Friday, June 21, 2013

Hypnosis as remote mental interaction

In TGD framework one can argue that hypnosis represents an example about the fact that brain is not "private property": hypnotist uses the biological body and brain of the subject as instrument. Therefore remote mental interaction is in question. This idea generalizes: if one accepts self hierarchy, one can assign to any kind of higher level structure - family, organization, species, .... - a higher level self and magnetic body carrying dark matter, and these magnetic bodies can use lower level magnetic bodies as their instruments to realize their intentions. Biological bodies would be an important level in the hierarchy, which would continue down to cellular, molecular, and perhaps to even lower levels.

This view challenges the prevailing views about brain as a sole seat of consciousness and the assumption that conscious entities assigned with brains are completely isolated. Given magnetic body can use several biological bodies although one can assign to it the one providing the sensory input - at least during wake-up state. Note however that it is easy to produce illusion that some foreign object is part of biological body.

For more than decade ago I proposed a model for so called bicamerality based on the notion of semitrance. In semitrance the brain of subject becomes partially entangled with a higher level self - in this case the self of family or more general social group uses the biological body of member for its purposes. Higher level self gives its commands and advice interpreted by the bicameral as "God's voice". The consciousness of schizophrenic might be basically bicameral. Also hypnotic state and dream consciousness are candidates for bicameral consciousness.

Hypnosis as hijacking of brain?

In TGD framework hypnotist and subject would partially share the biological body of the subject, and hypnotist could realize motor actions using the biological body of the subject and also induce sensory experiences by sending suggestions generating virtual sensory input to the sense organs of the subject (this if one accepts TGD view about the role of sensory organs).

One could see hypnosis as a kind of hijacking of some parts of the subject's brain. Could one identify these parts? The general finding is that there is no universal neural or EEG signature of hypnotic state and possible changes in neural activity can be interpreted as neural correlates of imagination. Only in the case of persons highly susceptible to hypnotic induction one can identify a change of neural activity pattern identifiable as a correlete of hypnotic state.

"Hijacking" can be of course criticized for its negative tone. A more positive manner to express the idea is to say that the subject is voluntarily provides part of her brain to the use of the hypnotist's magnetic body. This conforms with the acronym "TEAM" symbolizing the subject's orientation to hypnosis in terms of "trust", "expectation", "attitude", and "motivation".

The neurophysiological findings conform with the view that the really interesting phenomena take at the level of magnetic bodies. The changes - when they occur - take place in prefrontal cortex (PFC) and anterior cingulate cortex (ACC): this together what is known about methods of hypnotic induction provides hints about what might occur in the hijacking process. The almost-prediction would be a correlation between EEGs of the hypnotist and subject person reflecting the sharing of parts of the subject's brain. It would be therefore highly interesting to study the correlations of the EEGs of subject and hypnotist.

Strongly focused attention to hypnotic suggestion is mentioned as a basic aspect of hypnosis and distinguishes it sharply from sleep. This feature brings in mind various altered states of consciousness reached in meditation and it has been suggested that meditation is one form of self-hypnosis. In TGD framework personal magnetic body has layered onyon-like structure with layers characterized by p-adic length and time scales and the value of hbareff. Thefore meditative state could be seen as a resharing of biological body and brain by these layers and even by foreign magnetic bodies.

Do social interactions share something with hypnosis?

More generally, one can also ask whether the phenomena of collaboration and synergy on one hand, and influence, "power" and fight for power on the other hand, could be modelled in terms of the partial ownership of the biological bodies by magnetic bodies identified as intentional agents.

Social structures and organizations are complex networks in which the arrows characterizing relationships between individuals in the simplest situations are uni-directional and static. The person at either end of the arrow is in command. In more complex situtations members are connected by several arrows of this kind, their directions can vary, and need not be static.

Should one therefore give up what physicist would call "single-particle" view and replace it with "many-particle" view by bringing in the notion of magnetic body attaching to several biological bodies and organizing them to loosely bound states of individuals? Under what conditions this kind of partial fusion of conscious entities can take place? Does it occur only only when there is complete trust in either direction or can fear about consequences be enough? It would not be surprising if immune systems against hijacking of the biological body would have evolved: this would allow to understand why the reality of remote mental interactions is so difficult to demonstrate. They could however take place on daily basis in social interactions if the proposed picture makes sense.

