensory experience. The flow of photons to retina would be accompanied by classical em and color fields and therefore a flow of gluons. Also quark flow between the plates of sensory capacitor could generate the color qualia.

  5. A simple model for the visual qualia is in terms of a phase transition transforming gluons of a scaled copy of QCD to ordinary gluons. Dark gluons would form a BE condensate and force a formation its shadow at the level of ordinary matter. This is a variant of sensory receptor as quantum capacitor. The plates of capacitor correspond to dark and ordinary phase and the analog of electric breakdown means formation of the dark phase. Cooper pairs of quarks with quantum numbers of gluon would be second option but gluons in TGD framework are actually this kind of pairs!!

See the article Quantum self-organization by heff changing phase transitions or the chapter General theory of qualia.

Zero energy ontology and quantum model for nerve pulse

In TGD based model of nerve pulse axonal membrane is generalized cylindrical Josephson junction defined by axonal membrane consisting of smaller Josephson junctions defined by membrane proteins.

  1. A sequence of mathematical penduli along axon in rotation in the same direction is the mechanical analog. Oscillation frequency Ω transforming to a rotation frequency above critical value is proportional to the resting potential V. When V is overcritical, the pendulum starts to rotate instead of oscillating. The system should be near quantum criticality for the transformation of rotation to oscillation or vice versa.

  2. During nerve pulse membrane potential and therefore also rotation frequency is reduced and changes sign and then returns back to the original value. The first guess is that at criticality there is a kick reducing the rotation frequency Ω and continuing to change its sign and then return it to original.

The basic condition is that resting state becomes critical at critical hyper-polarization. There are two options for the resting state.
  1. According to the original model resting state can be regarded as a soliton sequence associated with the phase difference over the membrane. More concretely, the mathematical penduli rotate in same direction with phase difference between determining the propagation velocity of solitons. The rotation frequency is slightly above that for oscillation. There is a preferred direction along axon. This conforms with the reduction and change of sign of potential and thus of Ω.

    Problem: Hypo- rather than hyper-polarization should cause the nerve pulse as a transformation of rotation to oscillation. Something goes wrong.

  2. Alternatively, the penduli almost rotate being near criticality for the rotation: the penduli almost reaches the vertical position at each oscillation as required by criticality. That hyper-polarization would cause the nerve pulse as propagating soliton conforms with this idea.

    Problem: Ω and thus V should increase rather than reduce and even change sign temporarily.

Neither option seems to work as such but the first option is more plausible as a starting point of an improved model.

The membrane potential changes sign suggesting quantum jump. Could zero energy ontology (ZEO) based view about quantum jump as "big" (ordinary) state function reduction (BSFR) help? Could nerve pulse correspond to BSFR?

  1. Could BSFR occur changing temporarily the arrow of time in ZEO and induce nerve pulse. Could opposite BSFR take place after this in millisecond scale and establish the original arrow of time. Using the language of TGD inspired theory of consciousness a conscious entity, sub-self or mental image, would die and reincarnate with an opposite arrow of time, live for the duration of nerve pulse and then die and reincarnate with the original arrow of time. Nerve pulse would be a propagation of a temporary neuron death along the axon and would occur as neuron becomes hyper-polarized.

  2. In the article about the recent findings of Minev et al related to quantum jump in atomic physics are discussed. ZEO predicting that the arrow of time is changed in BSFR. This would create the illusion that discontinuous quantum jumps correspond to a classical time evolution leading smoothly and deterministically to the final state.

    This because BSFR leads to a state with reversed arrow of time, which corresponds to a superposition of classical time evolutions leading from the final state to the geometric past and it this, which is observed.
    This would also explain why the removal of the irradiation inducing quantum jumps has no effect during the transition process and why a stimulation inducing opposite quantum jump can stop the process. Also the findings of Libet related to the active aspects of consciousness showing that neural activity seems to preceded volitional act can be understood in this framework without giving up the notion of free will.

    The first half of the nerve pulse would correspond to this apparent evolution to the time reversed final state with opposite membrane potential but actually being time reversed evolution from the final state. The second half of nerve pulse would correspond to opposite state function reduction establishing the original arrow of time. This model looks attractive but many details remain to be checked.

