The Hilbert Book Model

The Hilbert Book ModelA simple model of fundamental physics

By J.A.J. van Leunen

http://www.e-physics.eu

http://www.e-physics.eu/

http://www.e-physics.eu/

2

Physical RealityIn no way a model can give a precise

description of physical reality. At the utmost it presents a correct view on

physical reality. But, such a view is always an abstraction.

Mathematical structures might fit onto observed physical reality because their relational structure is isomorphic to the relational structure of these observations.

3

ComplexityPhysical reality is very complicatedIt seems to belie Occam’s razor. However, views on reality that apply

sufficient abstraction can be rather simple

It is astonishing that such simple abstractions exist

4

What is complexity?Complexity is caused by the number

and the diversity of the relations that exist between objects that play a role

A simple model has a small diversity of its relations.

5

Relational StructuresThe part of mathematics that treats relational

structures is lattice theory. Logic systems are particular applications of lattice

theory.

Classical logic has a simple relational structure. However since 1936 we know that physical reality

cheats classical logic. Since then we think that nature obeys quantum logic. Quantum logic has a much more complicated

relational structure.

Logic

6

Physical Reality & MathematicsPhysical reality is not based on mathematics.

Instead it happens to feature relational structures that are similar to the relational structure that some mathematical constructs have.

That is why mathematics fits so well in the formulation of physical laws.

Physical laws formulate repetitive relational structure and behavior of observed aspects of nature.

7

Logic systemsClassical logic and quantum logic only

describe the relational structure of sets of propositions

The content of these proposition is not part of the specification of their axioms

They only control static relationsTheir specification does not cover dynamics

8

FundamentThe Hilbert Book Model (HBM) is strictly based on traditional quantum logic.

This foundation is lattice isomorphic with the set of closed subspaces of an infinite dimensional separable Hilbert space.

9

Correspondences≈1930 Garret Birkhoff and John von Neumann discovered

the lattice isomorphy:

Infinite, butcountablenumber ofatoms / base vectors

Quantum logic Hilbert spacePropositions: Vectors:

atoms Base vectors:

Relational complexity:

Inner product:

Inclusion: Sum:

For atoms : Subspace

10

Atoms & base vectorsAtom

Contents not importantSet is unorderedMany sets possible

LogicLattice

Only relations important

11


Contents not important

Set is unorderedMany sets possible

Base vectorSet is unorderedMany sets possibleCan be eigenvector

Eigenvalue Real Complex Quaternionic

LogicLattice

Only relations important

12


Contents not important

Set is unorderedMany sets possible



Hilbert spaceInner product

RealComplexQuaternionic

Constantin Piron:Inner product must be real, complex or quaternionic

The eigenvalues are the same type of numbers as the inner products

First Model

Traditional

Quantum Logic

Separable Hilbert Space

Countable

Eigenspace

Only static status quo&

No fields

Classical

Logic

isomorphism


Particle location operato

r

Weaker modularit

y

About 25 axioms

14

Representation

Quantum logic

Hilbert space}

No full isomorphismCannot represent

continuums

Solution:

• Refine to Hilbert logic• Add Gelfand triple

15

Discrete sets and continuumsA Hilbert space features operators that have countable eigenspaces

A Gelfand triple features operators that have continuous eigenspaces

Static Status Quo of the Universe

Traditional

Quantum Logic


Separable Hilbert SpaceSeparable Hilbert SpaceGelfand Triple

Countable Eigenspac

e

ContinuumEigensp

aceParticl

e locatio

n

location

Classical

Logic

Hilbert Logic

isomorphisms

Isomorphism’s

Subspaces

vectors

embedding

Threefold hierarchyThe sub-models form a threefold hierarchy

IsomorphismsRelationalstructure

QuantumLogic

Hilbert space

Set of particles

Quantum LogicAtomicquantumlogicproposition

Subspace Swarmof stepstones

Hilbert logic

Atomic HilbertLogicproposition

Base vector Step stone

18

Three structures, three levels

19

No support for dynamics

None of the three structures has a built-in

mechanism for supporting dynamics

Implementing dynamicsThe sub-models can only implement

a static status quo

21

RepresentationQuantum logic

Hilbert logic

Hilbert space

}Cannot represent

dynamicsCan only implement a

static status quo

Solution:

An ordered sequence of sub-modelsThe model looks like a book where the sub-models are the pages.

