Hierarchy of Planck Constants

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TOPOLOGICAL GEOMETRODYNAMICS What
Might be the First Principles? Article
http//www.helsinki.fi/matpitka/articles/tgd.pdf
Slides as pdfhttp///www.helsinki.fi/matpitka/t
gdppat/vision.pdf
Matti Pitkänen
http//www.helsinki.fi/matpitka/
Books about TGD
matpitka_at_rock.helsinki.fi
2
Two approaches to physics constructive and
analytic
To the beginning

• Einstein
• We can distinguish various kind of
  theories in physics. Most of them are
  constructive. They attempt to build up a picture
  of the more complex phenomena out of the
  materials of a relatively simple formal scheme
  from which they start out. Thus the kinetic
  theory of gases seeks to reduce mechanical,
  thermal, and diffusional processes to movements
  of molecules - i.e., to build them up out of the
  hypothesis of molecular motion. When we say that
  we have succeeded in understanding a group of
  natural processes, we invariably mean that a
  constructive theory has been found which covers
  the processes in question.
• Along with this most important class
  of theories there exists a second, which I will
  call "principle-theories." These employ the
  analytic, not the synthetic, method. The elements
  which form their basis and starting-point are not
  hypothetically constructed but empirically
  discovered ones, general characteristics of
  natural processes, principles that give rise to
  mathematically formulated criteria which the
  separate processes or the theoretical
  representations of them have to satisfy. Thus the
  science of thermodynamics seeks by analytical
  means to deduce necessary conditions, which
  separate events have to satisfy, from the
  universally experienced fact that perpetual
  motion is impossible.
• The advantages of the constructive theory
  are completeness, adaptability, and clearness,
  those of the principle theory are logical
  perfection and security of the foundations. The
  theory of relativity belongs to the latter class.
  

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Problem some basic principle might be wrong!
To the beginning

• Landscape problem of M theory. Is reductionism
  extrapolated to Planck length scale might be the
  reason?
  
• Perhaps one must tolerate the tension between
  constructive and analytic approaches.
• In TGD this tension has been present all the
  time. Path integral formalism failed. The
  attempt to construct S-matrix led to a long
  process forcing to modify existing visions about
  ontology of physics.
  
• New view about time, the notion of many-sheeted
  space-time, zero energy ontology, p-adic physics
  as physics of intentionality and cognition,
  hierarchy of Planck constants, role of von
  Neumann algebras known as hyperfinite factors of
  type II1 in the construction of theory,....

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Plan of the talk
To the beginning

• Represent various visions about basic
  principles behind quantum TGD keeping in mind the
  tension present also between them and trying to
  tolerate uncertainty.
  
  
• From Equivalence Principle to zero energy
  ontology ?
  
• Physics as spinor geometry of the world of
  classical worlds?
• The tree strands of physics as generalized number
  theory vision fusion of p-adic and real
  physics, classical number fields and physics,
  infinite primes and physics.
• Quantum TGD from hyperoctonionic generalization
  of conformal field with values in HFF of type II?
  
  
  
• Hierarchy of Planck constants and generalization
  of imbedding space H M4xCP2
  
  
  
• Finite measurement resolution as basic dynamical
  principle of quantum theory? Hyperfinite
  factors of type II1 (HFFs) as a basic building
  block.
  
  
• Should quantum physics be extended to a theory of
  consciousness?
  
  
  
  
  

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From Equivalence Principle to Zero Energy Ontology
To the beginning

• In Einstein's GRT the tension has been present
  from the beginning.
• Equivalence Principle (EP) gravitational and
  inertial masses are identical.
  
  
• Einstein's equations identify gravitational and
  inertial energy momentum tensors. Purely local
  statement. No global variant because
  gravitational and inertial four-momenta are not
  defined at all unless space-time has translations
  as symmetries. Something wrong?
• Cure space-time as a 4-D surface in HM4xS,
  SCP2. CP2 from standard model symmetries and
  geometrization of classical gauge fields.
  
  
  
• Inertial energy momentum as conserved Noether
  charge from Poincare symmetries of H rather than
  space-time. Gravitational four- momentum defined
  but not conserved unless the action is
  curvature scalar, in which case Equivalence
  Principle as identity.

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• Curvature scalar would predict conserved
  gravitational four-momentum not consistent with
  cosmology.
  
