tgd universe as a conscious hologramtgd inspired theory of consciousness entered the scheme after...

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TGD UNIVERSE AS

A CONSCIOUS HOLOGRAM

Matti Pitkänen

Köydenpunojankatu D 11, 10900, Hanko, Finland

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Preface

This book belongs to a series of online books summarizing the recent state Topological Geometro-dynamics (TGD) and its applications. TGD can be regarded as a unified theory of fundamentalinteractions but is not the kind of unified theory as so called GUTs constructed by graduate stu-dents at seventies and eighties using detailed recipes for how to reduce everything to group theory.Nowadays this activity has been completely computerized and it probably takes only a few hours toprint out the predictions of this kind of unified theory as an article in the desired format. TGD issomething different and I am not ashamed to confess that I have devoted the last 32 years of my lifeto this enterprise and am still unable to write The Rules.

I got the basic idea of Topological Geometrodynamics (TGD) during autumn 1978, perhaps itwas October. What I realized was that the representability of physical space-times as 4-dimensionalsurfaces of some higher-dimensional space-time obtained by replacing the points of Minkowski spacewith some very small compact internal space could resolve the conceptual difficulties of general rela-tivity related to the definition of the notion of energy. This belief was too optimistic and only withthe advent of what I call zero energy ontology the understanding of the notion of Poincare invariancehas become satisfactory.

It soon became clear that the approach leads to a generalization of the notion of space-time withparticles being represented by space-time surfaces with finite size so that TGD could be also seen asa generalization of the string model. Much later it became clear that this generalization is consistentwith conformal invariance only if space-time is 4-dimensional and the Minkowski space factor ofimbedding space is 4-dimensional.

It took some time to discover that also the geometrization of also gauge interactions and elementaryparticle quantum numbers could be possible in this framework: it took two years to find the uniqueinternal space providing this geometrization involving also the realization that family replicationphenomenon for fermions has a natural topological explanation in TGD framework and that thesymmetries of the standard model symmetries are much more profound than pragmatic TOE buildershave believed them to be. If TGD is correct, main stream particle physics chose the wrong track leadingto the recent deep crisis when people decided that quarks and leptons belong to same multiplet of thegauge group implying instability of proton.

There have been also longstanding problems.

• Gravitational energy is well-defined in cosmological models but is not conserved. Hence theconservation of the inertial energy does not seem to be consistent with the Equivalence Princi-ple. Furthermore, the imbeddings of Robertson-Walker cosmologies turned out to be vacuumextremals with respect to the inertial energy. About 25 years was needed to realize that the signof the inertial energy can be also negative and in cosmological scales the density of inertial energyvanishes: physically acceptable universes are creatable from vacuum. Eventually this led to thenotion of zero energy ontology which deviates dramatically from the standard ontology beinghowever consistent with the crossing symmetry of quantum field theories. In this framework thequantum numbers are assigned with zero energy states located at the boundaries of so calledcausal diamonds defined as intersections of future and past directed light-cones. The notion ofenergy-momentum becomes length scale dependent since one has a scale hierarchy for causaldiamonds. This allows to understand the non-conservation of energy as apparent. EquivalencePrinciple generalizes and has a formulation in terms of coset representations of Super-Virasoroalgebras providing also a justification for p-adic thermodynamics.

• From the beginning it was clear that the theory predicts the presence of long ranged classicalelectro-weak and color gauge fields and that these fields necessarily accompany classical electro-magnetic fields. It took about 26 years to gain the maturity to admit the obvious: these fieldsare classical correlates for long range color and weak interactions assignable to dark matter.The only possible conclusion is that TGD physics is a fractal consisting of an entire hierarchyof fractal copies of standard model physics. Also the understanding of electro-weak massivationand screening of weak charges has been a long standing problem, and 32 years was needed todiscover that what I call weak form of electric-magnetic duality gives a satisfactory solution ofthe problem and provides also surprisingly powerful insights to the mathematical structure ofquantum TGD.

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I started the serious attempts to construct quantum TGD after my thesis around 1982. Theoriginal optimistic hope was that path integral formalism or canonical quantization might be enoughto construct the quantum theory but the first discovery made already during first year of TGD was thatthese formalisms might be useless due to the extreme non-linearity and enormous vacuum degeneracyof the theory. This turned out to be the case.

• It took some years to discover that the only working approach is based on the generalizationof Einstein’s program. Quantum physics involves the geometrization of the infinite-dimensional”world of classical worlds” (WCW) identified as 3-dimensional surfaces. Still few years hadto pass before I understood that general coordinate invariance leads to a more or less uniquesolution of the problem and implies that space-time surfaces are analogous to Bohr orbits. Stilla coupled of years and I discovered that quantum states of the Universe can be identified asclassical spinor fields in WCW. Only quantum jump remains the genuinely quantal aspect ofquantum physics.

• During these years TGD led to a rather profound generalization of the space-time concept.Quite general properties of the theory led to the notion of many-sheeted space-time with sheetsrepresenting physical subsystems of various sizes. At the beginning of 90s I became dimlyaware of the importance of p-adic number fields and soon ended up with the idea that p-adicthermodynamics for a conformally invariant system allows to understand elementary particlemassivation with amazingly few input assumptions. The attempts to understand p-adicity frombasic principles led gradually to the vision about physics as a generalized number theory asan approach complementary to the physics as an infinite-dimensional spinor geometry of WCWapproach. One of its elements was a generalization of the number concept obtained by fusing realnumbers and various p-adic numbers along common rationals. The number theoretical trinityinvolves besides p-adic number fields also quaternions and octonions and the notion of infiniteprime.

• TGD inspired theory of consciousness entered the scheme after 1995 as I started to write a bookabout consciousness. Gradually it became difficult to say where physics ends and consciousnesstheory begins since consciousness theory could be seen as a generalization of quantum measure-ment theory by identifying quantum jump as a moment of consciousness and by replacing theobserver with the notion of self identified as a system which is conscious as long as it can avoidentanglement with environment. ”Everything is conscious and consciousness can be only lost”summarizes the basic philosophy neatly. The idea about p-adic physics as physics of cognitionand intentionality emerged also rather naturally and implies perhaps the most dramatic gener-alization of the space-time concept in which most points of p-adic space-time sheets are infinitein real sense and the projection to the real imbedding space consists of discrete set of points.One of the most fascinating outcomes was the observation that the entropy based on p-adicnorm can be negative. This observation led to the vision that life can be regarded as somethingin the intersection of real and p-adic worlds. Negentropic entanglement has interpretation asa correlate for various positively colored aspects of conscious experience and means also thepossibility of strongly correlated states stable under state function reduction and different fromthe conventional bound states and perhaps playing key role in the energy metabolism of livingmatter.

• One of the latest threads in the evolution of ideas is only slightly more than six years old.Learning about the paper of Laurent Nottale about the possibility to identify planetary orbitsas Bohr orbits with a gigantic value of gravitational Planck constant made once again possible tosee the obvious. Dynamical quantized Planck constant is strongly suggested by quantum classicalcorrespondence and the fact that space-time sheets identifiable as quantum coherence regions canhave arbitrarily large sizes. During summer 2010 several new insights about the mathematicalstructure and interpretation of TGD emerged. One of these insights was the realization thatthe postulated hierarchy of Planck constants might follow from the basic structure of quantumTGD. The point is that due to the extreme non-linearity of the classical action principle thecorrespondence between canonical momentum densities and time derivatives of the imbeddingspace coordinates is one-to-many and the natural description of the situation is in terms of localsingular covering spaces of the imbedding space. One could speak about effective value of Planck

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constant coming as a multiple of its minimal value. The implications of the hierarchy of Planckconstants are extremely far reaching so that the significance of the reduction of this hierarchy tothe basic mathematical structure distinguishing between TGD and competing theories cannotbe under-estimated.

From the point of view of particle physics the ultimate goal is of course a practical constructionrecipe for the S-matrix of the theory. I have myself regarded this dream as quite too ambitious takinginto account how far reaching re-structuring and generalization of the basic mathematical structureof quantum physics is required. It has indeed turned out that the dream about explicit formulais unrealistic before one has understood what happens in quantum jump. Symmetries and generalphysical principles have turned out to be the proper guide line here. To give some impressions aboutwhat is required some highlights are in order.

• With the emergence of zero energy ontology the notion of S-matrix was replaced with M-matrixwhich can be interpreted as a complex square root of density matrix representable as a diagonaland positive square root of density matrix and unitary S-matrix so that quantum theory in zeroenergy ontology can be said to define a square root of thermodynamics at least formally.