22

Sequence · · · |-|-|-|-|-|-|-|-|-|-|-|-| · · · · · · · · · · |-|-|-|-|-|-|-|-|-| · · ·

PrehistoryReference sub-model

hasdensest packaging

current future

Reference Hilbert space delivers via its enumeration operator the “flat” Rational Quaternionic Enumerators

Gelfand triple of reference Hilbert space delivers via its enumeration operator the reference continuum

HBM has no Big Bang!

23

The Hilbert Book ModelSequence ⇔ book ⇔ HBMSub-models ⇔ sequence members ⇔ pages

Sequence number ⇔page number ⇔ progression parameter This results in a

paginated space-progression model

24

Paginated space-progression modelSteps through sequence of static sub-

modelsUses a model-wide clockIn the HBM the speed of information

transfer is a model-wide constantThe step size is a smooth function of progression

Space expands/contracts in a smooth way

25

Progression stepThe dynamic model proceeds with

universe wide progression stepsThe progression steps have a rather

fixed sizeThe progression step size corresponds

to an super-high frequency (SHF)The SHF is the highest frequency that

can occur in the HBM

26

RecreationThe whole universe is recreated at every progression step

If no other measures are taken,the model will represent dynamical chaos

27

Dynamic coherence 1An external correlation

mechanism must take care such that sufficient coherence between

subsequent pages exist

28

Dynamic coherence 2The coherence must not be

too stiff, otherwise no dynamics occurs

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Storage

The eigenspaces of operators

can act as storage places

30

Storage detailsStorage places of information that

changes with progressionThe countable eigenspaces of Hilbert space

operators The continuum eigenspaces of the Gelfand

triple

The information concerns the contents of logic propositions

The eigenvectors store the corresponding relations.

31

Correlation VehicleSupports recreation of the universe

at every progression stepMust install sufficient cohesion

between the subsequent sub-modelsOtherwise the model will result in dynamic chaos.

Coherence must not be too stiff, otherwise no dynamics occurs

32

Correlation Vehicle DetailsEstablishes

Embedding of particles in continuumCauses

Singularities at the location of the embeddingSupported by:

Hilbert space (supports operators)Gelfand triple (supports operators)Huygens principle (controls information transport)

Implemented by:Enumeration operatorsBlurred allocation function

Requires identification of atoms / base vectors

33

Correlation vehicle requirementsRequires ID’s for atomic propositionsID generator

Dedicated enumeration operator Eigenvalues ⇒ rational quaternions ⇒ enumerators

Blurred allocation function Maps parameter enumerators onto embedding

continuum

Requires a reference continuum

RQE = RationalQuaternionicEnumerator

34

Reference continuumSelect a reference Hilbert space

Has countable number of dimensions/base vectors

Criterion is densest packaging of enumerators*.Take its Gelfand triple (rigged “Hilbert space”)

Has over-countable number of dimensions/base vectorsHas operators with continuum eigenspaces

Select equivalent of enumeration operator in Hilbert space

Use its eigenspace as reference continuum

(*Cyclic: Densest with respect to reference continuum)

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Set is unorderedMany sets possibleContents not important



36


Set is unorderedMany sets possibleContents not important



Hilbert space & Hilbert logicInner product

RealComplexQuaternionic

Enumerator operatorEigenvalues

Rational quaternionic enumerators(RQE’s)

Enumerates atoms

37

EnumerationHilbert space & Hilbert

logicEnumerator operator

EigenvaluesRational

quaternionic enumerators(RQE’s)

38



EigenvaluesRational quaternionic

enumerators(RQE’s)

ModelAllocation function

ParametersRQE’s

ImageQtargets

39





ModelEnumeration function

ParametersRQE’s

ImageQtargets

Function Blurred Sharp Spread

function Blur

40





ModelEnumeration function

ParametersRQE’s

ImageQtargets

Function Blurred Sharp Spread

function Blur

Swarm

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Blurred allocation function Function

Blurred ⇒ Produces swarm ⇒ QtargetSharp ⇒ Produces planned QpatchSpread function ⇒ Produces Qpattern ⇒ Swarm