• Kähler action (Maxwell action for induce Kähler
  form of CP2) more natural physically.
  Gravitational momentum exists but not conserved.
  Robertson Walker cosmologies vacuum extremals
  (vanishing energy momentum and other conserved
  charges) but non-vanishing and non-conserved
  gravitational four-momentum.
  
  
• Does Equivalence Principle fail? Or is the
  interpretation wrong?
  
  
  
  
  
  
• The problem might have resolution in zero
  energy ontology. All physical states have
  vanishing net conserved quantum numbers.
  Positive and negative energy parts of states
  correspond to initial and final states of
  scattering event in positive energy ontology.
  Quantum states as events.
  
  
• Basic principle every quantum state is creatable
  from vacuum.

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• 
  
  
  
  

To the beginning
Elt0
Causal diiamond as pair of lightcones
M4-
T/2
T
M4
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Egt0

• Physical state can be visualized in terms of
  causal diamond. Lower lightcone boundary contains
  3-D surfaces with positive energy and upper
  lightcone boundary those with negative energy.
  

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• 
  
• Equivalence Principle in TGD
  
  
• Elementary partides as CP2 type vacuum extremals
  of Kähler action . Random lightlike curve as M4
  projection virtual particles. For extremals of
  curvature scalar projection light-like
  geodesic on mass shell particles.
  
  
  
• EP at 4-D level Topologically condensed CP2
  type vacuum extremal creates a non-vacuum region
  around around it. The resulting inertial
  four-momentum equals to the gravitational
  four-momentum.
  
• EP at macro level Space-time surfaces
  containing gravitons must have double sheeted
  structure (positive and negative energy
  space-time sheets). Near the vicinity of
  wormhole contacts (pieces of CP2 type vacuum
  extremals) vacuum extremals are deformed to
  non-vacuum extremals and carry inertial
  four-momentum equal to the gravitational four-
  momentum of the vacuum extremal.
  
  

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• 
  
• 
  
• 
  
• EP at parton level Gravitational momentum of
  CP2 type extremal inertial Chern-Simons
  four-momentum, which non-vanishing only if
  Kähler gauge potential has pure gauge part in
  M4/- equal to Aa constant (a is lightcone
  proper time). Aa expressible in terms of G/R2.
  Quantum criticality fixes this ratio. No
  breaking of Poincare invariance if configuration
  space union of configuration spaces assignable to
  lightcones.
  

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Physics as classical physics for configuration
space spinor fields
To the beginning

• Generalization of Einstein's geometrization
  program of classical physics to quantum physics.
• The world of classical worlds (configuration
  space) consisting of 3-surfaces of HM4xCP2 arena
  of quantum dynamics. Quantum states classical
  spinor fields in this space.
• Geometrize configuration space.
  
• Kähler geometry required in order to geometrize
  Hermitian conjugation. Kahler function K.
  General coordinate invariance definition of K
  assigns to 3-surface more or less unique
  4-surface analogous to Bohr orbit. Classical
  physics exact part of quantum theory.
  
  
  
• Mathematical existence of geometry extremely
  powerful constraint. For loop spaces Kähler
  geometry unique. In 3-D case even stronger
  constraints from existence of Riemann connection
  and finiteness. HM4xCP2 be the only possible
  choice? Infinite-D Kähler geometric existence
  unique?
  

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• Quantum dynamics from quantum criticality.
  Exponent of Kähler function defines a universal
  vacuum functional analogous to expoment of
  Hamiltonian. Kähler couplings strength analogous
  to critical temperature and quantized. All
  coupling parameters as predictions of the theory.
  
  
• Quantum states as classical spinor fields of
  configuration space. Only quantum jumps genuinely
  quantal element of theory.
• Geometrization of Fermi statistics. Configuration
  space spinors as Fock states for fermions.
  Anticommuting configuration space gamma matrices
  linear combinations of fermionic oscillator
  operators for free second quantized induced
  spinor fields at 3-surface.
  
  
• Configuration space gamma matrices generate
  infinite-D Clifford algebra. Canonical
  representation for von Neumann algebra known as
  hyper-finite factor of type II1 (HFF). Encodes
  quantum group and non-commutative physics.
  
  
  

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Quantum TGD as almost topological quantum field
theory?
To the beginning

• General coordinate invariance again! 3-surfaces
  can be chosen to be light-like 3-surfaces.
  