Why hyper-polarization should cause the temporary death of neuron or its subself?
  1. Metabolic energy feed is needed to preserve the polarization of neuron since membrane potential tends to get reduced by second law stating that all gradients are bound to decrease. There should be some maximal polarization possible to preserve using the existing metabolic energy resources.

  2. Does quantum jump to a state with opposite arrow of time happen as this limit is reached? Why? Could the metabolic energy feed stop causing the neuron to die to starvation? Why the death of neuron should happen so fast? Could the quantum criticality against the change of rotation to oscillation be the reason. When neuron cannot rotate anymore it would die immediately: the mental image "I am rotating" would die and reincarnate as its time reversal. Does the neuron feeded by metabolic energy become a provider metabolic energy during this period somewhat like dead organisms after their death. Can one conclude that this energy goes to some purpose inside neuron?

See the article Quantum self-organization by heff changing phase transitions or the chapter Quantum model for nerve pulse.

Quantum self-organization by heff changing phase transitions

The TGD based model for biological self-organization relies on the hierarchy heff=nh0 of effective Planck constants labelling dark phases of ordinary particles residing at magnetic flux quanta. This model generalizes and suggests the replacement of non-equilibrium thermodynamics as basis of self-organization with its quantum variant based on dark matter hierarchy. The challenge is to formulate basic thermodynamical notions like work in terms TGD based quantum theory.

The basic mechanism would be a phase transition creating dark matter phase as a Bose-Einstein condensate like state with particles having identical conserved quantum numbers. Conservation laws would force the ordinary matter to have opposite total charges. For instance, in the case of work one has momentum or angular momentum as a conserved charge. In the case of charge separation and high Tc superconductivity it would be em charge. Even color charges can correspond to conserved charges in TGD framework allowing scaled variants of strong interaction physics.

Basic biological functions involving the notion of work and also the formation of sensory percepts would rely on this mechanism. Also the ZEO based theory of consciousness predicting the change the arrow of time in ordinary state function reduction plays a central role and a model of nerve pulse is discussed as an example.

See the article Quantum self-organization by heff changing phase transitions or the chapter Quantum Theory of Self-Organization.

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

Articles and other material related to TGD.

Friday, July 19, 2019

About the mathematics needed in TGD


The following is a comment from FB discussion. Since the answer developed to a summary of the mathematics needed in TGD, I decided to make it blog post.

I think that TGD is a "problem" for anyone in the sense that it is very difficult to get graps of what it really is. The reason is that TGD have been silenced for 4 decades - censorship in archives started around 93 or so and has had fatal consequences. The idea about the hegemony of M-theory estabilished by censorship was terribly silly.

TGD is an outcome of concentrated effort lasted more than 4 decades and involves 24 books. I guess that the minimum time to get some perspective to TGD is one year. For instance, I have worked with twistors for about 10 years and gradually begin to really understand the twistorialization of TGD. I am skeptic about communication of TGD without a long series of lectures and personal face to face discussions. This has not been possible, and now also my age poses strong limitations.

Concerning math, I am not interested in technical things such as producing a new p-adic variant of self-interacting phi4 scalar field theory. Usually mathematically oriented people do this kind of things in lack of wider physics perspective. I have a big developing a vision binding physics, consciousness, and biology, and I want to identify and even develop the mathematics needed if needed.

  1. The math involves sub-manifold geometry intended to geometrize field theory by replacing field patterns with 4-surfaces using generalization of the induction procedure for metric, spinor connection, and spinors (also twistors). Kaehler geometry is in central role. Induction is something new for physics, but well-known for mathematicians.

  2. The great vision involves geometrization of quantum theory in terms of infinite-D Kaehler geometry for the world of "classical world". Wheeler with his superspace was pioneer in general relativity and loop spaces are predecessors in string theory. Infinite-D symmetries as generalization of superstringy conformal symmetries are in pivotal role: they guarantee the existence of infinite-D Kaehler geomery.