The dynamical sharing of biological bodies can be seen also positively: this sharing would make possible collaboration and synergy at much deeper level than we have been used to think. This kind of shared use of biological bodies perhaps defines the direction to which human kind should proceed. Also the possibility to directly experience what it is to be "the other one" - something not allowed by the standard view about consciousness confined inside individual brain - is implicated.

The new view about influence and power might allow to understand better the often highly irrational looking behaviors of organizations and their members - in particular blind obediance of orders and fight for power. The hierarchy of magnetic bodies could serve as a physical correlate for the hierarchy of biological and social structures. In particular, the fight for power could be seen as fight between magnetic bodies for the ownership of biological bodies or lower level magnetic bodies. The dark matter realized as a hierarchy of phases with non-standard value of effective Planck constant would represent a new physics necessary for understanding the physical correlates of these phenomena.

In the new chapter devoted to hypnosis as remote mental interaction I will introduce some basic notions, ideas and theories about hypnosis: the Wikipedia article gives a good overall view about the subject. The techniques of hypnotic induction provide valuable clues if one wants to imagine what hypnosis is. I will also describe the classical test for hypnotic susceptibility using Chevreul pendulum (to me it was quite a stunning experience to find that I am highly susceptible to hypnotic induction!), and propose an explanation in terms of hijacking of PFC and ACC by the magnetic body of hypnotist. The model makes an assumption about the logic of brain functions. Imagined motor action "Don't (really) do this" is realized as "Do this" followed by "Don't" stopping the imagined motor action proceeding otherwise from the magnetic body to PFC to motor regions of cortex via ACC to a real motor action.

In TGD framework sensory perception and motor action are related by time reversal and therefore an analogous mechanism applies to imagination realized as a genuine hallucination unless "Don't" is realized. Hypnotist should therefore hijack the brain regions realizing "Don't" by catching their attention so that they cannot perform their function. ACC is a good candidate for the region in which "Don't" is realized under normal circumstances. This logic makes possible to induce motor actions and sensory hallucinations analogous to dreams. Dreams would be realized in terms of virtual sensory input to sensory organs (REM) rather than only to higher levels in hierarchy of sensory representations at cortex, which do not carry visual qualia conscious-to-us.

For details see the new chapter Hypnosis as remote mental interaction of "TGD based view about living matter and remote mental interactions" or the article with the same title.

Thursday, June 20, 2013

Great Unconformity as a new piece of support for Expanding Earth model

I wrote for some years ago to "Genes and Memes" a chapter entitled Expanding Earth model and Precambrian evolution of continents, climate and life . Single hypothesis - a sudden phase transition increasing the radius of Earth by a factor 2 natural in the many-sheeted space-time of TGD - explains Cambrian explosion in biology (a sudden emergence of huge number of life forms after very slow Precambrian evolution, and also provides a model for Precambrian evolution of continents, climate and life.

Already Darwin realized that the absence of fossils from Precambrian era is a deep problem for his theory and assumed that this is an artefact due to the incomplete fossil record. Fossils of Precambrian origin have been indeed found after Darwin's time but they are simple and very rare, and the conclusion is that Cambrian explosion meaning huge diversification was real. Two mysteries therefore remain. Why the development of life was so slow during Precambrian era? Why the diversification was so incredibly fast during Cambrian explosion? Various explanations have been proposed. Did the oxygen content of the atmosphere reach a critical value and lead to the diversification? Or did predation pose the evolutionary pressure making the pace of evolution dramatically faster?