  
• Gauge bosons and Higgs as wormhole contacts
  wormhole throats at which induced metric changes
  signature are light-like. Carry fermionic and
  antifermionic quantum numbers. Fermions as
  topologically condensed CP2 type extremals.
  Lightlike 3-surrfaces look locally random orbits
  of partonic 2-surfaces with light velocity.
  
  
• Metric 2-dimensionality implies generalization of
  the super-conformal invariance of string models.
  Kac-Moody symmetries as isometries of the Kähler
  metric. Lightlike boundary of M4/- gives rise
  to additional superconformal symmetries.
  
  
  
• Light-likeness parton level formulation of TGD
  as almost topological quantum field
  theory. Chern-Simons action and its fermionic
  counterpart. Almost means that notions of
  energy and momentum make sense although theory
  relies on the formalism of TQFTs.
  
  
  

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To the beginning

• 
  
• TGD does not reduce to string model although
  causal determinants 1-dimensional! D
  4,3,2,1-dimensionality in discretized sense.
  Locally 3,2,1,0 dimensionality.
  
• At the bottom discrete number theoretical
  braids replace strings. Braids are basic objects
  of TQFTs. Interpretation in terms of finite
  measurement resolution.
  
  
• Tension Kähler function of configuration space
  expressible in terms of data associated with
  modified Dirac operator at points of number
  theoretic braid.
  

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• First thread p-adic physics.
  
• Reals and p-adic numbers, p2,3,5,7...
  completions of rationals .
  
  
• p-Adic mass calculations.
  
  
• What is the interpretation of p-adic physics?
  P-Adic space-time sheets define correlates for
  cognitions and intentions . Mind stuff of
  Descartes.
  
• How to glue real and various p-adic physics
  p2,3,5,7,... to single coherent whole?
• Basic principle Real and p-adic physics
  completions of rational physics .
  
  
• Generalization of number concept. Glue all these
  number fields together along rationals and common
  algebraics to form book like structure.
  
  

The three threads of Physics as generalized
number theory program
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• P-Adic and real space-time sheets intersect along
  common rational and algebraic points.
  Interpretation in terms of cognitive
  representations and discreteness of mathematical
  cognition and finite measurement and sensory
  resolution .
• P-Adic transcendentals literally infinite as
  real numbers. Most points of p-adic space-time
  sheets and spatial and temporal infinity.
  Cognition and intentionality cosmic phenomena not
  localizable to finite space-time volume.
  
• P-Adic topology induces effective p-adic topology
  of real space-time sheet when the number of
  common points large. P-Adic fractality predicted
  and explains the success of p-adic mass
  calculations. Cognition present already at
  elementary particle level.
  
  
• TensionThe discretization required by
  p-adicization implies the notion of number
  theoretic braid needed in almost TQFT approach.
  
  
• Tension Exponent of the configuration space
  Kähler function as Dirac determinant using only
  the data defined by braid. Construction assigns
  a preferred space-time surface to a given
  collection of light-like 3-surfaces.
  

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• Second thread classical number
  fields
• Imbedding space, space-time surface, partonic
  2-surface, and causal determinant of conformal
  field theory (strings) have dimensions of
  classical number fields.
  
  
• Could one also formulate QTGD by replacing
  M4xCP2 wth M8 HO space of hyper-octonions
  identifiable as subspace of complefixiifed
  octonions?
  
• Could associativity and commutativity fix
  dynamics?
  
• Observations about subspaces of M8
  
  
• Associative subspaces are hyperquaternionic
  planes M4 subset M8. Commutative subspaces
  are hypercomplex planes M2.
  
• M2 space of non-physical polarizations selected
  also in gauge theories and string models.
  Gauge choice would have purely number theoretical
  meaning.
  
• Subspaces M4 containing M2 parameterized by
  CP2!

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• 
  
  
• HO-H duality(number theoretic compactification)
  .
• Hyper-quaternionic space-time surfaces of M8
  for which hyper-quaternionic tangent planes M4
  contain fixed hypercomplex plane M2 can be mapped
  to M4xCP2.
  
• Bohr orbitology at light-like 3 surface X3 M2
  defines the direction of tangent space and one
  can assign unique 4-surface to X3 .
  
  
• Are these 4-surfaces of M8 mapped to preferred
  extremals of Kähler action?
  
  
  
  
• M4xCP2 and standard model symmetries have
  purely number theoretic origin! Also
  classical TGD!
  

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• Third thread infinite primes and
  further generalization of number concept
• Take product of all primes and add to it 1. Prime
  results. Construction generalizes. Infinite
  hierarchy of infinite primes.
  