• A decisive step was the strengthening of the General Coordinate Invariance to the requirementthat the formulations of the theory in terms of light-like 3-surfaces identified as 3-surfaces atwhich the induced metric of space-time surfaces changes its signature and in terms of space-like3-surfaces are equivalent. This means effective 2-dimensionality in the sense that partonic 2-surfaces defined as intersections of these two kinds of surfaces plus 4-D tangent space data atpartonic 2-surfaces code for the physics. Quantum classical correspondence requires the codingof the quantum numbers characterizing quantum states assigned to the partonic 2-surfaces tothe geometry of space-time surface. This is achieved by adding to the modified Dirac action ameasurement interaction term assigned with light-like 3-surfaces.

• The replacement of strings with light-like 3-surfaces equivalent to space-like 3-surfaces meansenormous generalization of the super conformal symmetries of string models. A further general-ization of these symmetries to non-local Yangian symmetries generalizing the recently discoveredYangian symmetry of N = 4 supersymmetric Yang-Mills theories is highly suggestive. Here thereplacement of point like particles with partonic 2-surfaces means the replacement of conformalsymmetry of Minkowski space with infinite-dimensional super-conformal algebras. Yangian sym-metry provides also a further refinement to the notion of conserved quantum numbers allowingto define them for bound states using non-local energy conserved currents.

• A further attractive idea is that quantum TGD reduces to almost topological quantum fieldtheory. This is possible if the Kähler action for the preferred extremals defining WCW Kählerfunction reduces to a 3-D boundary term. This takes place if the conserved currents are so calledBeltrami fields with the defining property that the coordinates associated with flow lines extendto single global coordinate variable. This ansatz together with the weak form of electric-magneticduality reduces the Kähler action to Chern-Simons term with the condition that the 3-surfacesare extremals of Chern-Simons action subject to the constraint force defined by the weak formof electric magnetic duality. It is the latter constraint which prevents the trivialization of thetheory to a topological quantum field theory. Also the identification of the Kähler function ofWCW as Dirac determinant finds support as well as the description of the scattering amplitudesin terms of braids with interpretation in terms of finite measurement resolution coded to thebasic structure of the solutions of field equations.

• In standard QFT Feynman diagrams provide the description of scattering amplitudes. Thebeauty of Feynman diagrams is that they realize unitarity automatically via the so calledCutkosky rules. In contrast to Feynman’s original beliefs, Feynman diagrams and virtual parti-cles are taken only as a convenient mathematical tool in quantum field theories. QFT approachis however plagued by UV and IR divergences and one must keep mind open for the possibilitythat a genuine progress might mean opening of the black box of the virtual particle.

In TGD framework this generalization of Feynman diagrams indeed emerges unavoidably. Light-like 3-surfaces replace the lines of Feynman diagrams and vertices are replaced by 2-D partonic

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2-surfaces. Zero energy ontology and the interpretation of parton orbits as light-like ”wormholethroats” suggests that virtual particle do not differ from on mass shell particles only in thatthe four- and three- momenta of wormhole throats fail to be parallel. The two throats of thewormhole defining virtual particle would contact carry on mass shell quantum numbers butfor virtual particles the four-momenta need not be parallel and can also have opposite signs ofenergy. Modified Dirac equation suggests a number theoretical quantization of the masses of thevirtual particles. The kinematic constraints on the virtual momenta are extremely restrictiveand reduce the dimension of the sub-space of virtual momenta and if massless particles arenot allowed (IR cutoff provided by zero energy ontology naturally), the number of Feynmandiagrams contributing to a particular kind of scattering amplitude is finite and manifestly UVand IR finite and satisfies unitarity constraint in terms of Cutkosky rules. What is remarkablethat fermionic propagatos are massless propagators but for on mass shell four-momenta. Thisgives a connection with the twistor approach and inspires the generalization of the Yangiansymmetry to infinite-dimensional super-conformal algebras.

What I have said above is strongly biased view about the recent situation in quantum TGD andI have left all about applications to the introductions of the books whose purpose is to provide abird’s eye of view about TGD as it is now. This vision is single man’s view and doomed to containunrealistic elements as I know from experience. My dream is that young critical readers could takethis vision seriously enough to try to demonstrate that some of its basic premises are wrong or todevelop an alternative based on these or better premises. I must be however honest and tell that 32years of TGD is a really vast bundle of thoughts and quite a challenge for anyone who is not able tocheat himself by taking the attitude of a blind believer or a light-hearted debunker trusting on thepower of easy rhetoric tricks.

Matti Pitkänen

Hanko,September 15, 2010

Acknowledgements

Neither TGD nor these books would exist without the help and encouragement of many people.The friendship with Heikki and Raija Haila and their family have been kept me in contact with theeveryday world and without this friendship I would not have survived through these lonely 32 yearsmost of which I have remained unemployed as a scientific dissident. I am happy that my children haveunderstood my difficult position and like my friends have believed that what I am doing is somethingvaluable although I have not received any official recognition for it.

During last decade Tapio Tammi has helped me quite concretely by providing the necessary com-puter facilities and being one of the few persons in Finland with whom to discuss about my work. Ihave had also stimulating discussions with Samuli Penttinen who has also helped to get through theeconomical situations in which there seemed to be no hope. The continual updating of fifteen onlinebooks means quite a heavy bureaucracy at the level of bits and without a systemization one ends upwith endless copying and pasting and internal consistency is soon lost. Pekka Rapinoja has offered hishelp in this respect and I am especially grateful for him for my Python skills. Also Matti Vallinkoskihas helped me in computer related problems.

The collaboration with Lian Sidorov was extremely fruitful and she also helped me to surviveeconomically through the hardest years. The participation to CASYS conferences in Liege has beenan important window to the academic world and I am grateful for Daniel Dubois and Peter Marcerfor making this participation possible. The discussions and collaboration with Eduardo de Luna andIstvan Dienes stimulated the hope that the communication of new vision might not be a missionimpossible after all. Also blog discussions have been very useful. During these years I have receivedinnumerable email contacts from people around the world. In particualr, I am grateful for MarkMcWilliams and Ulla Matfolk for providing links to possibly interesting web sites and articles. Thesecontacts have helped me to avoid the depressive feeling of being some kind of Don Quixote of Scienceand helped me to widen my views: I am grateful for all these people.

In the situation in which the conventional scientific communication channels are strictly closedit is important to have some loop hole through which the information about the work done can at

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least in principle leak to the publicity through the iron wall of the academic censorship. Without anyexaggeration I can say that without the world wide web I would not have survived as a scientist noras individual. Homepage and blog are however not enough since only the formally published result isa result in recent day science. Publishing is however impossible without a direct support from powerholders- even in archives like arXiv.org.

Situation changed for five years ago as Andrew Adamatsky proposed the writing of a book aboutTGD when I had already got used to the thought that my work would not be published during my lifetime. The Prespacetime Journal and two other journals related to quantum biology and consciousness- all of them founded by Huping Hu - have provided this kind of loop holes. In particular, DainisZeps, Phil Gibbs, and Arkadiusz Jadczyk deserve my gratitude for their kind help in the preparationof an article series about TGD catalyzing a considerable progress in the understanding of quantumTGD. Also the viXra archive founded by Phil Gibbs and its predecessor Archive Freedom have been ofgreat help: Victor Christianto deserves special thanks for doing the hard work needed to run ArchiveFreedom. Also the Neuroquantology Journal founded by Sultan Tarlaci deserves a special mentionfor its publication policy. And last but not least: there are people who experience as a fascinatingintellectual challenge to spoil the practical working conditions of a person working with somethingwhich might be called unified theory: I am grateful for the people who have helped me to survivethrough the virus attacks, an activity which has taken roughly one month per year during the lasthalf decade and given a strong hue of grey to my hair.

For a person approaching his sixty year birthday it is somewhat easier to overcome the hard feelingsdue to the loss of academic human rights than for an inpatient youngster. Unfortunately the economicsituation has become increasingly difficult during the twenty years after the economic depression inFinland which in practice meant that Finland ceased to be a constitutional state in the strong senseof the word. It became possible to depose people like me from the society without fear about publicreactions and the classification as dropout became a convenient tool of ridicule to circumvent theethical issues. During last few years when the right wing has held the political power this trend hasbeen steadily strengthening. In this kind of situation the concrete help from individuals has been andwill be of utmost importance. Against this background it becomes obvious that this kind of work isnot possible without the support from outside and I apologize for not being able to mention all thepeople who have helped me during these years.