In New Scientist geologists Robert Gaines and Shanan Peters describe a geological finding perhaps related to the Cambrian Explosion: the mysterious "Great Unconformity", which is a juxtaposition of two different types of rock of very different geological ages along a prominent surface of erosion. This surface represents a very long span of "missing" time. More than 1 billion years of geological record is missing in many places! From the figure of the Wikipedia article about Great Unconformity visible in Grand Canyon the thickness of the missing layer can be estimated to be about 12.6 km. Somehow before the Cambrian the uppermost rocks of the continents were stripped away exposing the underlying crystalline basement rocks. The cause of this gap remains a complete mystery so that we have three mysteries! Plus the mysteries related to the evolution of climate (problems of Snowball Earth model).

The authors suggest that the formation of Great Unconformity relates to the Cambrian explosion. Large scale erosion and chemical weathering of the the exposed crystalline rock caused mineralization of the sea water. The hypothesis is that this led to bio-mineralization: animal groups possessing mineral skeletons - such as silica shells and calcium carbonate shells - emerged. This hypothesis looks rather plausible but does not solve the three great mysteries.

The authors indeed leave open the question about the origin of Great Unconformity and of Cambrian explosion. The TGD based explanation of Cambrian explosion comes from the model realizing the old idea about Expanding Earth in terms of TGD inspired new physics. Already Wegener observed that continents can be fit together nicely and this led to the recent view about plate tectonics. Wegener's model however fits only "half" of the continent boundaries together. One could however do much better: the observation is that the continents would fit nicely to cover the entire surface of Earth if the radius of Earth were 1/2 of its recent value! Expanding Earth model postulates that the radius of Earth grows slowly. Geologists have not taken Expanding Earth model seriously: one good reason is that there is no physics allowing it.

TGD predicts this physics.

  1. At given sheet of the many-sheeted space-time cosmic expansion is predicted to take place as sudden phase transitions in which the size of some space-time sheet suddenly increases. By p-adic length scale hypothesis the preferred scaling factors are powers of 2 and the most favored scaling factor is just two. The proposal is that during the Precambrian era life resided in underground seas being thus shielded from meteor bombardment and cosmic rays. This explains the scarcity of the fossil records and the simplicity of the fossils found. The sudden phase transition was a very violent process increasing the area of the Earth's surface by a factor of 4. The area of continents is 29.1 per cent from the recent area of the Earth's surface - not too far from the naively predicted fraction 1/4.

  2. It is easy to imagine that the uppermost rocks of the continent covering the entire Earth were stripped away and correspond nowadays to 100 km thick continental tectonic plates consisting of mainly silicon and aluminium). This expansion created split first the topmost layer as continental plates and regions between them giving rise to oceans. The magma which was uncovered by the process cooled down and solidifed and the continued expansion gave rise to ocean plates with different composition (mainly silicon and magnesium).

  3. The expansion phase corresponds to criticality so that fractality of the expansion is expected. At least for continental plates this process could have been fractal occurring in various length scales characterizing the thickness and the area of the sub-plates generated in the process. p-Adic length scale hypothesis suggests that the scales involved should appear as powers of 21/2 or 2. Generation of Great Unconformity as a process in which the underlying crystalline basement rocks were uncovered could correspond to a splitting of a layer of the continental plates to pieces. The length scale characterizing the thickness is 12.6 km from the above estimate and with 1 per cent accuracy by a factor 1/8 shorter than 100 km length scale for tectonic plates. This conforms with p-adic fractality. If the process of expansion involved a cascade of scalings by factor 2, one can wonder whether it proceeded from long to short length scales or vice versa. In other words: did continental and oceanic tectonic plates form first and after than the smaller structures such as the Great Unconformity or vice versa?

  4. Note that the p-adic length scale L(237) corresponding p∼ 2237 is 88 km - ten per cent smaller than 100 km. Maybe thermal expansion could account the discrepancy if the original thickness was L(237). There is a nice fractal analogy with cell membrane. The p-adic length scale L(239) defined by the Gaussian Mersenne Mk,G=(1+i)k-1 , k=239- the first one after the Gaussian Mersenne M167,G defining the size of cell nucleus - equals 2× L(237). Remarkably, also M241,G is Gaussian Mersenne. What it interesting that the scale L(127)=88 km would be in the same relation to L(239) associated with Mk=239,G as the thickness L(149) of the lipid layer of cell membrane to the cell membrane thickness L(151) characterized by Gaussian Mersenne M151,G. The two kind tectonic plates (continental and oceanic) would be analogous to the lipid layers of cell membrane. Note that 88 km is rather precisely the thickness of the atmosphere above which begins ionosphere. The thickness of Kennelly–Heaviside layer inside which radiowaves used in terrestrial radio communications propagate, has thickness about 150 km which roughly corresponds to L(239). Also the fact Continental litosphere has typical thickness of 200 km (L(239)) whereas oceanic litosphere is 100 km thick (L(237)) fits nicely with the proposed formation mechanism of continental tectonic plates.