QPDDQuaternionic

ProbabilityDensityDistribution

Swarm

Convolution

Described by the QPDD

⇓QPDD

42


Blurred ⇒ Produces swarm ⇒ QtargetSharp ⇒ Produces planned QpatchSpread function ⇒ Produces Qpattern

QPDD Quaternionic


Only exists at current instanceQPDD

Convolution

43


Blurred ⇒ Produces swarm ⇒ QtargetSharp ⇒ Produces planned QpatchSpread function ⇒ Produces Qpattern

QPDD Quaternionic


Only exists at current instance

Curved

space

QPDD

44


Blurred ⇒ Produces swarm ⇒ QtargetSharp ⇒ Produces planned QpatchS ⇒ Produces Qpattern

QPDD Quaternionic


Only exists at current instance

Curved

space

QPDD

45


Blurred ⇒ Produces QPDD ⇒ QtargetSharp ⇒ Produces planned QpatchS ⇒ Produces Qpattern

QPDD Quaternionic


Curved

space

Swarm

Allocation function

46

Hilbert space choices

The Hilbert space and its Gelfand triple can be defined usingReal numbersComplex numbersQuaternions

The choice of the number system determines whether blurring is straight forward

47

Real Hilbert space modelProgression separatedUse rational eigenvalues in Hilbert spaceUse real eigenvalues in Gelfand tripleCohesion not too stiff (otherwise no dynamics!)

Keep sufficient interspacing ⇛ 1D blur ?Define lowest rational

May introduce scaling as function of progressionRather fixed progression steps

48

Complex Hilbert space modelProgression at real axisUse rational complex numbers in Hilbert spaceUse real complex numbers in Gelfand tripleCohesion not too stiff (otherwise no dynamics!)

Keep sufficient interspacing ⇛ 1D blur ?Lowest rational at both axes (separately)

May introduce scaling as function of progressionNo scaling or blur at progression axis

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Quaternionic Hilbert space model

Progression at real axisUse rational quaternions in Hilbert space and in Gelfand tripleCohesion not too stiff (otherwise no dynamics!)

Keep sufficient interspacing⇛ 3D blurLowest rational at all axes (same for imaginary axes)

May introduce scaling as function of progression No scaling and no blur at progression axis

Blur installed by correlation vehicle

50

Why blurred ?Pre-enumerated objects (atoms, base vectors) are not orderedNo origin

Affine-like space

Enumeration must not introduce extra propertiesNo preferred directions

51

Swarming conditions 1In order to ensure sufficient coherence

the correlation mechanism implements swarming conditions

A swarm is a coherent set of step stonesA swarm can be described by a continuous object density distribution

That density distribution can be interpreted as a probability density distribution

52

Swarming conditions 2A swarm moves as one unitIn first approximation this movement can

be described by a linear displacement generator

This corresponds to the fact that the probability density distribution has a Fourier transform

The swarming conditions result in the capability of the swarm to behave as part of interference patterns

53

Swarming conditions

The swarming conditions distinguish this type of

swarm from normal swarms

54

Mapping Quality CharacteristicThe Fourier transform of the density

distribution that describes the planned swarm can be considered as a mapping quality characteristic of the correlation mechanism

This corresponds to the Optical Transfer Function that acts as quality characteristic of linear imaging equipment

It also corresponds to the frequency characteristic of linear operating communication equipment

55

Quality characteristicOptics versus quantum physics

In the same way that the Optical Transfer Function is the Fourier transform of the Point Spread Function

Is the Mapping Quality Characteristic the Fourier transform of the QPDD, which describes the planned swarm. (The Qpattern)

This view integrates over the set of progression steps that the embedding process takes to consume the full Qpattern, such that it must be regenerated

56

Target spaceThe quality of the picture that is formed by

an optical imaging system is not only determined by the Optical Transfer Function, it also depends on the local curvature of the imaging plane

The quality of the map produced by quantum physics not only depends on the Mapping Quality Characteristic, it also depends on the local curvature of the embedding continuum