Matti Pitkänen

Hanko,September 15, 2010

Contents

1 Introduction 11.1 Basic Ideas of TGD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 TGD as a Poincare invariant theory of gravitation . . . . . . . . . . . . . . . . 21.1.3 TGD as a generalization of the hadronic string model . . . . . . . . . . . . . . 21.1.4 Fusion of the two approaches via a generalization of the space-time concept . . 2

1.2 The threads in the development of quantum TGD . . . . . . . . . . . . . . . . . . . . 31.2.1 Quantum TGD as spinor geometry of World of Classical Worlds . . . . . . . . 31.2.2 TGD as a generalized number theory . . . . . . . . . . . . . . . . . . . . . . . . 51.2.3 Hierarchy of Planck constants and dark matter hierarchy . . . . . . . . . . . . 81.2.4 TGD as a generalization of physics to a theory consciousness . . . . . . . . . . 10

1.3 Bird’s eye of view about the topics of the book . . . . . . . . . . . . . . . . . . . . . . 151.4 The contents of the book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.4.1 PART I: THE NOTION OF TIME IN TGD UNIVERSE . . . . . . . . . . . . 161.4.2 PART II: BIO-SYSTEMS AS CONSCIOUS HOLOGRAMS . . . . . . . . . . . 181.4.3 PART III: WATER MEMORY AND METABOLISM . . . . . . . . . . . . . . 22

I THE NOTION OF TIME IN TGD UNIVERSE 43

2 Time and Consciousness 452.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.1.1 The concepts of self and subjective memory . . . . . . . . . . . . . . . . . . . . 462.1.2 Psychological time and its arrow . . . . . . . . . . . . . . . . . . . . . . . . . . 462.1.3 Cosmology of consciousness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.1.4 Four-dimensional brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.1.5 Evidence for TGD based time concept . . . . . . . . . . . . . . . . . . . . . . . 48

2.2 TGD based concept of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.2.1 ’Holy trinity’ of time developments . . . . . . . . . . . . . . . . . . . . . . . . . 482.2.2 Quantum jump as moment of consciousness and the notion of self . . . . . . . 512.2.3 Some aspects of classical non-determinism . . . . . . . . . . . . . . . . . . . . . 522.2.4 Two times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.2.5 About the arrow of psychological time . . . . . . . . . . . . . . . . . . . . . . . 532.2.6 What really distinguishes between future and past? . . . . . . . . . . . . . . . 552.2.7 Memory and time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.2.8 Cosmology of consciousness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.2.9 Communications in four-dimensional society . . . . . . . . . . . . . . . . . . . . 59

2.3 Four-dimensional brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.3.1 The paradigm of four-dimensional brain . . . . . . . . . . . . . . . . . . . . . . 612.3.2 Geometric and subjective memories . . . . . . . . . . . . . . . . . . . . . . . . 612.3.3 Memories with respect to geometric time as simulations . . . . . . . . . . . . . 622.3.4 Are long term memories geometric or subjective memories? . . . . . . . . . . . 63

2.4 Time delays of consciousness and quantum jumps between histories . . . . . . . . . . . 652.4.1 Dissipation as evidence for consciousness . . . . . . . . . . . . . . . . . . . . . . 652.4.2 Experiments related to the active role of consciousness . . . . . . . . . . . . . . 65

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2.4.3 Experiments related to the passive role of consciousness . . . . . . . . . . . . . 662.4.4 The experiment of Radin and Bierman as evidence for quantum jump between

quantum histories concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692.5 Good and Evil, Life and Death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

2.5.1 Life and Death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722.5.2 Good and Evil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3 Time, Space-Time, and Consciousness 1033.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

3.1.1 Quantum-classical correspondence . . . . . . . . . . . . . . . . . . . . . . . . . 1033.1.2 Classical physics as exact part of quantum theory . . . . . . . . . . . . . . . . 1033.1.3 Some basic ideas of TGD inspired theory of consciousness and quantum biology 107

3.2 Many-sheeted space-time, magnetic flux quanta, electrets and MEs . . . . . . . . . . . 1083.2.1 Dynamical quantized Planck constant and dark matter hierarchy . . . . . . . . 1083.2.2 p-Adic length scale hypothesis and the connection between thermal de Broglie

wave length and size of the space-time sheet . . . . . . . . . . . . . . . . . . . . 1113.2.3 Topological light rays (massless extremals, MEs) . . . . . . . . . . . . . . . . . 1113.2.4 Magnetic flux quanta and electrets . . . . . . . . . . . . . . . . . . . . . . . . . 113

3.3 Some applications of the many-sheeted space-time concept . . . . . . . . . . . . . . . . 1153.3.1 A general model for energy storage and energy utilization by remote metabolism 1153.3.2 Capacitor model of sensory qualia . . . . . . . . . . . . . . . . . . . . . . . . . 1163.3.3 Support for the notion of remote metabolism . . . . . . . . . . . . . . . . . . . 119

3.4 Time and intentionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1203.4.1 The notions of psychological time and self in zero energy ontology . . . . . . . 1213.4.2 Psychological time and intentionality . . . . . . . . . . . . . . . . . . . . . . . . 1253.4.3 Why p-adic intentionality does not reduce to quantum randomness? . . . . . . 1283.4.4 Some paradoxes solved by the new view about time . . . . . . . . . . . . . . . 1303.4.5 Comparison with the approach of Barbour . . . . . . . . . . . . . . . . . . . . . 132

3.5 Consciousness and time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1333.5.1 Passive and active aspects of consciousness . . . . . . . . . . . . . . . . . . . . 1333.5.2 Sensory perception, motor action, and time . . . . . . . . . . . . . . . . . . . . 1343.5.3 Long term memories and time . . . . . . . . . . . . . . . . . . . . . . . . . . . 1383.5.4 Remote mental interactions and time . . . . . . . . . . . . . . . . . . . . . . . . 142

3.6 About the nature of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1473.6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1473.6.2 The most recent vision about zero energy ontology and p-adicization . . . . . . 1483.6.3 Zero energy ontology, self hierarchy, and the notion of time . . . . . . . . . . . 1523.6.4 What arrow of time means at the level of quantum states . . . . . . . . . . . . 157

II BIO-SYSTEMS AS CONSCIOUS HOLOGRAMS 195

4 Macro-Temporal Quantum Coherence and Spin Glass Degeneracy 1974.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

4.1.1 Macrotemporal quantum coherence is suggested by quantum classical correspon-dence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

4.1.2 Macrotemporal quantum coherence from spin glass degeneracy? . . . . . . . . . 1984.1.3 Dynamical Planck constant and dark matter hierarchy . . . . . . . . . . . . . . 1984.1.4 Implications of macrotemporal quantum coherence . . . . . . . . . . . . . . . . 199

4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1994.2.1 The notions of quantum jump and self . . . . . . . . . . . . . . . . . . . . . . . 1994.2.2 Many-sheeted space-time, topological field quantization, and spin glass degeneracy206

4.3 Macro-temporal quantum coherence from spin glass degeneracy . . . . . . . . . . . . . 2074.3.1 What does quantum coherence mean in TGD Universe? . . . . . . . . . . . . . 2074.3.2 Spin glass degeneracy and classical gravitation as stabilizer of irreducible bound

state entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2084.4 Macro-temporal quantum coherence and dynamical ~ . . . . . . . . . . . . . . . . . . . 210

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4.4.1 Quantization of planetary orbits with a gigantic value of Planck constant anddark matter as a macroscopic quantum phase . . . . . . . . . . . . . . . . . . . 211

4.4.2 Criterion for the occurrence of a phase transition changing Planck constant . . 2114.4.3 Large value of Planck constant implies macroscopic and macrotemporal quan-

tum coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2114.4.4 Are the two explanations for the macro-temporal quantum coherence consistent? 211

4.5 Basic implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2124.5.1 Thermodynamical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2124.5.2 Energetic aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2124.5.3 Information theoretic aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

4.6 Macro-temporal quantum coherence, consciousness, and biology . . . . . . . . . . . . . 2174.6.1 Macro-temporal quantum coherence and states of ”one-ness” . . . . . . . . . . 2174.6.2 Macro-temporal quantum coherence and biology . . . . . . . . . . . . . . . . . 2184.6.3 Macro-temporal quantum coherence and long term memory . . . . . . . . . . . 219

4.7 Co-operation and competition as different aspects of quantum consciousness . . . . . . 2204.7.1 Breaking of super-conductivity, metabolism and homeostasis . . . . . . . . . . 2204.7.2 Combining macro-temporal quantum coherence and dissipation . . . . . . . . . 2234.7.3 Healing by time reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2234.7.4 Earth’s magnetic field as a structure analogous to Searl’s machine . . . . . . . 226

5 Bio-Systems as Conscious Holograms 2535.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

5.1.1 The notion of conscious hologram . . . . . . . . . . . . . . . . . . . . . . . . . . 2535.1.2 Time mirror mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2545.1.3 Biophotons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2545.1.4 The work of William Tiller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

