The Hilbert Book Model

The Hilbert Book ModelA simple model of fundamental physicsBy J.A.J. van Leunenhttp://www.e-physics.euPart two

The Hilbert Book Model contains my personal view on the fundaments of physics. It is an unorthodox and controversial view. The first ideas rose during my studies in the sixties and kept dormant during my career in high tech industry. After my retirement I restarted this thread. The paper that describes the model can be found at http://www.e-physics.eu/PhysicsOfTheHilbertBookModel.pdf1Quaternionic physics

How to use Quaternionic Distributions andQuaternionic Probability Density Distributions

The model concerns quaternionic physics rather than complex physics. 2The 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 modelThe complex Hilbert space model is considered as an abstraction of the quaternionic Hilbert space modelThis can only be done properly in the right circumstances3

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. It means that the blur will also occur in these lower dimension models and both lower dimension models will describe affine spaces.

3Continuous Quaternionic DistributionsDifferentialCouplingContinuityequation}{Two equationsThree kinds4

Quaternions can be interpreted as the combination of a (real) scalar and an (imaginary) 3D vector.The product splits in five terms.Continuous quaternionic distributions can be differentiated. We use the quaternionic nabla in order to simplify notation. Equations can be split in a real part and an imaginary part. 4Field equationsIs zero ?5

5QPDDsScalar fieldVector fieldDensity distributionCurrent density distributionCurrent density distributionDensity distribution6

QPDDs are special kinds of quaternionic distributions. They describe density distributions. Continuous quaternionic distributions describe potential fields. 6Coupling equation Flat space7

Applying differentiation to normalized quaternionic distributions reveals the coupling equation.The coupling factor stands for coupling energy.7Coupling in Fourier space8

8Dirac equation QpatternQPDDApproximately flat space9

The Dirac equation uses spinors and matrices. It can be split into two quaternionic equations.The Dirac equation uses a left handed and a right handed function.9Dirac matrices10

The matrices combine into 4X4 matrices.10PalestraCollection of QpatchesEmbedded in continuum11

The Palestra consists of the embedding continuum, which is covered by a set of Qpatches. 11Sign flavorsSign flavorsDiscrete symmetries12Continuous quaternionic distributions exist in 16 sign flavors. When restricted to positive progression 8 sign flavors result. QPDDs exist in 8 sign flavors. When two QPDDs couple then an elementary particle results. In this way 8x8=64 types of particles are possible.12Bundles of sign flavorsMostly continuous functions are functions that are continuous apart from a finite number of singular pointsMostly continuous quaternionic functions exist in 16 different sign flavorsMostly continuous quaternionic functions exist in bundles that contains all sign flavors of that functionSuch bundles are called sign flavor bundles.

13Mostly continuous functions are functions that are continuous apart from a finite number of singular points.Mostly continuous quaternionic functions exist in 16 different sign flavors.Mostly continuous quaternionic functions exist in bundles that contains all sign flavors of that function.Such bundles are called sign flavor bundles.

13Reference sign flavorThe curvature of the parameter space of the sign flavor bundle is flatThe parameter space is spanned by a quaternionic number systemQuaternionic number systems exist in 16 sign flavorsThe reference version of the sign flavor bundle has the same sign flavor as the parameter space of the bundle has14The curvature of the parameter space of the sign flavor bundle is flat.The parameter space is spanned by a quaternionic number system.Quaternionic number systems exist in 16 sign flavors.The reference version of the sign flavor bundle has the same sign flavor as the parameter space of the bundle has.

14Space HypothesesOur living space can be represented by a field that is represented by a sign flavor bundleThat field is the PalestraEverything in universe consists of features of the Palestra15Our living space can be represented by a field that is represented by a sign flavor bundle.That field is the Palestra.Everything in universe consists of features of the Palestra.

15Constituents of the PalestraElementary particles are recurrent singularities in the Palestra that represent very short lived couplings of two versions that belong to the sign flavor bundle.Other fields are representing averaged effects or oscillations of the Palestra.

16Elementary particles are recurrent singularities in the Palestra that represent very short lived couplings of two versions that belong to the sign flavor bundle.Other fields are representing averaged effects or oscillations of the Palestra.