57

CouplingFor swarms the coupling equation holds

and are normalized quaternionic functionsThey describe quaternionic probability density

distributions is the quaternionic nablaFactor is the coupling strength

P is the displacement generator

58

Swarms 1The correlation mechanism generates swarms of step

stones in a cyclic fashionThe swarm is prepared in advance of its usage

This planned swarm is a set of placeholders that is called Qpattern

A Qpattern is a coherent set of placeholdersThe step stones are used one by oneIn each static sub-model only one step stone is used

per swarmThis step stone is called Qtarget

When all step stones are used, then a new Qpattern is prepared

59

Planned and actual swarmSwarm of step stones

Set of placeholdersQpattern

Continuous

allocation function

Placeholder

generator

Random

selection

Qtarget

Embedding continuum

Reference continuum

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Swarms 2At each progression step, an image of the

planned swarm (Qpattern) is mapped by a continuous allocation function onto the embedding continuum

At each progression step, via random selection a single step stone is selected, whose image becomes the Qtarget

A swarm has a “center position”, called Qpatch that can be interpreted as the expectation value of location of the swarm

The Qtargets form a stochastic micro-path

61

Placeholders and Step stonesTogether with the allocation function a

placeholder defines where a selected particle can be

That location is a step stoneA coherent collection of these placeholders

represent the QpatternThe placeholders are generated by the stochastic

spatial spread function At each progression step a different step

stone becomes the Qtarget location of the particle

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Generation of placeholders and step stonesPer progression step only ONE Qtarget is

generated per QpatternGeneration of the whole Qpattern takes a

large and fixed amount of progression stepsWhen the Qpatch moves, then the pattern

spreads out along the movement pathWhen an event (creation, annihilation,

sudden energy change) occurs, then the enumeration generation changes its mode

63

Qpattern generation example (no preferred directions)Random enumerator generation at lowest scalesLet Poisson process produce smallest scale

enumeratorCombine this Poisson process with a binomial processThis is installed by a 3D spread functionGenerates a 3d “Gaussian” distribution (is example)

The distribution represents an isotropic potential of the form

This quickly reduces to 1 (form of gravitational potential)

The result is a Qpattern

64

Blurred allocation function Blurred function

Sharp maps RQE ⇒ QpatchSpread maps Qpatch ⇒ Qtarget

Function Produces QPDD

Stochastic spatial spread function Produces Qpattern Produces gravitation ()

Sharp Describes space curvature Delivers local metric d

Convolution

65

Micro-pathThe Qpatterns contain a fixed number of step

stonesThe step stones that belong to a Qpattern

form a micro-pathEven at rest, the Qpattern walks along its

micro-pathThis walk takes a fixed number of

progression stepsWhen the Qpattern moves or oscillates, then

the micro-path is stretched along the path of the Qpattern

This stretching is controlled by the third swarming condition

66

Wave frontsAt every arrival of the particle at a new step

stone the embedding continuum emits a wave front

The subsequent wave fronts are emitted from slightly different locations

Together, these wave fronts form super-high frequency waves

The propagation of the wave fronts is controlled by Huygens principle

Their amplitude decreases with the inverse of the distance to their source

67

Wave frontDepending on dedicated Green’s

functions, the integral over the wave fronts constitutes a series of potentials.

The Green’s function describes the contribution of a wave front to a corresponding potential

Gravitation potentials and electrostatic potentials have different Green’s functions

68

Potentials & wave frontsThe wave fronts and the potentials are traces

of the particle and its used step stones. The superposition of the singularities

smoothens the effect of these singularities.Neither the emitted wave fronts, nor the

potentials affect the particle that emitted the wave front

Wave fronts interfereThe wave fronts modulate a field

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Photon & gluon emissionA sudden decrease in the energy of the

emitting particle causes a modulation of the amplitude of the emitted wave fronts

The creation of this modulation lasts a full micro-walk

The modulation of the SHF carrier wave becomes observable as a photon or a gluon

The modulation represents an energy quantum

E=ℏ∙νThe energy is shown in the modulation

frequency ν

70

Embedding continuumA curved continuum embeds the

elementary particlesThe continuum is constituted by a

background field

71

Photon & gluon absorptionA modulation of the embedding

continuum can be absorbed by an elementary particle

The modulation frequency determines the absorbable energy quantum

The modulation must last during a full micro-walk

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Photons and gluonsPhotons and gluons are energy quanta

Photons and gluons are NOT electro-magnetic waves!