5.2 Conscious hologram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2555.2.1 What are the basic properties of conscious hologram? . . . . . . . . . . . . . . 2555.2.2 Stereo consciousness and the notion of conscious hologram . . . . . . . . . . . . 2565.2.3 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2565.2.4 Self-referentiality and space-time topology . . . . . . . . . . . . . . . . . . . . . 2595.2.5 Comparison of Maxwellian and TGD views about classical gauge fields . . . . . 263

5.3 Phase conjugation, negative energy topological light rays, and time mirror mechanism 2685.3.1 Do negative energy space-time sheets have counterparts in quantum field theory?2685.3.2 Is the TGD view about phase conjugate waves consistent with the existent

wisdom? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2695.4 Bio-photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

5.4.1 What bio-photons are? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2725.4.2 Some phenomena related to bio-photons . . . . . . . . . . . . . . . . . . . . . . 2735.4.3 General TGD based model for coherent bio-photons . . . . . . . . . . . . . . . 2745.4.4 The interpretation of biophotons and EEG as decay products of dark Josephson

radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2765.4.5 TGD based model for the delayed luminescence . . . . . . . . . . . . . . . . . . 2775.4.6 Kirlian effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

5.5 Bio-photons, radio waves, and genetic regulation . . . . . . . . . . . . . . . . . . . . . 2835.5.1 Frequency spectrum of radio waves . . . . . . . . . . . . . . . . . . . . . . . . . 2845.5.2 Basic questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2845.5.3 How to understand the spectrum? . . . . . . . . . . . . . . . . . . . . . . . . . 2845.5.4 Many-sheeted radio-wave laser excited by ordinary laser light . . . . . . . . . . 2865.5.5 Is the radio wave band structure for wheat seed a scaled-up version of the band

structure of EEG? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2875.6 Conscious hologram and remote mental interactions . . . . . . . . . . . . . . . . . . . 288

5.6.1 Big vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2885.6.2 Sketch for what could happen in a typical remote viewing experiment . . . . . 2895.6.3 Why it is so difficult to take remote mental interactions seriously? . . . . . . . 2905.6.4 About the physiological correlates of anomalous cognition . . . . . . . . . . . . 2925.6.5 Local sidereal time, geomagnetic fluctuations, and remote mental interactions . 293

xii CONTENTS

5.6.6 DelaWarr camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2965.7 The experimental work of William Tiller about intentional imprinting of electronic devices297

5.7.1 Experimental arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2975.7.2 Basic experimental findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2975.7.3 Explanation of the pH oscillations in terms of the general model of intentional

action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2985.7.4 The effects caused by the quartz crystal . . . . . . . . . . . . . . . . . . . . . . 3025.7.5 Relating Tiller’s hypothesis to TGD framework . . . . . . . . . . . . . . . . . . 3035.7.6 A model for the findings based on hierarchy of large Planck constants . . . . . 304

5.8 Formation of holograms by time mirror mechanism as a key mechanism of intentionalaction? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3055.8.1 Four-wave interaction as a mechanism of intentional action . . . . . . . . . . . 3055.8.2 Plasma oscillation patterns as generalized holograms . . . . . . . . . . . . . . . 3065.8.3 Nerve pulse generation and holograms . . . . . . . . . . . . . . . . . . . . . . . 3095.8.4 Generalized four-wave interaction in relation to some other anomalies . . . . . 311

5.9 Formation of holograms by time mirror mechanism as a key mechanism of intentionalaction? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3135.9.1 Four-wave interaction as a mechanism of intentional action . . . . . . . . . . . 3135.9.2 Plasma oscillation patterns as generalized holograms . . . . . . . . . . . . . . . 3145.9.3 Nerve pulse generation and holograms . . . . . . . . . . . . . . . . . . . . . . . 3175.9.4 Generalized four-wave interaction in relation to some other anomalies . . . . . 319

5.10 How to test the basic vision? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3205.10.1 Leakage of supra currents as basic mechanism . . . . . . . . . . . . . . . . . . . 3205.10.2 Time reversal for the leakage of supra currents . . . . . . . . . . . . . . . . . . 3215.10.3 Controlling metabolism by IR laser beams and DNA functioning by maser beams?3215.10.4 How to choose senders and receivers? . . . . . . . . . . . . . . . . . . . . . . . 3225.10.5 How to test the notion of conscious hologram? . . . . . . . . . . . . . . . . . . 322

6 General Theory of Qualia 3516.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

6.1.1 TGD in nutshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3516.1.2 TGD inspired theory of consciousness very briefly . . . . . . . . . . . . . . . . 3526.1.3 Biological realization of self hierarchy . . . . . . . . . . . . . . . . . . . . . . . 3546.1.4 Qualia and thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3586.1.5 Spectroscopy of consciousness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

6.2 General vision about the quantum correlates of qualia . . . . . . . . . . . . . . . . . . 3616.2.1 What qualia are? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3636.2.2 Classification of qualia in thermodynamical framework . . . . . . . . . . . . . . 3676.2.3 Critical questions and open problems . . . . . . . . . . . . . . . . . . . . . . . . 371

6.3 About the identification of the non-geometric qualia . . . . . . . . . . . . . . . . . . . 3746.3.1 Color vision and super-symplectic algebra . . . . . . . . . . . . . . . . . . . . . 3756.3.2 Chemical qualia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3786.3.3 Magnetic qualia as generalized chemical qualia . . . . . . . . . . . . . . . . . . 3806.3.4 Kinesthetic qualia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3816.3.5 Tactile qualia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3836.3.6 Emotions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3846.3.7 Dark matter hierarchy and emotions . . . . . . . . . . . . . . . . . . . . . . . . 3906.3.8 Dark matter hierarchy, hierarchical structure of nervous system, and hierarchy

of emotions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3916.4 A general model for sensory receptor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

6.4.1 Capacitor model for sensory receptor . . . . . . . . . . . . . . . . . . . . . . . . 3956.4.2 Capacitor model for color vision . . . . . . . . . . . . . . . . . . . . . . . . . . 3966.4.3 The structure of the retina and sensory organs as sites of sensory qualia . . . . 3986.4.4 Some examples about deficits of color vision as a test of the model for cognitive

representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4076.4.5 Odor perception and quantum coherence . . . . . . . . . . . . . . . . . . . . . . 408

6.5 Flag-manifold qualia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

CONTENTS xiii

6.5.1 Basic structure of the configuration space . . . . . . . . . . . . . . . . . . . . . 4146.5.2 Quantum honeybee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4146.5.3 Quantum honeybee and DNA as topological quantum computer . . . . . . . . 420

6.6 TGD based model for cell membrane as sensory receptor . . . . . . . . . . . . . . . . . 4236.6.1 Could cell correspond to almost vacuum extremal? . . . . . . . . . . . . . . . . 4246.6.2 General model for qualia and sensory receptor . . . . . . . . . . . . . . . . . . 4306.6.3 Some implications of the model of cell membrane as sensory receptor . . . . . . 4316.6.4 A general model of qualia and sensory receptor . . . . . . . . . . . . . . . . . . 4316.6.5 Detailed model for the qualia . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4336.6.6 Overall view about qualia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4366.6.7 About detailed identification of the qualia . . . . . . . . . . . . . . . . . . . . . 437

6.7 Constraints on the fermionic realization of genetic code from the model for color qualia 4376.7.1 Fermionic representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4386.7.2 Various options for the fermionic representation of A,T,C,G . . . . . . . . . . . 4386.7.3 Realization of color qualia for quark option . . . . . . . . . . . . . . . . . . . . 439

6.8 The roles of Josephson radiation, cyclotron radiation, and of magnetic body . . . . . . 4406.8.1 The role of Josephson currents . . . . . . . . . . . . . . . . . . . . . . . . . . . 4416.8.2 What is the role of the magnetic body? . . . . . . . . . . . . . . . . . . . . . . 442

III WATER MEMORY AND METABOLISM 473

7 Homeopathy in Many-Sheeted Space-time 4757.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

7.1.1 Frequency imprinting and entrainment . . . . . . . . . . . . . . . . . . . . . . . 4757.1.2 Scaling laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4767.1.3 A model for homeopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4767.1.4 Some applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

7.2 General view about homeostasis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4787.2.1 Super-conducting part of the ionic flow circuitry . . . . . . . . . . . . . . . . . 4787.2.2 How water represents? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4807.2.3 The role of micro-waves in homeostasis . . . . . . . . . . . . . . . . . . . . . . 4817.2.4 How the vision about dark matter hierarchy affects the picture? . . . . . . . . 482

7.3 Scaling law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4847.3.1 Various forms of scaling law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4847.3.2 Scaling law for the qualia about brain structure of given size scale . . . . . . . 4867.3.3 Scaling law and evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4907.3.4 Scaling law and sensory maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4957.3.5 Does the structure of neocortex correlate with the hierarchy of p-adic frequencies?496

