Zero energy ontology, holography = holomorphy vision and TGD view of qualia

Zero energy ontology (ZEO) and holography = holomorphy vision providing an exact solution of classical field equations allow to solve some earlier problems of TGD inspired theory of consciousness and to sharpen earlier interpretations. Holography = holomorphy vision generalizes 2-D conformal invariance to 4-D situation and provides a universal solution of field equations in terms of minimal surfaces defined as roots for pairs of generalized analytic functions of the generalized complex coordinates of H=M⁴× CP₂ (one of the coordinates is hypercomplex coordinate with light-like coordinate curves) (see this) and this).

Consider first the implications of ZEO (see this and this).

1. ZEO predicts that in "big" state function reductions (BSFRs) as counterparts of ordinary SFRs the arrow of time changes. "Small" SFRs (SSFRs) are the counterpart for repeated measurements of the same observables, which in standard QM leave the system unaffected (Zeno effect). In SSFRs, the state of the system however changes but the arrow of time is preserved. This has profound implications for the understanding of basic facts about consciousness.
2. The sequence of SSFR corresponds to a sequence of delocalizations in the finite-dimensional space of causal diamonds CD =cd× CP₂ (see this) and consists of delocalizations (dispersion) followed by localizations as analogs of position measurements in the moduli parameterizing the CD. This sequence gives rise to subjective existence, self.
3. BSFR has interpretation is accompanied by reincarnation with an opposite arrow of geometric time. BSFR means the death of self as a sequence of "small" SFRs (SSFRs) and corresponds to falling asleep or even death. Death is therefore a completely universal phenomenon. The next BSFR means birth with the original arrow of time: it can be wake-up in the next morning or reincarnation taking place considerably later, life time is the first guess for the time scale. This follows from the fact that causal diamond CD =cd× CP₂ increases in size during the sequence of SSFRs.
4. What forces the ZEO is holography which is slightly non-deterministic due to the classical non-determinism of an already 2-D minimal surface realized as a soap film for which the frame spanning it does not fix it uniquely. This means that the 4-D space-time surface located inside CD and identifiable as the analog of Bohr orbit determined by holography must be taken as a basic object instead of a 3-surface. In SSFRs, the state at the passive light-like boundary of CD is unaffected just as in Zeno effect but the state at the active boundary changes. Due to the dispersion in the space of CDs the size of CD increases in statistical sense and the geometric time identifiable as the distance between the tips of CD increases and correlates with the subjective time identifiable as sequence of SSFRs.
5. In standard quantum theory, the association of conscious experience with SFRs does not allow us to understand conscious memories since the final state of state function reduction does not contain any information about the earlier states and state function reductions. Zero energy ontology leads to a concrete view of how conscious memories can be realized in the TGD Universe (see this). The superposition of space-time surfaces between fixed initial state and changing final state of SSFR contains the classical information about previous states and state function reductions and makes memory possible. The slight non-determinism of the classical time evolution implies loci of non-determinism as analogs of soap film frames and memory recall corresponds to a quantum measurement at these memory seats.
6. SSFRs correspond to repeated measurements of the same observable and the eigenvalues of the measured observables characterize the conscious experience, "qualia", partially. Also new commuting observables related to the non-determinism can appear and the set of observables can be also reduced in size. The superposition of the space-time surfaces as analogs of non-deterministic Bohr orbits however changes in the sequence of SSFRs and the associated classical information changes and can give rise to conscious experiences perhaps involving also the qualia remaining constant as long as self exists.

   The eigenvalues associated with the repeatedly measured observables do not change during the sequence of SSFRs and one can ask if they can give rise to a conscious experience, which should be assignable to change. Could these constant qualia be experienced by a higher level self experiencing self as sub-self defining a mental image? This higher level self would indeed experience the birth and death of subself and therefore its qualia.

   The observables at the passive boundary of CD correspond qualia of higher level self and the additional observables associated with SSFRs correspond to those of self. They would be associated with self measurements.

7. Note that self dies when the measured observables do not commute with those which are diagonalized at the passive boundary. It is quite possible that these kinds of temporary deaths take place all the time. This would allow learning by trial and error making possible conscious intelligence and problem solving since the algebraic complexity is bound to increase: this is formulated in terms of Negentropy Maximization Principle (see this).

ZEO and holography = holomorphy vision allow us to understand some earlier problems of TGD inspired theory of consciousness and also to sharpen the existing views.

Two models for how sensory qualia emerge

Concerning sensory qualia (see this) I have considered two basic views.

1. The first view is that the sensory perception corresponds to quantum measurements of some observables. Qualia are labelled by the measured quantum numbers.
2. The second, physically motivated, view has been that qualia correspond to increments of quantum numbers in SFR (see this). This view can be criticized since the quantum numbers need not be well-defined for the initial state of the SFR. One can however modify this view: perhaps the redistribution of quantum numbers leaving the total quantum numbers unaffected, is what gives rise to the sensory qualia.

   The proposed physical realization is based on the sensory capacitor model of qualia. Sensory receptors would be analogous to capacitors and sensory perception would correspond to dielectric breakdown. Sensory qualia would correspond to the increments of quantum numbers assignable to either cell membrane in the generalized di-electric breakdown. The total charges of the sensory capacitor would vanish but they would be redistributed so that both membranes would have a vanishing charge. Membranes could be also replaced with cell exterior and interior or with cell membrane and its magnetic body. Essential would be emergence or disappearance of the charge separation.