Photons and gluons are NOT particles

73

PalestraCurved embedding continuumRepresents universe

The Palestra is the place where everything happens

Collection of Qpatches

Embedded in continuum

74

Mapping

Space curvature

Quantum physics

GRQuaternionic metric

Quaternionic metric

16 partial derivatives

No tensor needed

• Continuity equation

• Dirac equation

• In quaternion format

Quantum fluid dynamics

Quaternionic physics

How to use Quaternionic Distributions

andQuaternionic Probability Density Distributions

76

The HBM is a quaternionic modelThe HBM concerns quaternionic physics

rather than complex physics. The peculiarities of the quaternionic Hilbert

model are supposed to bubble down to the complex Hilbert space model and to the real Hilbert space model

The complex Hilbert space model is considered as an abstraction of the quaternionic Hilbert space modelThis can only be done properly in the right

circumstances

77

Continuous Quaternionic Distributions

Quaternions

c =

Quaternionic distributions Differential equation

DifferentialCouplingContinuity

equation}

{

Two equation

s

Three

kinds

78

Field equations

= Is zero

?

Spin of a field:

79

QPDD’sQuaternionic distribution

Quaternionic Probability Density Distribution

Scalar field

Vector field

Density distributio

n

Current density

distribution

Current density

distribution

Density distributio

n

80

Coupling equation Differential

Integral

and φ are normalized = total energy = rest mass + kinetic energyFlat

space

81

Coupling in Fourier space

In general is not an eigenfunction of operator . That is only true when and are equal.For elementary particles they are equal apart from their difference in discrete symmetry.

82

Dirac equation

Spinor Dirac matrices ,

In quaternion format

QpatternQPDD

Approximately flat space

83

Composites

Entanglement

84

EntanglementThe correlation mechanism manages

entanglementAt every progression instant the quantum

state function of an entangled system equals the superposition of the quantum state functions of its components

Entangled systems obey the swarming conditions

For entangled systems the coupling equation holds

and are normalizedEntanglement acts as a binding mechanism

85

BindingThe fact that superposition coefficients define

internal movements can best be explained by reformulating the definition of entangled systems.

Composites that are equipped with a quantum state function whose Fourier transform at any progression step equals the superposition of the Fourier transforms of the quantum state functions of its components form an entangled system.

Now the superposition coefficients can define internal displacements. As a function of progression they define internal oscillations.

86

GeoditchesIn an entangled system the micro-paths of the

constituting elementary particles are folded along the internal oscillation paths.

Each of the corresponding step stones causes a local pitch that describes the temporary (singular) curvature of the embedding continuum.

These pitches quickly combine in a ditch that like the micro-path folds along the oscillation path.

These ditches form special kinds of geodesics that we call “Geoditches”.

The geoditches explain the binding effect of entanglement.

87

Pauli principleIf two components of an entangled (sub)system that have the

same quantum state function are exchanged, then we can take the system location at the center of the location of the two components. Now the exchange means for bosons that the (sub)system quantum state function is not affected:

For all α and β{αφ(-x)+βφ(x)=αφ(x)+βφ(-x)}⇒φ(-x)=φ(x) and for fermions that the corresponding part of the (sub)system

quantum state function changes sign. For all α and β{αφ(-x)+βφ(x)=-αφ(x)-βφ(-x)}⇒φ(-x)=-φ(x)

This conforms to the Pauli principle.

88

Non-localityAction at a distance cannot be caused via

information transferNon-locality already plays a role inside the

realm of separate elementary particles. Hopping along the step stones occurs much

faster than the information carrying waves can follow.

Similar features occur inside entangled systems.

Due to the exclusion principle, observing the state of a sub-module has direct (instantaneous) consequences for the state of other sub-modules.

89

FocusIf in an entangled system the focus is on the

system, then the whole system acts as a swarm and the correlation mechanism causes hopping along ALL step stones that are involved in the system

When the focus shifts to one or more of the constituents, then the entanglement get at least partly broken

The separated particles and the resulting entangled system act as separate swarms

90

Composites

Binding

91

Binding mechanismWhen it is used, each step stone that is

involved in an entangled system produces a singularity. The influence of that singularity spreads over the embedding continuum in the form of a wave front that folds and thus curves this continuum

The traces of these Qtargets mark paths where the wave fronts dig pitches into the continuum that combine into channels that act as geodesics.

92

Composites

The effect of modularization

93

ModularizationModularization is a very powerful influencer.Together with the corresponding encapsulation

it reduces the relational complexity of the ensemble of objects on which modularization works.