7.4 TGD based model for homeopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4977.4.1 Basic claims about homeopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . 4977.4.2 Frequency signatures for the homeopathic remedies and endogenous frequencies

in acupuncture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4977.4.3 What could be the mechanism behind the homeopathic healing . . . . . . . . . 4987.4.4 TGD counterparts for the propagation and diffusion of coherence . . . . . . . . 4997.4.5 Frequency imprinting and de-imprinting . . . . . . . . . . . . . . . . . . . . . . 4997.4.6 A possible realization of water memory . . . . . . . . . . . . . . . . . . . . . . 5037.4.7 Could virtual DNAs allow a controlled development of the genome? . . . . . . 5057.4.8 Latest view about water memory . . . . . . . . . . . . . . . . . . . . . . . . . . 514

7.5 Further experimental findings related to water memory . . . . . . . . . . . . . . . . . . 5187.5.1 Genes and water memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5187.5.2 Water electric as protocell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5227.5.3 A model for chiral selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5257.5.4 Burning water and photosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . 527

7.6 DNA waves and water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5317.6.1 The basic findings of Montagnier’s group . . . . . . . . . . . . . . . . . . . . . 5327.6.2 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

xiv CONTENTS

7.6.3 TGD inspired answers to the questions . . . . . . . . . . . . . . . . . . . . . . . 533

7.7 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

7.8 The findings that one should understand . . . . . . . . . . . . . . . . . . . . . . . . . . 539

7.9 The model of remote replication consistent with DNA as topological quantum computermodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

7.9.1 Identification of phantom DNA . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

7.9.2 Dark DNA and frequency coding by quantum antenna mechanism . . . . . . . 541

7.9.3 Common explanation for the findings of Montagnier and Gariaev . . . . . . . . 542

7.9.4 Summing up the basic assumptions of the mechanism . . . . . . . . . . . . . . 543

7.10 Possible implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

7.10.1 Possible relevance for homeopathy and immune system . . . . . . . . . . . . . . 544

7.10.2 Frequency coding for DNA sequences by the value of Planck constant as a real-ization of divisor code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

7.11 Field codes associated with homeopathy and a model for the magnetic body . . . . . . 558

7.11.1 Plasmoids as primitive life forms associated with magnetic bodies . . . . . . . . 558

7.11.2 Field representations of information using codes . . . . . . . . . . . . . . . . . 560

7.11.3 Priore’s machine as a test bench for the model . . . . . . . . . . . . . . . . . . 563

7.11.4 Fields and genes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566

7.11.5 Magnetic mirrors, remote viewing and remote healing . . . . . . . . . . . . . . 570

7.12 The role of dark micro waves in living matter . . . . . . . . . . . . . . . . . . . . . . . 575

7.12.1 Dark microwaves and metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . 575

7.12.2 Poorly understood effects related to micro-waves . . . . . . . . . . . . . . . . . 577

7.12.3 X-ray images and remote realization of intentionality . . . . . . . . . . . . . . . 578

8 Macroscopic Quantum Coherence and Quantum Metabolism as Different Sides ofthe Same Coin: Part I 613

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613

8.1.1 Dark matter hierarchy, sensory representations, motor action, and metabolism 613

8.1.2 New ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

8.1.3 Many-sheeted photosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616

8.2 General view about sensory representations, motor control, and metabolism . . . . . . 617

8.2.1 General vision about living matter as a macroscopic quantum system . . . . . 617

8.2.2 A general view about quantum control, coordination and communication in-spired by dark matter hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . 618

8.2.3 Some mechanisms liberating metabolic energy and connection with free energyphenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622

8.2.4 The challenges posed by the new ideas . . . . . . . . . . . . . . . . . . . . . . . 626

8.3 General vision about metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

8.3.1 About metabolism in general . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

8.3.2 Cellular respiration and photosynthesis . . . . . . . . . . . . . . . . . . . . . . 635

8.4 TGD inspired view about metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . 639

8.4.1 Negentropic entanglement and covalent bond . . . . . . . . . . . . . . . . . . . 639

8.4.2 Questions about metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644

8.4.3 Hydrolysis of ATP in TGD universe . . . . . . . . . . . . . . . . . . . . . . . . 648

8.4.4 Could high energy phosphate bond be negentropic bond with negative bindingenergy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

8.5 Many-sheeted model for photosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . 655

8.5.1 A rough overall view about photosynthesis . . . . . . . . . . . . . . . . . . . . 655

8.5.2 A general model for energy storage and energy utilization by remote metabolism 656

8.5.3 The general model for photosynthesis . . . . . . . . . . . . . . . . . . . . . . . 656

8.5.4 Applying the general model of energy storage and utilization to ionic pumps . 658

8.5.5 Quantum coherence and photosynthesis . . . . . . . . . . . . . . . . . . . . . . 659

CONTENTS xv

9 Macroscopic Quantum Coherence and Quantum Metabolism as Different Sides ofthe Same Coin: Part II 6919.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691

9.1.1 Quantum view about energy economy in brain . . . . . . . . . . . . . . . . . . 6919.1.2 Molecular machines in many-sheeted space-time . . . . . . . . . . . . . . . . . 6929.1.3 Could super-luminality be understood in terms of remote metabolism? . . . . . 693

9.2 A model for brain metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6949.2.1 Metabolism in brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6959.2.2 Astrocytes and quantum control of brain . . . . . . . . . . . . . . . . . . . . . 6989.2.3 The effects of endogenous sound waves as a support for the scenario . . . . . . 702

9.3 Molecular machines in many-sheeted space-time . . . . . . . . . . . . . . . . . . . . . . 7049.3.1 TGD inspired questions and ideas relating to coherent locomotion . . . . . . . 7059.3.2 Some facts about molecular and cellular motors . . . . . . . . . . . . . . . . . . 7089.3.3 Molecular motors in single-sheeted space-time . . . . . . . . . . . . . . . . . . . 7099.3.4 Molecular machines in TGD framework . . . . . . . . . . . . . . . . . . . . . . 713

9.4 Explanation of super-luminal velocities in terms of remote metabolism . . . . . . . . . 7199.4.1 General explanations for effective super-luminal velocities . . . . . . . . . . . . 7209.4.2 Experiments involving super-luminal velocities . . . . . . . . . . . . . . . . . . 7219.4.3 Experiments believed to involve anomalous interference . . . . . . . . . . . . . 7239.4.4 The experiments involving crossed photon beams . . . . . . . . . . . . . . . . . 724

9.5 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7289.5.1 Older ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7289.5.2 Generalized-four wave mechanism as a basic mechanism of remote metabolism 732

1 Appendix 763A-1 Basic properties of CP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763

A-1.1 CP2 as a manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763A-1.2 Metric and Kähler structure of CP2 . . . . . . . . . . . . . . . . . . . . . . . . 763A-1.3 Spinors in CP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766A-1.4 Geodesic sub-manifolds of CP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 766

A-2 CP2 geometry and standard model symmetries . . . . . . . . . . . . . . . . . . . . . . 767A-2.1 Identification of the electro-weak couplings . . . . . . . . . . . . . . . . . . . . 767A-2.2 Discrete symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 770

A-3 Basic facts about induced gauge fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 771A-3.1 Induced gauge fields for space-times for which CP2 projection is a geodesic sphere771A-3.2 Space-time surfaces with vanishing em, Z0, or Kähler fields . . . . . . . . . . . 771

List of Figures

3.1 Time mirror mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1923.2 a) The structure of bi-filar coils and the mechanical analog of RCL circuit as a harmonic

oscillator. b) The reduction of the mass of the harmonic oscillator at the second halfof the magnetic pulse implies acceleration and generation of negative energy photonsin order to get energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

3.3 A mechanism of energy production based on negative energy topological light rays andpopulation inversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

3.4 Constant voltage pulse (a) and the corresponding electric (b) and magnetic (c) pulsesin the bi-filar coil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

3.5 Rational valued points x and y = x+ pn, which are close to each other p-adically, arefar from each other in real sense. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

3.6 The non-determinism of p-adic differential equations in the case of a free particle. a)In real case the initial position x0 and and velocity v determine the orbit. b) In thep-adic case x0 and v are piecewise constant functions of time and the orbit resemblesthat associated with Brown motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

3.7 Rational numbers are common to both reals R and all p-adic number fields Rp, p =2, 3, ... These number fields can be ”glued” together along the rational numbers to forma book like structure. Rational numbers correspond to the rim of the book and differentnumber fields to its pages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

6.1 The mechanism giving rise to the arrow of psychological time. What happens is thatmind like space-time sheet gradually drifts in direction of geometric future. Note thatmind like space-time sheet has finite time duration. . . . . . . . . . . . . . . . . . . . . 354

7.1 Illustration of a possible vision about dark nucleus as a nuclear string consisting ofrotating baryonic strings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

9.1 Schematic representation of the experimental arrangement of Cardone and collaborators.7239.2 Schematic representation of the experimental arrangement of Ranfagni and collabora-

tors discussed in [D16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

xvii

Chapter 1

Introduction

1.1 Basic Ideas of TGD

The basic physical picture behind TGD was formed as a fusion of two rather disparate approaches:namely TGD is as a Poincare invariant theory of gravitation and TGD as a generalization of theold-fashioned string model.