  5. The rapid expansion process could have also brought in daylight the underground seas and the highly developed life in them so that Cambrian diversification would have been only apparent. Skeptic can of course ask whether it is necessary to assume that life resided in underground seas during Precambrian era. Could just the violent geological process be enough to induce extremely fast diversification? This might of course be true.

  6. There is one further argument in favor of the Expanding Earth model. The fact that the solar constant was during proto Earth period only 73 per cent from its recent value, is a problem for the models of the very early evolution of life. If the radius of Earth was 1/2 of its recent value the duration of day and night was from conservation of angular momentum only 1/4:th of the recent value and thus 3 hours. This could have made the environment much more favorable for the evolution of life even at the surface of the Earth since the range for the temperature variation would have been much narrower.

This model relates also to the Snowball Earth model of Precambrian climate in an interesting manner. The reader interested in details should read the chapter Expanding Earth model and Precambrian evolution of continents, climate and life of "Genes and Memes".

Saturday, June 08, 2013

Biophysics of activated water and the mechanism of water memory

Applied Biophysics of Activated Water by Vysotskii et al gives a nice summary about the experiments carried out by using what they call activated water. One can say that the experiments provide a strong support for the notion of water memory. In the following I present a short summary about the contents of the book with associations to TGD inspired view about water memory and homeopathy. What comes as a surprise is the extreme simplicity of the basic mechanism of water memory and also the profound implications of this mechanism for the evolution.

For background and details see the chapter Homeopathy in Many-Sheeted Space-time or the article "Applied biophysics of activated water" and the basic mechanism of water memory in TGD framework".

Friday, June 07, 2013

Consciousness as a phenomenon in the operational architectonics of brain organization: Criticality and self-organization considerations

I received an interesting article by brothers Fingelkurts (Andrew and Alexander) and Carlos Neves to be published in Chaos, Solitons \& Fractals (to appear here). The title of the article is Consciousness as a phenomenon in the operational architectonics of brain organization: Criticality and self-organization considerations.

Already on basis of the title it is clear that article is interesting also from the point of view of Topological Geometrodynamics (TGD) (for overview see Topological Geometrodynamics: an Overview, especially the part II), where quantum criticality replaces thermodynamical criticality as a basic characteristic of the Universe dictating uniquely the dynamics fixing the geometry of the "world of classical worlds" (WCW) consisting of 3- surfaces in certain 8-dimensional space-time. Quantum criticality is also central in TGD inspired theory of consciousness and the basic picture is roughly the same as in OA model. The chapter Comparison of TGD Inspired Theory of Consciousness with Some Other Theories of Consciousness might help to get an overview about TGD inspired theory of consciousness.

Quantum self-organization is second key element of TGD inspired theory of consciousness and corresponds to a cascade of quantum jumps proceeding from level of given causal diamond (CD) defined as intersection of future and past directed light-cones of 4-D Minkowski space to shorter scales (sub-CDs, their sub-CDs, etc..). Quantum jump corresponds to a state function reduction at either boundary of CD and have interpretation as sensory perception and motor action (time reversed sensory perception). CD is identified as geometric correlate for "spotlight of consciousness".

In this article and also in the chapter "Quantum Model of EEG" of "TGD and EEG" I summarize the basic concepts and ideas of the article and compare them with TGD approach to consciousness. There is also a section devoted to quantum criticality in TGD Universe. The approach is certainly TGD centred and I can only apologize this.

Tuesday, June 04, 2013

What is the basic mechanism of homeopathic healing?