16Fermions and bosonsOne of the sign flavors of the Palestra is the reference sign flavor

Coupling of a sign flavor to the reference flavor produces fermions

Other couplings produce bosons17One of the sign flavors of the Palestra is the reference sign flavorCoupling of a sign flavor to the reference flavor produces fermionsOther couplings produce bosons

17Alternative of the Higgs mechanismThe bundle takes care of the fact that space curvature couples between fermions and bosons

This effect implements the action that is supposed to be implemented by the Higgs mechanism

18The bundle takes care of the fact that space curvature couples between fermions and bosonsThis effect implements the action that is supposed to be implemented by the Higgs mechanism

18Palestra and particle movement pathThe sign flavor determines the sign of the Frenet-Serret frame vectors. The embedded continuum and the embedded particle have different sign flavors.This difference is the reason that the embedded particle and the embedding continuum move in different directions.That is why the embedding process causes singularities in the embedding continuum

19Differential geometry offers formulas for a constant speed path in curved space. This path is characterized by three mutually perpendicular vectors, the speed, the curvature and the curl.The direction of the vectors depend on the reigning discrete symmetry set, which is also called sign flavor. Elementary particles represent the coupling of two fields that each have their own sign flavor. This means that the constant speed curves will differ.19Duration2020Tangent and principle normal21The first two vectors are the tangent unit vector and the principle normal unit vector.21Binormal unit vector22The third vector is the binormal unit vector and is obtained via the external vector product of the other two unit vectors.It will switch sign with the handedness of the sign flavor.22Path characteristics23Apart from its unit speed the path is characterized by its curvature and its torque.23Constant speed pathSince massless information carriers, such as photons move with constant speed c, they travel along a constant speed curve. Also particles can move along a constant speed curveThe infinitesimal particle path step is the sum of all hops that constitute the micro-path.The hops can also be divided in three mutually perpendicular stepsThe major step // tantrixThe intermediate step // principal normalThe minor step // binormalThe signs of these sub-steps are determined by the sign flavor

24Massless objects move with constant speed c.. As a consequence in curved space they move along a constant speed curve.The Qpatches of massive particles can also move in a constant speed curve. The Qpatch steps are formed by the sum of the hops that constitute the particles micro-path. Like the constant speed path of the Qpatches, the hops can be divided in three steps that are parallel to the corresponding Frenet Serret vectors.24CompositesEntanglement25The binding mechanism of composites is based on modularization and entanglement.25Entanglement26The correlation mechanism also plays an important role in the generation of composites and the entanglement of particles into subsystems and systems. Entanglement means that the quantum function of the system or subsystem can be described as the superposition of the quantum state functions of the constituting elementary particles. For entanglement it is not necessary that the system or subsystem forms a connected composite. 26BindingThe 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.

27Displacements in configuration space are represented in Fourier space by the phase of a normed quaternion.27GeoditchesIn 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.

28Geoditches keep the oscillating constituents together.28Pauli 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 and {(-x)+(x)=(x)+(-x)}(-x)=(x) and for fermions that the corresponding part of the (sub)system quantum state function changes sign. For all and {(-x)+(x)=-(x)-(-x)}(-x)=-(x)

This conforms to the Pauli principle.

29This conforms to the Pauli principle. It also indicates the correlation mechanism, which controls the entanglement, takes care of the fact that if one of these two twin components exposes any of its properties (e.g. its spin) that it has IMMEDIATE effect on the properties of the other component.The correlation mechanism supports the activity of the Pauli exclusion principle inside entangled systems. In this way non-locality becomes noticeable.29Non-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.

30Entanglement is often related to action at a distance. The Pauli principle plays a crucial role in these effects.30FocusIf 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 systemWhen the focus shifts to one or more of the constituents, then the entanglement gets at least partly brokenAfter that the separated particles and the resulting entangled system act as separate swarms31Entanglement can be broken by shifting focus to one or more of the constituents.31CompositesBinding32The binding mechanism of composites is based is effectuated by space curvature.32Binding mechanismWhen a step stone is involved in an entangled system, then it produces a singularity at the instance that it is used. The influence of that singularity spreads over the embedding continuum in the form of a wave front that folds and thus curves this continuumThe traces of these Qtargets mark paths where the wave fronts dig pitches into the continuum that combine into channels that act as geodesics.33Traces of Qtargets mark paths where the wave fronts dig pitches into the continuum that combine into channels that act as geodesics.