  
• Procedure equivalent with repeated second
  quantization of arithmetic quantum field theory
  with bosons and fermions labelled by primes of
  given level. All Fock states and bound states
  constructed at first level become elementary
  particles at the next level. Continue
  indefinitely.
  
  
  
• The hierarchical structure of many-sheeted
  space-time could correspond to that for infinite
  primes. Proton- although manyquark state -
  would be elementary fermion at appropriate level
  of hierarchy.
  
• Hierarchy could also correspond to the
  hierarchy of nth order logics.
  
  

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• 
  
• Also infinite integers and rationals exist.
  Infinite number of real units defined as ratios
  of infinite integers. Not equivalent number
  theoretically. Infinite-dimensional space U of
  real units.
  
• Point of imbedding space replaced with infinite-D
  space U8 of points equivalent in real sense.
  What Schrödinger amplitudes in this space could
  mean?
  
• Number theoretic Brahman Atman identity. Is the
  world of classical worlds and even the space of
  configuration space spinor fields representing
  quantum states of Universe representable in this
  generalized imbedding space which is 8-D in real
  sense? Algebraic holography.
  
• Can one map configuration space spinor fields to
  Schrödinger amplitudes in U8 in natural
  manner?
• Good hopes for mapping the basis of configuration
  space spinor fields associated with zero energy
  states inside given causal diamond and appearing
  as zero energy insertions to Schrodinger
  amplitudes in U8 !
  
  
• Stuff below measurement resolution experienced
  subjectively?

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Extension of Clifford algebra of CH to
hyper-octonionic conformal fields in HO?
To the beginning

• Configuration space Clifford algebra correspond
  to vibrational degrees of freedom of 3-surface
  with cm degrees of freedom fixed. How to
  include cm degrees of freedom in H?
  
  
• In string models gamma fields define conformal
  fields. Generalization replace complex argument
  z with hyper-octonionic argument. HFF valued
  conformal fields.
• Could local variant of HFF analogous to local
  gauge algebra provide first principle approach to
  quantum and classical TGD?
  
  
  
  
• By non-associativity of hyper-octonions the
  resulting algebra does not reduce to HFF as in
  case of other number fields. Could this unique
  local version of HFF underlie quantum TGD?
  
  

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• 
  
• Associativity n-point functions involving
  local Clifford algebra elements must be
  associative at least. Arguments restricted to 4-D
  hyper-quaternionic subspace M4 subset M8.
  
• Commutatitivity fix preferred imaginary unit by
  choosing subspace HCM2 subset M4 subset M8.
  
  
  
  
• Assume that partonic 2-surfaces X2 belong to the
  boundary of lightcone (causal diamond) of M8,,
  not only M4xCP2! ! Nontrivial condition.
  
  
• Stronger assumption also pre-images of lightlike
  3-surfaces X3 belong to M4/- subset M8.
  
  
• These assumptions would explain the preferred
  role of partonic 2-surfaces and of their
  lightlike orbits as being due to their
  associativity. Associativity not true in the
  interior of space-time surface in general.
  
  
  
  
  
  
  

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• 
  
  
• Commutativity of n-point functions at partonic
  2-surfaces if arguments belong to the
  intersection of X2 with lightlike ray. Integral
  over rays would give maximal information.
  Unique discrete set of points identifiable in
  terms number theoretic braids. With additional
  assumptions about X2 rational or algebraic
  points of H.
  
• If also light-like 3 surfaces in M4/- then
  commutative submanifolds 1-D curves and define
  the strands of braids.
  
  
  
  
  
• Conclusion Very many speculative must-be-trues
  of quantum TGD follow as a consequence!
  
  
• Critical question Octonions would be number
  theoretically more elegant. Could one replace
  hyper-octonions with octonions and interpret
  duality in terms of generalization of Wick
  rotation?

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• Is Planck constant really constant? Planetary
  orbits obey in reasonable approximation Bohr
  rules with gigantic Planck constant (see this and
  this). Effects of ELF em fields on vertebrate
  brain quantal although energies of the photons
  extremely small as compared to thermal energy for
  ordinary value of Planck constant (see this).
  Could hbar be quantized and have arbitrarily
  large values?
  