  3. Number theoretic vision is complementary to geometric vision and number theory including extensions of rationals, p-adic number fields and their extensions induced by extensions of rationals and classical number fields. Extending the physics to a description of also cognition is the great vision and brings in p-adic number fields, adeles, and predicts hierarchy of Planck constants characterizing dark matter in TGD sense. Cognitive representations are fundamental notion and provide a unique number theoretical discretization of classical and quantum physics. One powerful implication is discretization of coupling constant evolution forced solely by number theoretical universality.

  4. The generalization of twistors to 8-D context to solve basic problem of standard twistor approach (only massless particles are allowed) is part of the vision. A new element is the replacement of space-time surfaces with their twistor spaces represented as 6-surfaces in 12-D twistor space of imbedding space. One powerful prediction is that M4×CP_2 implied by standard model is the only possible choice for the imbedding space besides M8 which is equivalent dual choice: the reason is that only the spaces M4, E4 and CP2 allow twistor space with Kaehler structure. TGD is unique from its existence.

  5. I have considered also categories occasionally. I tend to see them as tools to organize and excellent for bureaucratic challenges: they do not seem to code for core ideas. As a physicist I see interpretations of quantum theory as as unsuccessful attempts to get rid of the basic problem of the measurement theory: here zero energy ontology (ZEO) provides the great vision and leads to a theory of consciousness and quantum biology.

    The great idea is terribly simple: transform initial value problem to boundary value problem by replacing initial values at t= constant hyperplane with boundary values characterizing deterministic time evolution t1→>t2 and by replacing quantum states with superpositions of deterministic time evolutions.

The mathematics of TGD has not been found by going to math library but developing the physical vision and generalizing the existing mathematical ideas appropriately. I trust to physics based arguments much more than mathematical proofs involving all kinds of technical assumptions.

Those interested in material about TGD can find links from Material about TGD.

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

Articles and other material related to TGD.

Sunday, July 14, 2019

What extensions of rationals could be winners in the fight for survival?

It would seem that the fight for survival is between extensions of rationals rather than individual primes p. Intuition suggests that survivors tend to have maximal number of ramified primes. These number theoretical speciei can live in the same extension - to "co-operate".

Before starting one must clarify for myself some basic facts about extensions of rationals.

  1. Extension of rationals are defined by an irreducible polynomial with rational coefficients. The roots give n algebraic
    numbers which can be used as a basis to generate the numbers of extension ast their rational linear combinations. Any number of extension can be expressed as a root of an irreducible polynomial. Physically it is is of interest, that in octonionic picture infinite number of octonionic polynomials gives rise to space-time surface corresponding to the same extension of rationals.

  2. One can define the notion of integer for extension. A precise definition identifies the integers as ideals. Any integer of extension are defined as a root of a monic polynomials P(x)=xn+pn-1xn-1+...+p0 with integer coefficients. In octonionic monic polynomials are subset of octonionic polynomials and it is not clear whether these polynomials could be all that is needed.

  3. By definition ramified primes divide the discriminant D of the extension defined as the product D=∏i≠ j (ri-rj) of differences of the roots of (irreducible) monic polynomial with integer coefficients defining the basis for the integers of extension. Discriminant has a geometric interpretation as volume squared for the fundamental domain of the lattice of integers of the extension so that at criticality this volume interpreted as p-adic number would become small for ramified primes an vanish in O(p) approximation. The extension is defined by a polynomial with rational coefficients and integers of extension are defined by monic polynomials with roots in the extension: this is not of course true for all monic polynomials polynomial (see this).

  4. The scaling of the n-1-tuple of coefficients (pn-1,.....,p1) to (apn-1,a2pn-1.....,anp0) scales the roots by a: xn→ axn. If a is rational, the extension of rationals is not affected. In the case of monic polynomials this is true for integers k. This gives rational multiples of given root.

    One can decompose the parameter space for monic polynomials to subsets invariant under scalings by rational k≠ 0. Given subset can be labelled by a subset with vanishing coefficients {pik}. One can get rid of this degeneracy by fixing the first non-vanishing pn-k to a non-vanishing value, say 1. When the first non-vanishing pk differs from p0, integers label the polynomials giving rise to roots in the same extension. If only p0 is non-vanishing, only the scaling by powers kn give rise to new polynomials and the number of polynomials giving rise to same extension is smaller than in other cases.