After a work of more than decade after the realisation that homeopathy might be understood in TGD Universe, I still find that I have not given an absolutely convincing answer to the question "What is the exact mechanism of homeopathy?". The basic rules is that "like cures alike". Why should this be the case? Let us go our arguments through once again.

  1. Certainly the imprinting of water using molecules causing the illness - call these molecules just I for brevity - must be an essential part of the healing mechanism. The imprinting means imprinting of water with some frequencies in the low frequency spectrum of I. The TGD inspired idea is that the magnetic body of appropriate water cluster or even dark nucleon sequence representing DNA sequence, call this entity I*, is able to mimic I in the sense that its cyclotron frequency spectrum is same.

  2. This in turn strongly suggests that the molecules in the organism to be healed - call them P - have a long range interaction with molecules I induced by dark photons with cyclotron frequencies but having energies above thermal threshold. The interaction involves a formation of a magnetic flux tube accompanied by a parallel topological light ray/ "massless extremal" (ME) along which dark photons at specific resonance frequencies propagate and induce resonant interaction between P and I. Thus both the formation of flux tube bridge and the resonant interaction made possible by it, would be essential for the homeopathic healing to take place. In fact, in TGD inspired theory of consciousness, the formation of resonating flux tube connections makes possible the quantum coherence for the combined system I+P and serves as a correlate for attention between I and P.

  3. The presence of the entities I* able to mimic the cyclotron frequency spectrum of I and forming resonant flux tube bonds with molecules H is however not enough to explain the healing effect (I have already considered some answers but they do not convince me). To understand this, one must be able to understand how I causes the illness. The answer of the standard medicine is that the mechanism is chemical and thus requires contact interaction between I and P. It is easy to believe this. Standard medicine also tells that in order to prevent the chemical interaction between I and P , one must use some medicine molecules M, preventing this chemical interaction. It is easy to believe also this.

    In TGD Universe there is indeed a very natural mechanism preventing the chemical interaction between I and P. The reduction of the value of the effective Planck constant associated with the flux tubes connecting I and P leads to a contraction of the flux tube length (proportional to hbareff). This indeed makes possible a chemical contact interaction between both I and P causing the illness. In fact, I have proposed this mechanism as a completely general mechanism of catalyst action allowing biomolecules to find each other in the the dense bio-molecular soup. But this holds true also for I* and P! Using terms of "molecular psychology" , the entities I* mimicking I steal the attention of molecules P so that molecules I cannot cause the illness anymore!

This indeed looks extremely simple and natural and thus also convincing. What is important is that the proposed mechanism is not in conflict with standard medicine: it only makes possible the miracles of bio-chemistry and provides a completely new mechanism of healing. It is easy to imagine that a new kind of medicine using only water imprinted by the cyclotron frequency spectra of molecules responsible for the illness. This medicine would be completely free of the negative -basically chemical - side effects of the ordinary drugs. This mechanism would also use all the knowledge gained by ordinary biochemistry based medicine: if the relevant molecule I is known, it can be used to imprint water to get I*.

Also the effect of vaccines could rely on the "like cures alike" mechanism albeit in different form. Now the molecules or organisms - call them just B - causing the disease would be injected directly into the body rather than water. Water memory could give rise to a mimicry of B:s and give rise to primitive immunity. A more refined mechanism proposed earlier would involve dark DNA mimicking B:s and translating to ordinary DNA sequences coding for proteins able to catch B:s by the same flux tube mechanism.

The proposed mechanism of homeopathic healing leaves open the exact mechanism behind the cyclotron mimicry. The entities I* could be water clusters with magnetic bodies mimicking those of I, they could be water clusters which have stolen the magnetic bodies of I, or they could be even dark DNA accompanying water molecules and able to mimic I. Of course, the least science fictive option is that the possibly existing dark DNA couples only with ordinary DNA by the flux tube mechanism.