1.1.1 Background

T(opological) G(eometro)D(ynamics) is one of the many attempts to find a unified description of basicinteractions. The development of the basic ideas of TGD to a relatively stable form took time of abouthalf decade [K2]. The great challenge is to construct a mathematical theory around these physicallyvery attractive ideas and I have devoted the last twenty-three years for the realization of this dreamand this has resulted in seven online books about TGD and eight online books about TGD inspiredtheory of consciousness and of quantum biology.

Quantum T(opological) G(eometro)D(ynamics) as a classical spinor geometry for infinite-dimensionalconfiguration space, p-adic numbers and quantum TGD, and TGD inspired theory of consciousnessand of quantum biology have been for last decade of the second millenium the basic three stronglyinteracting threads in the tapestry of quantum TGD.

For few years ago the discussions with Tony Smith initiated a fourth thread which deserves thename ’TGD as a generalized number theory’. The basic observation was that classical number fieldsmight allow a deeper formulation of quantum TGD. The work with Riemann hypothesis made timeripe for realization that the notion of infinite primes could provide, not only a reformulation, but adeep generalization of quantum TGD. This led to a thorough and extremely fruitful revision of thebasic views about what the final form and physical content of quantum TGD might be. Together withthe vision about the fusion of p-adic and real physics to a larger coherent structure these sub-threadsfused to the ”physics as generalized number theory” th

A further thread emerged from the realization that by quantum classical correspondence TGDpredicts an infinite hierarchy of macroscopic quantum systems with increasing sizes, that it is not atall clear whether standard quantum mechanics can accommodate this hierarchy, and that a dynam-ical quantized Planck constant might be necessary and certainly possible in TGD framework. Theidentification of hierarchy of Planck constants whose values TGD ”predicts” in terms of dark matterhierarchy would be natural. This also led to a solution of a long standing puzzle: what is the properinterpretation of the predicted fractal hierarchy of long ranged classical electro-weak and color gaugefields. Quantum classical correspondences allows only single answer: there is infinite hierarchy of p-adically scaled up variants of standard model physics and for each of them also dark hierarchy. ThusTGD Universe would be fractal in very abstract and deep sense.

Every updating of the books makes me frustrated as I see how badly the structure of the repre-sentation reflects my bird’s eye of view as it is at the moment of updating. At this time I realizedthat the chronology based identification of the threads is quite natural but not logical and it is muchmore logical to see p-adic physics, the ideas related to classical number fields, and infinite primesas sub-threads of a thread which might be called ”physics as a generalized number theory”. In the

1

2 Chapter 1. Introduction

following I adopt this view. This reduces the number of threads to four! I am not even sure aboutthe number of threads! Be patient!

TGD forces the generalization of physics to a quantum theory of consciousness, and representTGD as a generalized number theory vision leads naturally to the emergence of p-adic physics asphysics of cognitive representations. The seven online books [K91, K68, K54, K50, K69, K79, K77]about TGD and eight online books about TGD inspired theory of consciousness and of quantumbiology [K84, K12, K61, K10, K35, K42, K45, K76] are warmly recommended to the interested reader.

1.1.2 TGD as a Poincare invariant theory of gravitation

The first approach was born as an attempt to construct a Poincare invariant theory of gravitation.Space-time, rather than being an abstract manifold endowed with a pseudo-Riemannian structure, isregarded as a surface in the 8-dimensional space H = M4×CP2, where M

4 denotes Minkowski space andCP2 = SU(3)/U(2) is the complex projective space of two complex dimensions [A15, A4, A10, A3].

The identification of the space-time as a submanifold [A2, A14] of M4 × CP2 leads to an ex-act Poincare invariance and solves the conceptual difficulties related to the definition of the energy-momentum in General Relativity.

It soon however turned out that submanifold geometry, being considerably richer in structurethan the abstract manifold geometry, leads to a geometrization of all basic interactions. First, thegeometrization of the elementary particle quantum numbers is achieved. The geometry of CP2 explainselectro-weak and color quantum numbers. The different H-chiralities of H-spinors correspond to theconserved baryon and lepton numbers. Secondly, the geometrization of the field concept results. Theprojections of the CP2 spinor connection, Killing vector fields of CP2 and of H-metric to four-surfacedefine classical electro-weak, color gauge fields and metric in X4.

1.1.3 TGD as a generalization of the hadronic string model

The second approach was based on the generalization of the mesonic string model describing mesonsas strings with quarks attached to the ends of the string. In the 3-dimensional generalization 3-surfaces correspond to free particles and the boundaries of the 3- surface correspond to partons inthe sense that the quantum numbers of the elementary particles reside on the boundaries. Variousboundary topologies (number of handles) correspond to various fermion families so that one obtainsan explanation for the known elementary particle quantum numbers. This approach leads also to anatural topological description of the particle reactions as topology changes: for instance, two-particledecay corresponds to a decay of a 3-surface to two disjoint 3-surfaces.

This decay vertex does not however correspond to a direct generalization of trouser vertex ofstring models. Indeed, the important difference between TGD and string models is that the analogsof string world sheet diagrams do not describe particle decays but the propagation of particles viadifferent routes. Particle reactions are described by generalized Feynman diagrams for which 3-Dlight-like surface describing particle propagating join along their ends at vertices. As 4-manifolds thespace-time surfaces are therefore singular like Feynman diagrams as 1-manifolds.

1.1.4 Fusion of the two approaches via a generalization of the space-timeconcept

The problem is that the two approaches to TGD seem to be mutually exclusive since the orbit of aparticle like 3-surface defines 4-dimensional surface, which differs drastically from the topologicallytrivial macroscopic space-time of General Relativity. The unification of these approaches forces aconsiderable generalization of the conventional space-time concept. First, the topologically trivial 3-space of General Relativity is replaced with a ”topological condensate” containing matter as particlelike 3-surfaces ”glued” to the topologically trivial background 3-space by connected sum operation.Secondly, the assumption about connectedness of the 3-space is given up. Besides the ”topologicalcondensate” there could be ”vapor phase” that is a ”gas” of particle like 3-surfaces (counterpart ofthe ”baby universies” of GRT) and the nonconservation of energy in GRT corresponds to the transferof energy between the topological condensate and vapor phase.

What one obtains is what I have christened as many-sheeted space-time. One particular aspectis topological field quantization meaning that various classical fields assignable to a physical system

1.2. The threads in the development of quantum TGD 3

correspond to space-time sheets representing the classical fields to that particular system. One canspeak of the field body of a particular physical system. Field body consists of topological light rays,and electric and magnetic flux quanta. In Maxwell’s theory system does not possess this kind offield identity. The notion of magnetic body is one of the key players in TGD inspired theory ofconsciousness and quantum biology.

This picture became more detailed with the advent of zero energy ontology (ZEO). The basic notionof ZEO is causal diamond (CD) identified as the Cartesian product of CP2 and of the intersectionof future and past directed light-cones and having scale coming as an integer multiple of CP2 size isfundamental. CDs form a fractal hierarchy and zero energy states decompose to products of positiveand negative energy parts assignable to the opposite boundaries of CD defining the ends of the space-time surface. The counterpart of zero energy state in positive energy ontology is in terms of initialand final states of a physical event, say particle reaction.

General Coordinate Invariance allows to identify the basic dynamical objects as space-like 3-surfaces at the ends of space-time surface at boundaries of CD: this means that space-time sur-face is analogous to Bohr orbit. An alternative identification is as light-like 3-surfaces at which thesignature of the induced metric changes from Minkowskian to Euclidian and interpreted as lines ofgeneralized Feynman diagrams. Also the Euclidian 4-D regions would have similar interpretation. Therequirement that the two interpretations are equivalent, leads to a strong form of General CoordinateInvariance. The outcome is effective 2-dimensionality stating that the partonic 2-surfaces identifiedas intersections of the space-like ends of space-time surface and light-like wormhole throats are thefundamental objects. That only effective 2-dimensionality is in question is due to the effects caused bythe failure of strict determinism of Kähler action. In finite length scale resolution these effects can beneglected below UV cutoff and above IR cutoff. One can also speak about strong form of holography.