   This picture conforms with the recent view about the role of electric and gravitational quantum coherence assignable to charged and massive systems. In particular, electric Planck constant would be very large for charged systems like cell, neuron, and DNA and in the dielectric breakdown and its time reversal its value would change dramatically. If this is the case the dynamic character of effective Planck constant involving phase transition of ordinary to dark matter and vice versa would be essential for understanding qualia.

3. As the above argument demonstrated, the qualia can be decomposed to internal and external qualia. The internal qualia correspond to self-measurements of sub-self occurring in SSFRs whereas the external qualia correspond to the qualia measured by self having sub-self as a mental image. They are not affected during the life-time of the mental image. Whether the self can experience the internal qualia of subself is far from clear. The sensory capacitor model would suggest that this is the case. Also the model for conscious memories suggests the same. The internal qualia would correlate with the classical dynamics for the space-time surfaces appearing in the superposition defining the zero energy state and make possible, not only conscious memory and memory recall based on the failure of precise classical determinism, but also sensory qualia as subselves experienced as sensory mental images.

Geometric and flag manifold qualia and the model for the honeybee dance

One can decompose qualia to the qualia corresponding to the measurement of discrete observables like spin and to what might be called geometric qualia corresponding to a measurement of continuous observables like position and momentum. Finite measurement resolution however makes these observables discrete and is realized in the TGD framework in terms of unique number theoretic discretization of the space-time surface.

Especially interesting qualia assignable to twistor spaces of M⁴ and CP₂.

1. Since these twistor spaces are flag manifolds, I have talked about flag-manifold qualia. Their measurement corresponds to a position measurement in the space of quantization axes for certain quantum numbers. For angular momentum this space would be S²= SO(3)/SO(2) and the localization S² would correspond to a selection of the quantization axis of spin. For CP₂=SU(3)U(2) the space of the quantization axis for color charges corresponds to 6-D SU(3)(U(1)× U(1), which is identifiable as a twistor space of CP₂.
2. The twistor space of M⁴ can be identified locally as M⁴× S², where S² is the space of light-like rays from a point of M⁴. This space however has a non-trivial bundle structure since for two points of M⁴ connected by a light-like ray, the fibers intersect.

What is the corresponding flag manifold for M⁴?

1. The counterpart of the twistor sphere would be SO(1,3)/ISO(2), where ISO(2) is the isotropy group of massless momentum identifiable as a semidirect product of rotations and translations of 2-D plane. SO(1,3)/ISO(2) corresponds to the 3-D light-cone boundary (other boundary of CD) rather than S² since it has one additional light-like degree of freedom. Is the twistor space as a flag manifold of the Poincare group locally M⁴× SO(1,3)/ISO(2). This is topologically 7-D but metrically 6-D. Since light rays are parametrized by S² one can also consider the possibility of replacing M⁴× SO(1,3)/ISO(2) with S² in which case the twistor space would be 6-D and represented a non-trivial bundle structure.
2. Could one restrict M⁴ to E³ or to hyperbolic 3-sphere H³ for which light-cone proper time is constant? In these cases the bundle structure would trivialize. What about the restriction of M⁴ to the light-like boundaries of CD? The restriction to a single boundary gives non-trivial bundle structure but seems otherwise trivial. What about the union of the future and past boundaries of CD? The bundle structure would be non-trivial at both boundaries and there would also be light-like rays connecting future and past light-like boundaries.

   The unions ∪_i H³_i(a_i) of hyperbolic 3-spaces corresponding different values a=a_i of the light-cone propert time a emerge naturally in M⁸-H duality and could contain the loci of the singularities of space-time surfaces as analogs of frames of soap filmas. Also these would give rise to a non-trivial bundle structure.

   These identifications differ from the usual identification of the M⁴ twistor space as CP₃: note that this identification of the M⁴ twistor space is problematic since it involves compactification of M⁴ not consistent with the Minkowski metric. Holography = holomorphy vision in its recent form involves a general solution ansatz in terms of roots of two analytic functions f₁ and f₂ and f₂=0 (see this), which identifies the twistor spheres of the twistor spaces of M⁴ and CP₂ represented as metrically 6-D complex surfaces of H. M⁴ twistor sphere corresponds to the light-cone boundary in this identification. This identification map also defines cosmological constant as a scale dependent dynamical parameter.

A basic application for the twistor space of CP₂ has been in the TGD based model (see this and this) for the findings of topologist Barbara Shipman (see this) who made the surprising finding that the twistor space of CP₂, naturally assignable to quarks and color interactions, emerges in the model for the dance of honeybee. This kind of proposal is nonsensical in the standard physics framework but the predicted hierarchy of Planck constants and p-adic length scales make possible scaled variants of both color and electroweak interactions and there is a lot of empirical hints for the existence of this hierarchy, in particular for the existence as a scaled up variants of hadron physics leading to a rather radical proposal for the physics of the Sun (see this).

Shipman found that the honeybee dance represents position in SU(3)/U(1)× U(1) coding for the direction and distance of the food source in 2-D plance! Why should this be the case? The explanation could be that the space-time surfaces as intersections of 6-D counterparts of the twistor spaces ISO(2)× ∪_i H³(a=a_i) resp. SU(3)/U(1)× U(1) identified as a root of analytic function f₁ resp. f₂ (see this) have space-time surface as 4-D intersection so that honeybee dance would map the point of the flag manifold SU(3)/U(1)× U(1) to a point of M⁴× S² or ∪_i H³(a=a_i)× ISO(2) (locally). The restriction to a 2-D subset of points could be due to the measurement of the distance of the food source represented by the point of H³_i (or M⁴).

See the article Some objections against TGD inspired view of qualia or the chapter General Theory of Qualia.

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

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