The interpretation of biophotons as decay products of dark photons in energy conserving phase transition hbareff→ hbar suggests that the dark photons involved with the communications have rather large value of hbareff given by hbareff=fh/fl. The simplest working hypothesis is that dark photons have same energy spectrum as biophotons. The prediction would be that biophoton spectrum from a homeopathic remedy - in particular its fluctuations - should correlate with the spectrum of the cyclotron frequencies. A weaker hypothesis is that the energies of dark photons are above thermal energy at physiological temperature.

For background see the chapter Homeopathy in Many-Sheeted Space-time of "Biosystems as Conscious Holograms".

Monday, June 03, 2013

More precise formulation of Negentropy Maximization Principle

Negentropy Maximization Principle (NMP) is assumed to be the variational principle telling what can happen in quantum jump and says that the information content of conscious experience for the entire system is maximized. In zero energy ontology (ZEO) the definition of NMP is far from trivial and the recent progress - as I believe - in the understanding of structure of quantum jump forces to check carefully the details related to NMP. A very intimate connection between quantum criticality, life as something in the intersection of realities and p-adicities, hierarchy of effective vales of Planck constant, negentropic entanglement, and p-adic view about cognition emerges. One ends up also with an argument why p-adic sector is necessary if one wants to speak about conscious information.

The anatomy of quantum jump in zero energy ontology (ZEO)

Zero energy ontology emerged around 2005 and has had profound consequences for the understanding of quantum TGD. The basic implication is that state function reductions occur at the opposite light-like boundaries of causal diamonds (CDs) forming a hierarchy, and produce zero energy states with opposite arrows of imbedding space time. Also concerning the identification of quantum jump as moment of consciousness ZEO encourages rather far reaching conclusions. In ZEO the only difference between motor action and sensory representations on one hand, and intention and cognitive representation on the other hand , is that the arrows of imbedding space time are opposite for them. Furthermore, sensory perception followed by motor action corresponds to a basic structure in the sequence of state function reductions and it seems that these processes occur fractally for CDs of various size scales.

  1. State function reduction can be performed to either boundary of CD but not both simultaneously. State function reduction at either boundary is equivalent to state preparation giving rise to a state with well defined quantum numbers (particle numbers, charges, four-momentum, etc...) at this boundary of CD. At the other boundary single particle quantum numbers are not well defined although total conserved quantum numbers at boundaries are opposite by the zero energy property for every pair of positive and negative energy states in the superposition. State pairs with different total energy, fermion number, etc.. for other boundary are possible: for instance, t coherent states of super-conductor for which fermion number is ill defined are possible in zero energy ontology and do not break the super-selection rules.

  2. The basic objects coding for physics are U-matrix, M-matrices and S-matrix. M-matrices correspond to a orthogonal rows of unitary U-matrix between zero energy states, and are expressible as products of a hermitian square root of density matrix and of unitary S-matrix which more or less corresponds to ordinary S-matrix. One can say that quantum theory is formally a square root of thermodynamics. The thermodynamics in question would however relate more naturally to NMP rather than second law, which at ensemble level and for ordinary entanglement can be seen as a consequence of NMP.

    The non-triviality of M-matrix requires that for given state reduced at say the "lower" boundary of CD there is entire distribution of statesat "upper boundary" (given initial state can lead to a continuum of final states). Even more, all size scales of CDs are possible since the position of only the "lower" boundary of CD is localized in quantum jump whereas the location of upper boundary of CD can vary so that one has distribution over CDs with different size scales and over their Lorentz boots and translates.

  3. The quantum arrow of time follows from the asymmetry between positive and negative energy parts of the state: the other is prepared and the other corresponds to the superposition of the final states resulting when interactions are turned on. What is remarkable that the arrow of time at imbedding space level at least changes direction when quantum jump occurs to opposite boundary.

    This brings strongly in mind the old proposal of Fantappie that in living matter the arrow of time is not fixed and that entropy and its diametric opposite syntropy apply to the two arrows of the imbedding space time. The arrow of subjective time assignable to second law would hold true but the increase of syntropy would be basically a reflection of second law since only the arrow of the geometric time at imbedding space level has changed sign. The arrow of geometric at space-time level which conscious observer experiences directly could be always the same if quantum classical correspondence holds true in the sense that the arrow of time for zero energy states corresponds to arrow of time for preferred extremals. The failure of strict non-determinism making possible phenomena analogous to multifurcations makes this possible.