There is a further generalization of the space-time concept inspired by p-adic physics forcing ageneralization of the number concept through the fusion of real numbers and various p-adic numberfields. Also the hierarchy of Planck constants forces a generalization of the notion of space-time.

A very concise manner to express how TGD differs from Special and General Relativities couldbe following. Relativity Principle (Poincare Invariance), General Coordinate Invariance, and Equiva-lence Principle remain true. What is new is the notion of sub-manifold geometry: this allows to realizePoincare Invariance and geometrize gravitation simultaneously. This notion also allows a geometriza-tion of known fundamental interactions and is an essential element of all applications of TGD rangingfrom Planck length to cosmological scales. Sub-manifold geometry is also crucial in the applicationsof TGD to biology and consciousness theory.

The worst objection against TGD is the observation that all classical gauge fields are expressible interms of four imbedding space coordinates only- essentially CP2 coordinates. The linear superpositionof classical gauge fields taking place independently for all gauge fields is lost. This would be acatastrophe without many-sheeted space-time. Instead of gauge fields, only the effects such as gaugeforces are superposed. Particle topologically condenses to several space-time sheets simultaneouslyand experiences the sum of gauge forces. This transforms the weakness to extreme economy: in atypical unified theory the number of primary field variables is countered in hundreds if not thousands,now it is just four.

1.2 The threads in the development of quantum TGD

The development of TGD has involved several strongly interacting threads: physics as infinite-dimensional geometry; TGD as a generalized number theory, the hierarchy of Planck constants inter-preted in terms of dark matter hierarchy, and TGD inspired theory of consciousness. In the followingthese threads are briefly described.

1.2.1 Quantum TGD as spinor geometry of World of Classical Worlds

A turning point in the attempts to formulate a mathematical theory was reached after seven yearsfrom the birth of TGD. The great insight was ”Do not quantize”. The basic ingredients to the newapproach have served as the basic philosophy for the attempt to construct Quantum TGD since thenand have been the following ones:


1. Quantum theory for extended particles is free(!), classical(!) field theory for a generalizedSchrödinger amplitude in the configuration space CH consisting of all possible 3-surfaces inH. ”All possible” means that surfaces with arbitrary many disjoint components and witharbitrary internal topology and also singular surfaces topologically intermediate between twodifferent manifold topologies are included. Particle reactions are identified as topology changes[A9, A17, A19]. For instance, the decay of a 3-surface to two 3-surfaces corresponds to the decayA→ B+C. Classically this corresponds to a path of configuration space leading from 1-particlesector to 2-particle sector. At quantum level this corresponds to the dispersion of the gener-alized Schrödinger amplitude localized to 1-particle sector to two-particle sector. All couplingconstants should result as predictions of the theory since no nonlinearities are introduced.

2. During years this naive and very rough vision has of course developed a lot and is not anymorequite equivalent with the original insight. In particular, the space-time correlates of Feynmangraphs have emerged from theory as Euclidian space-time regions and the strong form of GeneralCoordinate Invariance has led to a rather detailed and in many respects un-expected visions.This picture forces to give up the idea about smooth space-time surfaces and replace space-time surface with a generalization of Feynman diagram in which vertices represent the failure ofmanifold property. I have also startd introduced the word ”world of classical worlds” (WCW)instead of rather formal ”configuration space”. I hope that ”WCW” does not induce despair inthe reader having tendency to think about the technicalities involved!

3. WCW is endowed with metric and spinor structure so that one can define various metric relateddifferential operators, say Dirac operator, appearing in the field equations of the theory. Themost ambitious dream is that zero energy states correspond to a complete solution basis for theDirac operator of WCW so that this classical free field theory would dictate M-matrices whichform orthonormal rows of what I call U-matrix. Given M-matrix in turn would decompose to aproduct of a hermitian density matrix and unitary S-matrix.

M-matrix would define time-like entanglement coefficients between positive and negative energyparts of zero energy states (all net quantum numbers vanish for them) and can be regarded as ahermitian quare root of density matrix multiplied by a unitary S-matrix. Quantum theory wouldbe in well-defined sense a square root of thermodynamics. The orthogonality and hermiticityof the complex square roots of density matrices commuting with S-matrix means that theyspan infinite-dimensional Lie algebra acting as symmetries of the S-matrix. Therefore quantumTGD would reduce to group theory in well-defined sense: its own symmetries would define thesymmetries of the theory. In fact the Lie algebra of Hermitian M-matrices extends to Kac-Moody type algebra obtained by multiplying hermitian square roots of density matrices withpowers of the S-matrix. Also the analog of Yangian algebra involving only non-negative powersof S-matrix is possible.

4. By quantum classical correspondence the construction of WCW spinor structure reduces to thesecond quantization of the induced spinor fields at space-time surface. The basic action is socalled modified Dirac action in which gamma matrices are replaced with the modified gammamatrices defined as contractions of the canonical momentum currents with the imbedding spacegamma matrices. In this manner one achieves super-conformal symmetry and conservation offermionic currents among other things and consistent Dirac equation. This modified gammamatrices define as anticommutators effective metric, which might provide geometrization forsome basic observables of condensed matter physics. The conjecture is that Dirac determinantfor the modified Dirac action gives the exponent of Kähler action for a preferred extremalas vacuum functional so that one might talk about bosonic emergence in accordance with theprediction that the gauge bosons and graviton are expressible in terms of bound states of fermionand antifermion.

The evolution of these basic ideas has been rather slow but has gradually led to a rather beautifulvision. One of the key problems has been the definition of Kähler function. Kähler function is Kähleraction for a preferred extremal assignable to a given 3-surface but what this preferred extremal is?The obvious first guess was as absolute minimum of Kähler action but could not be proven to be rightor wrong. One big step in the progress was boosted by the idea that TGD should reduce to almosttopological QFT in which braids wold replace 3-surfaces in finite measurement resolution, which could


be inherent property of the theory itself and imply discretization at partonic 2-surfaces with discretepoints carrying fermion number.

1. TGD as almost topological QFT vision suggests that Kähler action for preferred extremalsreduces to Chern-Simons term assigned with space-like 3-surfaces at the ends of space-time(recall the notion of causal diamond (CD)) and with the light-like 3-surfaces at which thesignature of the induced metric changes from Minkowskian to Euclidian. Minkowskian andEuclidian regions would give at wormhole throats the same contribution apart from coefficientsand in Minkowskian regions the

√g4 factor would be imaginary so that one would obtain sum of

real term identifiable as Kähler function and imaginary term identifiable as the ordinary actiongiving rise to interference effects and stationary phase approximation central in both classicaland quantum field theory. Imaginary contribution - the presence of which I realized only after33 years of TGD - could also havetopological interpretation as a Morse function. On physicalside the emergence of Euclidian space-time regions is something completely new and leads to adramatic modification of the ideas about black hole interior.

2. The manner to achieve the reduction to Chern-Simons terms is simple. The vanishing of Coulom-bic contribution to Kähler action is required and is true for all known extremals if one makes ageneral ansatz about the form of classical conserved currents. The so called weak form of electric-magnetic duality defines a boundary condition reducing the resulting 3-D terms to Chern-Simonsterms. In this manner almost topological QFT results. But only ”almost” since the Lagrangemultiplier term forcing electric-magnetic duality implies that Chern-Simons action for preferredextremals depends on metric.

3. A further quite recent hypothesis inspired by effective 2-dimensionality is that Chern-Simonsterms reduce to a sum of two 2-dimensional terms. An imaginary term proportional to the totalarea of Minkowskian string world sheets and a real tem proportional to the total area of partonic2-surfaces or equivalently strings world sheets in Euclidian space-time regions. Also the equalityof the total areas of strings world sheets and partonic 2-surfaces is highly suggestive and wouldrealize a duality between these two kinds of objects. String world sheets indeed emerge naturallyfor the proposed ansatz defining preferred extremals. Therefore Kähler action would have verystringy character apart from effects due to the failure of the strict determinism meaning thatradiative corrections break the effective 2-dimensionality.