33CompositesThe effect of modularization34The binding mechanism of composites is based on modularization and entanglement.34ModularizationModularization 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.35Modularization is a very powerful influencer35ModularizationElementary 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.

36Elementary particles can be considered as the lowest level of modules. All composites are higher level modules.36ComplexityPotential 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.37Relational complexity is the ratio of the number of actual relations divided by the number of potential relations.

37Relations and interfacesModules connect via interfaces. Relations that act within modules are hidden from 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.

38Physics is based on relations. Quantum logic is a set of axioms that restrict the relations that exist between quantum logical propositions. Interfaces are collections of relations that are used by interactions.

38Types 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.

39Cyclic interactions bind the corresponding modules together. 39Modular 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

40All composites are modular systems40Binding in sub-systems41The binding factor is the total energy of the sub-system minus the sum of the total energies of the separate constituents.

41

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.

42With intelligent modularization, evolution switched to a higher acceleration.42QuantaThe noise of low dose imaging

Low dose X-ray imaging Film of cold cathode emission 43Physical fields and cosmology are the subjects of large scale physics. The theory is based on quaternionic fluid dynamics.43Gamma quanta noise44

Low dose X-ray image of the moonhttp://en.wikipedia.org/wiki/File:Moon_in_x-rays.gifAn image of the moon as seen in X-rays from X-ray fluorescence initiated by solar X-ray flux. Astronomy picture of the day caption: "This x-ray image of the Moon was made by the orbiting ROSAT (Rntgensatellit) Observatory on June 29, 1990. In this digital picture, pixel brightness corresponds to x-ray intensity. Consider the image in three parts: the bright hemisphere of the x-ray moon, the darker half of the moon, and the x-ray sky background. The bright lunar hemisphere shines in x-rays because it scatters x-rays emitted by the sun. The background sky has an x-ray glow in part due to the myriad of distant, powerful active galaxies, unresolved in the ROSAT picture but recently detected in Chandra Observatory x-ray images. The dark side of the Moon's disk shadows this X-ray background radiation coming from the deep space. But why isn't the dark half of the moon completely dark? New Chandra results also suggest that a few x-rays only seem to come from the shadowed lunar hemisphere. Instead, they originate in Earth's geocorona or extended atmosphere which surrounds the orbiting x-ray observatories."44Shot noise45

http://en.wikipedia.org/wiki/Shot_noise Shot noiseis a type ofelectronic noisewhich originates from thediscrete natureof electric charge. The term also applies to photon counting in optical devices, where shot noise is associated with theparticle natureof light.45Large scale physicsLarge scale fluid dynamics46Physical fields and cosmology are the subjects of large scale physics. The theory is based on quaternionic fluid dynamics.46Physical fields-1SHF wave modulationsPhotonGluon

Energy quanta

SHF wave potentialsElectromagnetic fieldGravitation fieldharmonic47}Physical fields comprise photons, gluons, the gravitation field and the electromagnetic field.The gravitation field represents the influence of the masses that form the sources of the field.The electromagnetic field represents the influence of the electric charges that form the sources of the field.

47Physical fields-2Fields from step stone distributionsScalar step stone density distribution & Vector hop density distributionQuaternionic quantum state functionQPDDQuaternionic Probability Density DistributionsQuaternionic distributionsCharges are preserved48Quaternionic quantum state functions are QPDDs that describe building blocks or composites of building blocks.

QPDDs describe the density of coherent distributions of discrete objects. They also describe the current density distribution of these objects.

48Inertia-1Inertia is implemented via the embedding continuum

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

49The influence from distant particles on the local situation results in a uniform background field that is omnipresent. This field acts as the continuum that embeds the particles.49Omnipresent Background FieldAll particles emit a contribution to the omnipresent background field

The largest contribution to the omnipresent background field is delivered by the set of most distant particles50The largest contribution to the omnipresent background field is delivered by the set of most distant particles.50Inertia-2Potential fields of distant particlesEverywhere present background field51The influence from distant particles on the local situation results in a uniform background field that is omnipresent. Denis Sciama indicates that this field is related to the graphical constant G. A constant uniform speed corresponds to a uniform vector field. An acceleration goes together with an extra field. 51Inertia-352The extra field counteracts the acceleration.