  4. This picture differs radically from the standard view and if quantum jump represents a fundamental algorith, this
    variation of the arrow of geometric time from quantum jump to quantum jump should manifest itself in the functioning of brain and living organisms. The basic building brick in the functioning of brain is the formation of sensory representation followed by motor action. These processes look very much like temporal mirror images of each other such as the state function reductions to opposite boundaries of CD look like. The fundamental process could correspond to a sequences of these two kinds of state function reductions for opposite boundaries of CDs and maybe independently for CDs of different size scales in a "many-particle" state defined by a union of CDs.

How the formation of cognitive and sensory representations could relate to quantum jump?
  1. ZEO allows quantum jumps between different number fields so that p-adic cognitive representations can be formed and intentional actions realized. How these quantum jumps are realized at the level of generalized Feynman diagrams is non-trivial question: one possibility suggested by the notion of adele combining reals and various p-adic number fields to a larger structure is that the lines and vertices of generalized Feynman diagrams can correspond to different number fields.

    The formation of cognitive representation could correspond to a quantum jump in which real space-time sheet identified as a preferred extremal is mapped to its p-adic counterpart or superposition of them with the property that the discretized versions of all p-adic counterparts are identical. In the latter case the chart map of real preferred extremal would be quantal and correspond to delocalized state in WCW. The p-adic chart mappings are not expected to take place but with some probabilities determined by the number theoretically universal U-matrix.

  2. Similar consideration applies to intentional actions realized as real chart maps for p-adically realized intention. The natural interpretation of the process is as a time reversal of cognitive map. Cognitive map would be generated from real sensory represention and intentional action would transform time reversed cognitive map to real "motor" action identifiable as time reversal of sensory perception. This would occur in various length scales in fractal manner.

  3. The formation of superpositions of preferred extremals associated with discrete p-adic chart maps from real preferred extremals could be interpretated as an abstraction process. Similar abstraction could take place also in the mapping of p-adic space-time surface to a superposition of real preferred extrmals representing intentional action. U-matrix should give also the probability amplitudes for these processes, and the intuitive idea is that the larger then number of common rational and algebraic points of real and p-adic surfaces is, the higher the probability for this is: the first guess is that the amplitude is proportional the number of common points. On the other hand, large number of common points means high measurement resolution so that the number of different surfaces in superposition tends to be smaller.

  4. One should not make any un-necessary assumptions about the order of various kinds of quantum jumps. For the most general option real-to-padic and p-adic-to-real quantum jumps can follow any quantum jumps and state function reductions to opposite boundaries of CD can also occur any time in any length scale. Also the length scale of resolution scale assignable to the cognitive representation should be determined probabilistically. Quantal probabilities for quantum jumps should therefore apply to all aspect of quantum jump and now ad hoc assumptions should be made. Very probably internal consistency allows only very few alternative scenarios. The assumption that the cascade beginning from given CD continues downwards until stops due to the emergence of negentropic entanglement looks rather natural constraint.

What happens in single state function reduction?

State function reduction is a measurement of density matrix. The condition that a measurement of density matrix takes place implies standard measurement theory on both real and p-adic sectors: system ends to an eigen-space of density matrix. This is true in both real and p-adic sectors. NMP is stronger principle at the real side and implies state function reduction to 1-D subspace - its eigenstate.

The resulting N-dimensional space has however rational entanglement probabilities p=1/N so that one can say that it is the intersection of realities and p-adicities. If the number theoretic variant of entanglement entropy is used as a measure for the amount of entropy carried by entanglement rather than either entangled system, the state carries genuine information and is stable with respect to NMP if the p-adic prime p divides N. NMP allows only single p-adic prime for real → p-adic transition: the power of this prime appears is the largest power of prime appearing in the prime decomposition of N. Degeneracy means also criticality so that that ordinary quantum measurement theory for the density matrix favors criticality and NMP fixes the p-adic prime uniquely.