1.2.2 TGD as a generalized number theory

Quantum T(opological)D(ynamics) as a classical spinor geometry for infinite-dimensional configu-ration space, p-adic numbers and quantum TGD, and TGD inspired theory of consciousness, havebeen for last ten years the basic three strongly interacting threads in the tapestry of quantum TGD.The fourth thread deserves the name ’TGD as a generalized number theory’. It involves three sep-arate threads: the fusion of real and various p-adic physics to a single coherent whole by requiringnumber theoretic universality discussed already, the formulation of quantum TGD in terms of hyper-counterparts of classical number fields identified as sub-spaces of complexified classical number fieldswith Minkowskian signature of the metric defined by the complexified inner product, and the notionof infinite prime.

p-Adic TGD and fusion of real and p-adic physics to single coherent whole

The p-adic thread emerged for roughly ten years ago as a dim hunch that p-adic numbers might beimportant for TGD. Experimentation with p-adic numbers led to the notion of canonical identificationmapping reals to p-adics and vice versa. The breakthrough came with the successful p-adic masscalculations using p-adic thermodynamics for Super-Virasoro representations with the super-Kac-Moody algebra associated with a Lie-group containing standard model gauge group. Although thedetails of the calculations have varied from year to year, it was clear that p-adic physics reduces notonly the ratio of proton and Planck mass, the great mystery number of physics, but all elementaryparticle mass scales, to number theory if one assumes that primes near prime powers of two are in aphysically favored position. Why this is the case, became one of the key puzzless and led to a number


of arguments with a common gist: evolution is present already at the elementary particle level andthe primes allowed by the p-adic length scale hypothesis are the fittest ones.

It became very soon clear that p-adic topology is not something emerging in Planck length scaleas often believed, but that there is an infinite hierarchy of p-adic physics characterized by p-adiclength scales varying to even cosmological length scales. The idea about the connection of p-adicswith cognition motivated already the first attempts to understand the role of the p-adics and inspired’Universe as Computer’ vision but time was not ripe to develop this idea to anything concrete (p-adicnumbers are however in a central role in TGD inspired theory of consciousness). It became howeverobvious that the p-adic length scale hierarchy somehow corresponds to a hierarchy of intelligences andthat p-adic prime serves as a kind of intelligence quotient. Ironically, the almost obvious idea aboutp-adic regions as cognitive regions of space-time providing cognitive representations for real regionshad to wait for almost a decade for the access into my consciousness.

There were many interpretational and technical questions crying for a definite answer.

1. What is the relationship of p-adic non-determinism to the classical non-determinism of thebasic field equations of TGD? Are the p-adic space-time region genuinely p-adic or does p-adictopology only serve as an effective topology? If p-adic physics is direct image of real physics,how the mapping relating them is constructed so that it respects various symmetries? Is thebasic physics p-adic or real (also real TGD seems to be free of divergences) or both? If it is both,how should one glue the physics in different number field together to get The Physics? Shouldone perform p-adicization also at the level of the configuration space of 3-surfaces? Certainlythe p-adicization at the level of super-conformal representation is necessary for the p-adic masscalculations.

2. Perhaps the most basic and most irritating technical problem was how to precisely define p-adicdefinite integral which is a crucial element of any variational principle based formulation of thefield equations. Here the frustration was not due to the lack of solution but due to the too largenumber of solutions to the problem, a clear symptom for the sad fact that clever inventionsrather than real discoveries might be in question. Quite recently I however learned that theproblem of making sense about p-adic integration has been for decades central problem in thefrontier of mathematics and a lot of profound work has been done along same intuitive linesas I have proceeded in TGD framework. The basic idea is certainly the notion of algebraiccontinuation from the world of rationals belonging to the intersection of real world and variousp-adic worlds.

Despite these frustrating uncertainties, the number of the applications of the poorly defined p-adicphysics growed steadily and the applications turned out to be relatively stable so that it was clearthat the solution to these problems must exist. It became only gradually clear that the solution ofthe problems might require going down to a deeper level than that represented by reals and p-adics.

The key challenge is to fuse various p-adic physics and real physics to single larger structures.This has inspired a proposal for a generalization of the notion of number field by fusing real numbersand various p-adic number fields and their extensions along rationals and possible common algebraicnumbers. This leads to a generalization of the notions of imbedding space and space-time concept andone can speak about real and p-adic space-time sheets. The quantum dynamics should be such thatit allows quantum transitions transforming space-time sheets belonging to different number fields toeach other. The space-time sheets in the intersection of real and p-adic worlds are of special interestand the hypothesis is that living matter resides in this intersection. This leads to surprisingly detailedpredictions and far reaching conjectures. For instance, the number theoretic generalization of entropyconcept allows negentropic entanglement central for the applications to living matter.

The basic principle is number theoretic universality stating roughly that the physics in variousnumber fields can be obtained as completion of rational number based physics to various numberfields. Rational number based physics would in turn describe physics in finite measurement resolutionand cognitive resolution. The notion of finite measurement resolution has become one of the basicprinciples of quantum TGD and leads to the notions of braids as representatives of 3-surfaces andinclusions of hyper-finite factors as a representation for finite measurement resolution.


The role of classical number fields

The vision about the physical role of the classical number fields relies on the notion of number theoreticcompactifiction stating that space-time surfaces can be regarded as surfaces of either M8 or M4×CP2.As surfaces of M8 identifiable as space of hyper-octonions they are hyper-quaternionic or co-hyper-quaternionic- and thus maximally associative or co-associative. This means that their tangent spaceis either hyper-quaternionic plane of M8 or an orthogonal complement of such a plane. These surfacecan be mapped in natural manner to surfaces in M4×CP2 [K82] provided one can assign to each pointof tangent space a hyper-complex plane M2(x) ⊂M4. One can also speak about M8 −H duality.

This vision has very strong predictive power. It predicts that the extremals of Kähler actioncorrespond to either hyper-quaternionic or co-hyper-quaternionic surfaces such that one can assignto tangent space at each point of space-time surface a hyper-complex plane M2(x) ⊂ M4. As aconsequence, the M4 projection of space-time surface at each point contains M2(x) and its orthogonalcomplement. These distributions are integrable implying that space-time surface allows dual slicingsdefined by string world sheets Y 2 and partonic 2-surfaces X2. The existence of this kind of slicingwas earlier deduced from the study of extremals of Kähler action and christened as Hamilton-Jacobistructure. The physical interpretation of M2(x) is as the space of non-physical polarizations and theplane of local 4-momentum.

One can fairly say, that number theoretical compactification is responsible for most of the under-standing of quantum TGD that has emerged during last years. This includes the realization of Equiv-alence Principle at space-time level, dual formulations of TGD as Minkowskian and Euclidian stringmodel type theories, the precise identification of preferred extremals of Kähler action as extremalsfor which second variation vanishes (at least for deformations representing dynamical symmetries)and thus providing space-time correlate for quantum criticality, the notion of number theoretic braidimplied by the basic dynamics of Kähler action and crucial for precise construction of quantum TGDas almost-topological QFT, the construction of configuration space metric and spinor structure interms of second quantized induced spinor fields with modified Dirac action defined by Kähler actionrealizing automatically the notion of finite measurement resolution and a connection with inclusionsof hyper-finite factors of type II1 about which Clifford algebra of configuration space represents anexample.

The two most important number theoretic conjectures relate to the preferred extremals of Kähleraction. The general idea is that classical dynamics for the preferred extremals of Kähler action shouldreduce to number theory: space-time surfaces should be either associative or co-associative in somesense.

1. The first meaning for associativity (co-associativity) would be that tangent (normal) spaces ofspace-time surfaces are quaternionic in some sense and thus associative. This can be formu-lated in terms of octonionic representation of the imbedding space gamma matrices possible indimension D = 8 and states that induced gamma matrices generate quaternionic sub-algebra ateach space-time point. It seems that induced rather than modified gamma matrices must be inquestion.

2. Second meaning for associative (co-associativity) would be following. In the case of complexnumbers the vanishing of the real part of real-analytic function defines a 1-D curve. In oct-nionic case one can decompose octonion to sum of quaternion and quaternion multiplied by anoctonionic imaginary unit. Quaternionicity could mean that space-time surfaces correspond tothe vanishing of the imaginary part of the octonion real-analytic function. Co-quaternionicitywould be defined in an obvious manner. Octonionic real analytic functions form a function fieldclosed also with respect to the composition of functions. Space-time surfaces would form theanalog of function field with the composition of functions with all operations realized as algebraicoperations for space-time surfaces. Co-associaty could be perhaps seen as an additional featuremaking the algebra in question also co-algebra.

3. The third conjecture is that these conjectures are equivalent.

Infinite primes

The discovery of the hierarchy of infinite primes and their correspondence with a hierarchy defined by arepeatedly second quantized arithmetic quantum field theory gave a further boost for the speculations


about TGD as a generalized number theory. The work with Riemann hypothesis led to further ideas.

After the realization that infinite primes can be mapped to polynomials representable as surfacesgeometrically, it was clear how TGD might be formulated as a generalized number theory with infiniteprimes forming the bridge between classical and quantum such that real numbers, p-adic numbers, andvarious generalizations of p-adics emerge dynamically from algebraic physics as various completions ofthe algebraic extensions of rational (hyper-)quaternions and (hyper-)octonions. Complete algebraic,topological and dimensional democracy would characterize the theory.

What is especially satisfying is that p-adic and real regions of the space-time surface could

tgd universe as a conscious hologramtgd inspired theory of consciousness entered the scheme after...

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