  
• Possible only if the notion of imbedding space is
  generalized. Imbedding space has a book like
  structure. Each page covering or factor space of
  original imbedding space. The pages are glued
  together like pages of book.
• The matters at different pages of book dark
  relative to each other in sense that only
  particles from same page can appear in vertices
  of Feynman diagrams. Classical interactions
  between different pages possible. Also exchange
  of particles if phase transition changing hbar
  occurs (particle moves from page to another one).
  
  

Hierarchy of Planck constants
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To the beginning

• 
  
• Dark matter as matter with nonstandard value of
  Planck constant. Macroscopic quantum phases
  possible even in astrophysical length scales.
  Condensation of visible matter around dark matter
  with large Planck constant explains Bohr orbits
  for planets.
  
• This picture consistent with what is known about
  dark matter since classical em fields are not
  assumed to be of importance in astrophysical
  length scales.
  
  
• The anomalies associated with living cell
  understood if considerable fraction of
  biologically important ions dark and in
  macroscopic quantum phase.
  
• Tension Is the hierarchy of Planck constant
  necessary for quantum TGD. The generalization of
  imbedding space essential for the realization of
  quantum criticality and construction of exponent
  of Kähler function of configuration space.
• 
  

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• Clifford algebra for configuration space HFF of
  type II1 algebraic fractal. Infinite hierarchies
  of inclusions of HFF to itself as subalgebra.
  What could be the interpretation?
  
  
• Subalgebra N defines finite measurement
  resolution. Complex rays of state space replaced
  with N rays.
• In zero energy ontology elements of N insert to
  the positive or negative energy part of state
  zero energy part. The added part corresponds to
  time scale T/2, or more generally, T/2n.
• Interpretation in terms of radiative corrections
  which correspond to the increase of measurement
  resolution. Coupling constant evolution not
  continuous but comes in powers of 2.
  
  
• p-Adic length scale hypothesis as a consequence
  p-adic primes near powers of 2 preferred.
  

Could finite measurement resolution fix the
quantum dynamics?
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• 
  
• Additional prediction the temporal distances
  between tips of causal diamond macroscopic time
  scale for elementary particles. Argument goes
  as follows.
  
• Light-like 3-surfaces locally as random
  light-like orbits of partonic 2-surfaces.
  Brownian motions.
  
• During time T particles moves average distance
  given by p-adic length scale Lp. Analogy with
  Brownian motion implies
  
  T Lp2/cR, R CP2
  length.
  
  
• T corresponds to secondary time p-adic time scale
  
  
  T Tp,2 sqrt(p)Lp/c
  
  
• For electron T .1 seconds. Fundamental
  biorhythm!
• Zero energy ontology necessary in order to
  understand biology.
  

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• Definition of generalized S-matrix, M-matrix, as
  time-like entanglement coefficients between
  positive and negative energy parts of zero energy
  state interpreted as initial and final states of
  particle scattering experiment.
  
  
• Unitarity not necessary. M-matrix complex
  square root of density matrix. Product of
  positive square root of density matrix and of
  unitary S-matrix. Matrix generalizations of
  modulus and phase of Schrödinger amplitude.
  Quantum physics as a square root of
  thermodynamics.
  
• M-matrix must commute with hermitian elements of
  algebra N defining measurement resolution. N
  acts as infinite-D symmetry algebra. Connection
  with integrable QFTs and conformal invariance.
  
  
• M-matrix identifable in terms of Connes tensor
  product and is highly unique. Decomposition of
  HFF to direct summands implies non-uniquess which
  corresponds to thermal states.

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• 
  
• Tension How closely this vision relates to
  other visions?
• Configuration space Clifford algebra as HFF this
  is essential. Finite measurement resolution
  means discretization at space-time level.
  Conformal field theories and TQFTs relate
  closely to HFFs and inclusions. Connection with
  geometric, almost TQFT, and number theoretic
  visions.
  
• Hyper- octonionic analog of HFF might imply
  generalized imbedding space as emergent structure.

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• Quantum measurement theory the black sheet of
  quantum physics. Before one can speak of TOE
  one must be able to make observer a genuine part
  of Universe.
  
• Quantum jump and self basic notions of TGD
  inspired theory of consciousness.
  
  
• Quantum jump has complex anatomy unitary
  process, state function reduction, state
  preparation.
  
• Unitary process corresponds to unitary matrix U
  between zero energy states. M-matrix property of
  zero energy state.
• U-matrix can be assigned with the
  non-determinism of volition and intentional
  action. U-matrix tells also the probabilities for
  p-adic to real transitions characterizing
  intentional action. U-matrix probably almost
  trivial.
  