If one - contrary to the above conclusion - assumes that NMP holds true in the entire p-adic sector, NMP gives in p-adic sector rise to a reduction of the negentropy in state function reduction if the original situation is negentropic and the eigen-spaces of the density matrix are 1-dimensional. This situation is avoided if one assumes that state function reduction cascade in real or genuinely p-adic sector occurs first (without NMP) and gives therefore rise to N-dimensional eigen spaces. The state is negentropic and stable if the p-adic prime p divides N. Negentropy is generated.

The real state can be transformed to a p-adic one in quantum jump (defining cognitive map) if the entanglement coefficients are rational or belong to an algebraic extension of p-adic numbers in the case that algebraic extension of p-adic numbers is allowed (number theoretic evolution gradually generates them). The density matrix can be expressed as sum of projection operators multiplied by probabilities for the projection to the corresponding sub-spaces. After state function reduction cascade the probabilities are rational numbers of form p=1/N.

Number theoretic entanglement entropy also allows to avoid some objections related to fermionic and bosonic statistics. Fermionic and bosonic statistics require complete anti-symmetrization/symmetrization. This implies entanglement which cannot be reduced away. By looking for symmetrized or antisymmetrized 2-particle state consisting of spin 1/2 fermions as the simplest example one finds that the density matrix for either particle is the simply unit 2× 2 matrix. This is stable under NMP based on number theoretic negentropy. One expects that the same result holds true in the general case. The interpretation would be that particle symmetrization/antisymmetrization carries negentropy.

The degeneracy of the density matrix is of course not a generic phenomenon and one can argue that it corresponds to some very special kind of physics. The identification of space-time correlates for the hierarchy for the effective values hbareff=n×hbar of Planck constant as n-furcations of space-time sheet suggests strongly the identification of this physics in terms of this hierarchy. Hence quantum criticality, the essence of life as something in the rational intersection of realities and p-adicities, the hierarchy of effective values of hbar, negentropic quantum entanglement, and the possibility to make real-p-adic transitions and thus cognition and intentionality would be very intimately related. This is a highly satisfactory outcome, since these ideas have been rather loosely related hitherto.

What happens in quantum jump?

Suppose that everything can be reduced to what happens for a given CD characterized by a scale. There are at least two questions to be answered.

  1. There are two processes involved. State function reduction and quantum jump transforming real state to p-adic state (matter to cognition) and vice versa (intention to action). Do these transitions occur independently or not? Does the ordering of the processes matter? The proposed view about state function reduction strongly suggests that the p-adic ↔real transition (if possible at all) can occur any time without affecting the outcome of the state function reduction.

  2. State function reduction cascade in turn consists of two different kinds of state function reductions. The M-matrix characterizing the zero energy state is product of square root of density matrix and of unitary S-matrix and the first step means the measurement of the projection operator. It defines a density matrix for both upper and lower boundary of CD and these density matrices are essentially same.

    1. At the first step a measurement of the density matrix between positive and negative energy parts of the quantum state takes place for CD. One can regard both the lower and upper boundary as an eigenstate of density matrix in absence of negentropic entanglement. The measurement is thus completely symmetric with respect to the boundaries of CDs. At the real sector this leads to a 1-D eigen-space of density matrix if NMP holds true. In the intersection of real and p-adic sectors this need not be the case if the eigenvalues of the density matrix have degeneracy. Zero energy state becomes stable against further state function reductions! The interactions with the external world can of course destroy the stability sooner or later. An interesting question is whether so called higher states of consciousness relate to this kind of states.

    2. If the first step gave rise to 1-D eigen-space of the density matrix, a state function reduction cascade at either upper of lower boundary of CD proceeding from long to short scales. At given step divides the sub-system into two systems and the sub-system-complement pair which produces maximum negentropy gain is subject to quantum measurement maximizing negentropy gain. The process stops at given subsystem resulting in the process if the resulting eigen-space is 1-D or has negentropic entanglement (p-adic prime p divides the dimension N of eigenspace in the intersection of reality and p-adicity).

For details and background see the section "Updates since 2012" of chapter "Negentropy Maximization Principle"
of "TGD Inspired Theory of Consciousness".