The encapsulation keeps most relations internal to the module.

When relations between modules are reduced to a few types , then the module becomes reusable.

If modules can be configured from lower order modules, then efficiency grows exponentially.

94

ModularizationElementary particles can be considered as

the lowest level of modules. All composites are higher level modules.

Modularization uses resources efficiently.When sufficient resources in the form of

reusable modules are present, then modularization can reach enormous heights.

On earth it was capable to generate intelligent species.

95

ComplexityPotential complexity of a set of objects is a

measure that is defined by the number of potential relations that exist between the members of that set.

If there are n elements in the set,then there exist n·(n-1) potential relations.

Actual complexity of a set of objects is a measure that is defined by the number of relevant relations that exist between the members of the set.

Relational complexity is the ratio of the number of actual relations divided by the number of potential relations.

96

Relations and interfacesModules connect via interfaces. Relations that act within modules are lost to

the outside world of the module. Interfaces are collections of relations that are

used by interactions. Physics is based on relations. Quantum logic

is a set of axioms that restrict the relations that exist between quantum logical propositions.

97

Types of physical interfacesInteractions run via (relevant) relations. Inbound interactions come from the past. Outbound interactions go to the future. Two-sided interactions are cyclic.

They take multiple progression steps. They are either oscillations or rotations of the

inter-actor.Cyclic interactions bind the corresponding

modules together.

98

Modular systemsModular (sub)systems consist of connected

modules. They need not be modules. They become modules when they are

encapsulated and offer standard interfaces that makes the encapsulated system a reusable object.

All composites are modular systems

99

Binding in sub-systemsLet represent the renormalized

superposition of the involved distributions.

is the total energy of the sub-systemThe binding factor is the total energy of the

sub-system minus the sum of the total energies of the separate constituents.

100

Random versus intelligent designAt lower levels of modularization nature designs

modular structures in a stochastic way. This renders the modularization process rather slow. It takes a huge amount of progression steps in order to

achieve a relatively complicated structure. Still the complexity of that structure can be orders of

magnitude less than the complexity of an equivalent monolith.As soon as more intelligent sub-systems arrive, then

these systems can design and construct modular systems in a more intelligent way. They use resources efficiently. This speeds the modularization process in an enormous way.

101

Quanta

The noise of low dose imaging

Low dose X-ray imaging Film of cold cathode emission

http://www.scitech.nl/English/Science/QuantumLimitedLlowDoseImaging.avi

http://www.youtube.com/watch?v=U7qZd2dG8uI

102

Shot noise

Low dose X-ray image of the moon

103

Shot noise

104

Large scale physics

Large scale fluid dynamics

105

Physical fields-1SHF wave modulations

PhotonGluon

Energy quanta

SHF wave potentialsElectromagnetic fieldGravitation field

𝛻 𝜓=𝑚𝜑

∑𝑖

𝑛𝑖𝑒𝑖𝜓 𝑖

∑𝑖

𝑛𝑖𝑚𝑖𝜑 𝑖

𝑒𝑖=±𝑒

harmonic

}

106

Physical fields-2Fields from step stone

distributionsQuaternionic quantum state

functionQPDD

Quaternionic distributions Charges are preserved

𝛻 𝜓=𝑚𝜑

107

Inertia-1Inertia is implemented via the

embedding continuum

The embedding continuum is formed by a curved background field that forms our living space

108

Inertia-2

dV In a uniform

background: ; is constant

dV dV = 2π (Dennis Sciama) dV = ;

Potential fields of distant particles

Everywhere present

background field

109

Inertia-3is a scalar background field is a vector background field is gravitational constantAcceleration goes together with an extra field This field counteracts the acceleration

110

Inertia-4Starting from coupling equation

χ + χ represents particle at rest = χ + SmallSmall

Represents influence of

distant particles

111

Continuity equationBalance equationTotal change within V

= flow into V + production inside V

+

+

Gauss

112

Inversion surfaces

The criterion =0 divides universe in compartments

Inversion surface

113

Compartmentsuniverse

Huge BH

Black holesBlack holesBlack holesBlack holes

Compartments

BH ⇔ densest packagingHuge BH ⇔ s tart of new episode

Never ending story

Merge

114

History of CosmologyBlack hole represents natal state of

compartmentBlack holes suck all mass from their

compartment A passivized huge black hole represents start

of new episode of its compartmentDriving force is enormous mass present

outside compartment ⇒ expansionWhole universe is affine spaceResult is never ending story