• Self as a system able to remain unentangled. Self
  results as a fusion of quantum jumps. Self
  relates to quantum jumps like composite particle
  to elementary particles from which it consists of
  .
  

Should one extend quantum physics to a quantum
theory of consciousness?
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• Negative energy ontology means that also
  negative energy signals to geometric past are
  possible. Mechanisms of memory, intentional
  action, and remote metabolism.
  
  
  
• New view about relationship between geometric and
  experienced time. (see this and this) Quantum
  classical correspondence quantal time evolution
  by quantum jumps must have space-time correlate.
  Failure of strict determinism for Kähler action
  makes this possible.
  
  
• Attention of self directed to a fixed volume of
  imbedding space HM4xCP2 in standard picture it
  would gradually shift towards future.
  
  
• In quantum jump configuration space spinor field-
  superposition of space-time surface shifts
  backwards in geometric time in a good
  approximation this realizes quantum classical
  correspondence. Observer experiences that
  geometric future of space-time sheet emerges to
  the perceptive field from future. Time flows.
  Only approximation in question dissipative
  effects.
  
  
  
  

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• 
  
• Negentropy Maximization Principle the basic
  variational principle of quantum consciousness
  theory. Information content of conscious
  experience measured by the reduction of the
  entanglement entropy in state function reduction.
  
  
• For standard definition of entanglement entropy
  in terms of Shannon entropy pure state would
  always result in state function reduction.
  
  
• For rational or even algebraic entanglement
  probabilities one can define number theoretical
  variants of Shannon entropy by replacing
  logarithm of probabily with the logarithms of
  p-adic norm of probability . This entropy can be
  negative. Entanglement can carry genuine
  information. State function reduction can
  generate entanglement!
  
  
• Possible interpretation in terms of formation of
  macrosopically quantum coherent systems. Synergy.
  Experience of understanding associated with this
  kind of quantum jumps?

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• 
  
• Tension Relationship with other approaches
  
• 
  
• Consciousness theory generalization of quantum
  measurement theory.
  
• Consciousness theory not alternative brings in
  genuinely new elements. Solves problems of
  other approaches. Difficulties of quantum
  measurement theory. The problem of time. The
  notion of information.
  
  
• The hierarchy of conscious entities and
  evolutionary hierarchy corresponds naturally to
  the hierarchy of Planck constants. Evolution as
  growth of largest Planck constant assignable to
  personal magnetic body having onionlike
  structure.
  
  
• P-Adic physics forced by the necessity to
  describe properly cognition and intentionality .
  
  
  
  

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• 
  
  
• Philosophical comment about number theoretic
  BrahmanAtman
  
  
• Real units correspond to zero energy states of
  arithmetic QFT. Physical zero energy states must
  be mapped to these. Must correspond to zero
  energy insertions to positive or negative part of
  zero energy state. States below measurement
  resolution mapped to the points of number
  theoretic braid in the resolution used.
  
  
• Conformal hyperoctonionic fields O(hi) at points
  of number theoretic braid create these zero
  energy states. In better resolution nonlocal
  operators formed from Cliffod algebra. Small
  causal diamond inside bigger causal diamond.
  
• Physical measurements give information about
  universe above measurement resolution. The
  Schrödinger amplitudes in the space of real units
  below it. Subjective experience gives information
  about quantum state below resolution.
  
  

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• 
  
  
• Technical comment about number theoretic
  BrahmanAtman
  
  
• Operators O(hi) constructed using generators of
  supercanonical and super KM algebras . Map basis
  to basis. Enumerability mathematician would
  stop here.
  
• Infinite primes lt--gt hierarchy of space-time
  sheets. Map of CH spinor fields to real units
  induced at the lowest level from the map of
  qnumbers of superalgebra generators to finite
  primes. Find natural ordering of these quantum
  numbers/states. Map to primes must respect this
  ordering.
  
• Order states of irrep of given group by values
  of quantum numbers assuming ordering of quantum
  numbers.
  
• Order irreps of given group by the dimension of
  representation or by the highest weight of irrep.
  
  
• Order the groups involved first SU(3) xSO(3)
  associated with Hamiltonians of S2xCP2 first,
  then KM color group, KM ew group, and KM rotation
  group (say). This allows highly unique map of
  the labels of super generators to finite primes.
  
  
  

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