    Remark: For octonionic polynomials the scaling symmetry changes the space-time surface so that for generic polynomials the number of space-time surfaces giving rise to fixed extension is larger than for the special kind polynomials.

Could one gain some understanding about ramified primes by starting from quantum criticality? The following argument is poor man's argument and I can only hope that my modest technical understanding of number theory does not spoil it.
  1. The basic idea is that for ramified primes the minimal monic polynomial with integer coefficients defining the basis for the integers of extension has multiple roots in O(p)=0 approximation, when p is ramified prime dividing the discriminant of the monic polynomial. Multiple roots in O(p)=0 approximation occur also for the irreducible polynomial defining the extension of rationals. This would correspond approximate quantum criticality in some p-adic sectors of adelic physics.

  2. When 2 roots for an irreducible rational polynomial co-incide, the criticality is exact: this is true for polynomials of rationals, reals, and all p-adic number fields. One could use this property to construct polynomials with given primes as ramified primes. Assume that the extension allows an irreducible olynomial having decomposition into a product of monomials =x-ri associated with roots and two roots r1 and r2 are identical: r1=r2 so that irreducibility is lost.

    The deformation of the degenerate roots of an irreducible polynomial giving rise to the extension of rationals in an analogous manner gives rise to a degeneracy in O(p)=0 approximation. The degenerate root r1=r2 can be scaled in such a manner that the deformation r2=r1(1+q)), q=m/n=O(p) is small also in real sense by selecting n>>m.

    If the polynomial with rational coefficients gives rise to degenerate roots, same must happen also for monic polynomials. Deform the monic polynomial by changing (r1,r2=r1) to (r1,r1(1+r)), where integer r has decomposition r=∏piki to powers of prime. In O(p)=0 approximation the roots r1 and r2 of the monic polynomial are still degenerate so that pi represent ramified primes.

    If the number of pi is large, one has high degree of ramification perhaps favored by p-adic evolution as increase of number theoretic co-operation. On the other hand, large p-adic primes are expected to correspond to high evolutionary level. Is there a competition between large ramified primes and number of ramified primes? Large heff/h0=n in turn favors large dimension n for extension.

  3. The condition that two roots of a polynomial co-incide means that both polynomial P(x) and its derivative dP/dx vanish at the roots. Polynomial P(x)= xn +pn-1xn-1+..p0 is parameterized by the coefficients which are rationals (integers) for irreducible (monic) polynomials. n-1-tuple of coefficients (pn-1,.....,p0) defines parameter space for the polynomials. The criticality condition holds true at integer points n-1-D surface of this parameter space analogous to cognitive representation.

    The condition that critical points correspond to rational (integer) values of parameters gives an additional condition selecting from the boundary a discrete set of points allowing ramification. Therefore there are strong conditions on the occurrence of ramification and only very special monic polynomials are selected.

    This suggests octonionic polynomials with rational or even integer coefficients, define strongly critical surfaces, whose p-adic deformations define p-adically critical surfaces defining an extension with ramified primes p. The condition that the number of rational critical points is non-vanishing or even large could be one prerequisite for number theoretical fitness.

  4. There is a connection to catastrophe theory, where criticality defines the boundary of the region of the parameter space in which discontinuous catastrophic change can take place as replacement of roots of P(x) with different root. Catastrophe theory involves polynomials P(x) and their roots as well as criticality. Cusp catastrophe is the simplest non-trivial example of catastrophe surface with P(x)= x4/4-ax-bx2/2: in the interior of V-shaped curve in (a,b)-plane there are 3 roots to dP(x)=0, at the curve 2 solutions, and outside it 1 solution. Note that now the parameterization is different from that proposed above. The reason is that in catastrophe theory diffeo-invariance is the basic motivation whereas in M8 there are highly unique octonionic preferred coordinates.