115

GravitationThe Palestra is a curved space

is quaternion

Pythagoras

Minkowski

Flat spaceCurved space

c dt

dr

c dτ

16 partial derivatives

116

Metric is a quaternionic metricIt is a linear combination of 16 partial

derivatives

Avoids the need for tensors

117

Elementary particlesThe primary building blocks

118

Elementary particlesCoupling equation

Coupling occurs between pairs

Colors x, y, W

Right and left handednessR,L

L

Sign flavors

Discrete symmetries

Imaginary part

is theReferen

ceQPDD

119

Spin

HYPOTHESIS : Spin relates to the fact whether the coupled QPDD is the reference Qpattern .

Each generation has its own reference QPDD. Fermions couple to the reference QPDD . Fermions have half integer spin. Bosons have integer spin. The spin of a composite equals the sum of the

spins of its components.

120

Sign of spinThe micro-path can be walked in two

directionsThis determines the sign of spin

121

Electric chargeHYPOTHESIS : Electric charge depends on the

number of dimensions in which the discrete symmetry of Qpattern elements differ from the discrete symmetry of the embedding field.

Each sign difference stands for one third of a full electric charge.

Further it depends on the fact whether the handedness differs.

If the handedness differs then the sign of the count is changed as well.

122

Color chargeHYPOTHESIS : Color charge is related to the direction of the

anisotropy of the considered QPDD with respect to the reference QPDD.

The anisotropy lays in the discrete symmetry of the imaginary parts. The color charge of the reference QPDD is white. The corresponding anti-color is black. The color charge of the coupled pair is determined by the colors of its

members.

All composite particles are black or white. The neutral colors black and white correspond to isotropic QPPDs.

Currently, color charge cannot be measured. In the Standard Model the existence of color charge is derived via the

Pauli principle.

123

Total energy

Mass is related to the coupling factor of the involved QPPDs.

It is directly related to the square root of the volume integral of the square of the local field energy .

Any internal kinetic energy is included in .The same mass rule holds for composite

particles. The fields of the composite particles are

dynamic superpositions of the fields of their components.

124

LeptonsPair s-type e-

chargec-

chargeHanded

nessSM Name

fermion -1 LR electron

Anti-fermion

+1 RL positron

125

QuarksPair s-type e-charge c-charge Handedness SM Name

fermion -1/3 LR down-quark

Anti-fermion +1/3 RL Anti-down-quark





fermion +2/3 RR up-quark

Anti-fermion -2/3 LL Anti-up-quark





126

Reverse quarksPair s-type e-charge c-charge Handedness SM Name

fermion +1/3 RL down-r-quark

Anti-fermion -1/3 LR Anti-down-r-quark


Anti-fermion -1/3 LR Anti-down-r-quark


Anti-fermion -1/3 LR Anti-down-r_quark

fermion -2/3 RR up-r-quark

Anti-fermion +2/3 LL Anti-up-r-quark





127

W-particlesboson -1 RL

Anti-boson +1 R LR

boson -1 RL

Anti-boson +1 G LR

boson -1 RL

Anti-boson +1 B LR

boson -1 RL

Anti-boson +1 LR

boson -1 RL

Anti-boson +1 LR

boson -1 B RL

Anti-boson +1 LR

boson -1 RL

Anti-boson +1 LR

boson -1 RL

Anti-boson +1 LR

boson -1 RL

Anti-boson +1 LR

128

Z-particlesPair s-type e-charge c-charge Handedness SM Name

boson 0 LL

Anti-boson 0 RR

boson 0 LL

Anti-boson 0 RR

boson 0 LL

Anti-boson 0 RR

boson 0 LL

Anti-boson 0 RR

boson 0 LL

Anti-boson 0 RR

boson 0 LL

Anti-boson 0 RR

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Neutrinostype s-type e-charge c-charge Handedness SM Name

fermion 0 RR neutrino

Anti-fermion 0 LL neutrino

boson? 0 RR neutrino

Anti- boson? 0 LL neutrino





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Color confinement

The color confinement rule forbids the generation of individual particles that have non-neutral color charge