If p-adic length scale hypothesis holds true, primes near powers of 2, prime powers, in particular Mersenne primes should be ramified primes. Unfortunately, this picture does not allow to say anything about why ramified primes near power of 2 could be interesting. Could the appearance of ramified primes somehow relate to a mechanism in which p=2 as a ramified prime would precede other primes in the evolution. p=2 is indeed exceptional prime and also defines the smallest p-adic length scale.

For instance, could one have two roots a and a+2k near to each other 2-adically and could the deformation be small in the sense that it replaces 2k with a product of primes near powers of 2: 2k = ∏i 2ki→ ∏ipi, pi near 2ki? For the irreducible polynomial defining the extension of rationals, the deforming could be defined by a→ a+2k could be replaced by a→ a+2k/N such that 2k/N is small also in real sense.

See the article Trying to understand why ramified primes are so special physically or the chapter TGD View about Coupling Constant Evolution.

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

Articles and other material related to TGD.

Saturday, July 13, 2019

Trying to understand why ramified primes are so special physically

Ramified primes (see this and this) are special in the sense that their expression as a product of primes of extension contains higher than first powers and the number of primes of extension is smaller than the maximal number n defined by the dimension of the extension. The proposed interpretation of ramified primes is as p-adic primes characterizing space-time sheets assignable to elementary particles and even more general systems.

In the following Dedekind zeta functions (see this) as a generalization of Riemann zeta are studied to understand what makes them so special. Dedekind zeta function characterizes given extension of rationals and is defined by reducing the contribution from ramified reduced so that effectively powers of primes of extension are replaced with first powers.

If one uses the naive definition of zeta as analog of partition function and includes full powers Piei, the zeta function becomes a product of Dedekind zeta and a term consisting of a finite number of factors having poles at imaginary axis. This happens for zeta function and its fermionic analog having zeros along imaginary axis. The poles would naturally relate to Ramond and N-S boundary conditions of radial partial waves at light-like boundary of causal diamond CD. The additional factor could code for the physics associated with the ramified primes.

The intuitive feeling is that quantum criticality is what makes ramified primes so special. In O(p)=0 approximation the irreducible polynomial defining the extension of rationals indeed reduces to a polynomial in finite field Fp and has multiple roots for ramified prime, and one can deduce a concrete geometric interpretation for ramification as quantum criticality using M8-H duality.

See the article Trying to understand why ramified primes are so special physically or the chapter TGD View about Coupling Constant Evolution.

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

Articles and other material related to TGD.

Sunday, July 07, 2019

Libet's paradoxical findings and strange findings about state function reduction in atomic scales

Perceiving is basically quantum measuring, More precisely, perceptions correspond to the counterparts of so called weak measurements in TGD (zero energy ontology) analogous to classical measurements. The observables measured in weak measurements are such that they commute with the observables whose eigenstate is the permanent part of self, the "soul". Big ( that is ordinary) state function reductions mean the death of self and its reincarnation with opposite arrow of time. This holds universally in all scales.

For the change of the arrow of time the recent findings gave direct support in atomic scales (see this). Effectively there is a deterministic process leading to the final state of reduction. This is an illusion: reduction produces superposition of deterministic classical time evolutions beginning from the final state but backwards in time of observer. Experimenters misinterpreted this as time evolution with standard arrow of time leading to the final state of reduction.

Also Libet's findings about active aspects of consciousness can be interpreted in ZEO along the same lines. The observation that the neural activity begins before conscious decision can be understood by saying that the act of free will as a big state function reduction changed the arrow of time for an appropriate subsystem of the system studied. Tte time reversed classical evolutions from the outcome of the volitional action were interpreted erratically as a time evolution leading to the conscious decision. A less precise manner to say this is that conscious decision (big state function reduction) sent a classical signal to geometric past with opposite arrow of time initiating neural activity. Libet's finding led physicalistic neuroscientists to conclude that free will is an illusion. The actual illusions were physicalism and the belief that arrow of time is always the same.

See the article Copenhagen interpretation dead: long live ZEO based quantum measurement theory! or the chapter Life and Death and Consciousness of "TGD based view about living matter and remote mental interactions: Part I".

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

Articles and other material related to TGD.