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Color confinementColor confinement forbids the

generation of individual quarks

Quarks can appear in hadrons

Color confinement blocks observation of gluons

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Photons & gluonstype s-type e-charge c-charge Handedness SM Name

boson 0 R photon

boson 0 L photon

boson 0 R gluon

boson 0 L gluon

boson 0 R gluon

boson 0 L gluon

boson 0 R gluon

boson 0 L gluon

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Photons & gluonsPhotons and gluons are NOT

particles

Ultra-high frequency waves are constituted by wave fronts that at every progression step are emitted by elementary particles

Photons and gluons are modulations of ultra-high frequency carrier waves.

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Fundamental particlesDue to color confinement some

elementary particles cannot be created as individuals

Quarks can only be created combined in hadrons

Fundamental particles form a category of particles that are created in one integral action

The color charge of fundamental particles is neutral

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Other subjects

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Dual space distributionsA subset of the (quaternionic) distributions

have the same shape in configuration space and in the linear canonical conjugated space.

We call them dual space distributionsThese are functions that are invariant under

Fourier transformation.The Qpatterns and the harmonic and spherical

oscillations belong to this class.Fourier-invariant functions show iso-resolution,

that is, in the Heisenberg’s uncertainty relation.

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Why has nature a preference?Nature seems to have a preference for this

class of quaternionic distributions.A possible explanation is the two-step

generation process, where the first step is realized in configuration space and the second step is realized in canonical conjugated space.

The whole pattern is generated two-step by two-step.

The only way to keep coherence between a distribution and its Fourier transform that are both generated step by step is to generate them in pairs.

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ConclusionFundament

Quantum logicBook modelCorrelation vehicle

Main featuresFundamentally countable ⇛ QuantaEmbedded in continuum ⇛ FieldsFundamentally stochastic ⇛ Quantum PhysicsPalestra is curvedQuaternionic metric

} ⇛ Quaternionic “GR”

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ConclusionContemporary physics works (QED, QCD)But cannot explain fundamental features

Origin of dynamicsSpace curvatureInertiaExistence of Quantum PhysicsWhat photons are

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EndPhysics made its greatest misstep in

the thirties when it turned away from the fundamental work of Garret Birkhoff and John von Neumann.

This deviation did not prohibit pragmatic use of the new methodology.

However, it did prevent deep understanding of that technology because the methodology is ill founded.

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Logic SystemsLattices, classical logic and quantum logic

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Logic – Lattice structureA lattice is a set of elements that is closed for the

connections ∩ and ∪. These connections obey:

The set is partially ordered. With each pair of elements belongs an element , such that and .

The set is a ∩ half lattice if with each pair of elements an element exists, such that .

The set is a ∪ half lattice if with each pair of elements an element exists, such that .

The set is a lattice if it is both a ∩ half lattice and a ∪ half lattice.

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Partially ordered set The following relations hold in a lattice:

• has a partial order inclusion ⊂:

a ⊂ b ⇔ a ⊂ b = a• A complementary lattice

contains two elements and with each element a an complementary element a’

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Orthocomplemented latticeContains with each element an element such that:

Distributive lattice

Modular lattice

Classical logic is an orthocomplemented modular lattice

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Weak modular latticeThere exists an element such that

where obeys:

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AtomsIn an atomic lattice

is an atom

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LogicsClassical logic has the structure of an orthocomplemented distributive modular and atomic lattice.

Quantum logic has the structure of an orthocomplented weakly modular and atomic lattice.

Also called orthomodular lattice.

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Hilbert space

The set of closed subspaces of an infinite dimensional separable Hilbert space

forms an orthomodular latticeIs lattice isomorphic to

quantum logic

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Hilbert logicAdd linear propositions

Linear combinations of atomic propositionsAdd relational coupling measure

Equivalent to inner product of Hilbert spaceClose subsets with respect to realational

coupling measure

Propositions ⇔ subspacesLinear propositions ⇔ Hilbert vectors

Back

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Superposition principle

Linear combinations of linear propositions are again linear

propositions that belong to the same Hilbert logic system

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IsomorphismLattice isomorhic

Propositions ⇔ closed subspacesTopological isomorphic

Linear atoms ⇔ Hilbert base vectors

The Hilbert Book Model

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