52Inertia-4SmallSmallRepresents influence of distant particles53When the investigation starts from the other side via the coupling equation, then its appears that the left side term poses the same influence as the mirrors of the quantum state functions of distant particles.53Continuity equationGauss54The integral balance equation reveals the real part of the differential continuity equation. Gauss showed the equality of the surface and the volume integral.54Inversion surfacesInversion surface55The full integral continuity equation also contains a surface integral.The criterion that this term is zero defines a corresponding inversion surface.

55CompartmentsuniverseHuge BHBlack holesBlack holesBlack holesBlack holesCompartmentsBH densest packagingHuge BH s tart of new episodeNever ending storyMerge56Black holes indicate places where universe returns to its natal state. That natal state is characterized by a densest packaging of matter. The inversion surfaces divide universe in compartments. A black hole within the compartment sucks all matter that exists inside the compartment. Compartments may merge. When a very large black hole has grown and finally passives, then it may become the start of a new episode of this compartment.This makes the history of the cosmos a never ending story.56History of CosmologyBlack hole represents natal state of compartmentBlack holes suck all mass from their compartment An instable passivized huge black hole represents start of new episode of its compartmentDriving force is enormous mass present outside compartment expansionWhole universe is affine space

Result is never ending story57The universe is an affine space. The enormous amount of mass that consists outside a compartment causes the expansion of space inside the compartment. This is the driving force behind the mechanism of the never ending story.

57GravitationPythagorasMinkowskiFlat spaceCurved spacec dtdrc d16 partial derivatives5858Metric59The use of the quaternionic metric avoids the need for using tensors

59Elementary particlesThe primary building blocks60Elementary particles are the primary building blocks of nature.60Sign flavorsSign flavorsDiscrete symmetries61Continuous quaternionic distributions exist in 16 sign flavors. When restricted to positive progression 8 sign flavors result. QPDDs exist in 8 sign flavors. When two QPDDs couple then an elementary particle results. In this way 8x8=64 types of particles are possible.61Spin62Spin is one of the properties of elementary particles. It is indicated as half integer or full integer. Fermions have half integer spin. Fermions couple to the reference Qpattern. Bosons have integer spin. Bosons have integer spin. The spin of a composite equals the sum of the spins of its components.

62Sign of spinThe micro-path can be walked in two directionsThis determines the sign of spin63The micro-path can be walked in two directionsThis determines the sign of spin

63Electric 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.

64Electric charge is a property of massive elementary particles. Its value depends on how many directions change and in what direction the change takes place. Per sign switch an increase/decrease one third of a full charge is added. Further, when the handedness switches, then the sign of the charge is switched as well. 64Color 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.

65Color charge is related to the three main directions of anisotropy. These directions are coded with colors: red, green and blue. Isotropic fields are black or white. They have neutral color.65Total energy66For elementary particles the total (internal) energy equals the rest mass.66Computing total energy67The total energy can be computed from the quantum state function.67Leptons68Neutrinos are treated separately.

68Quarks69Quarks have an anisotropic quantum state function. They couple to the reference Qpattern. As a consequence quarks have color charge.69Reverse quarks70Reverse quarks have an isotropic quantum state function. They couple to an anisotropic Qpattern. As a consequence reverse quarks have color charge.

70Massive BosonsFermions couple their quantum state function to the standard discrete symmetry version of the background field. Bosons couple their quantum state function to one of the non-standard discrete symmetry versions of the background field.71Fermions couple to the space in which we live. Bosons couple to other sign flavors of the space in which we live71Higgs mechanism?All eight discrete symmetry versions of the background field share the same real part. With other words the curvature of the eight symmetry versions is exactly identical! Thus fermions and massive bosons live in the same gravitation potential.This coupling of versions implements the same task as the Higgs mechanism is supposed to implement

72The supposed task of the Higgs mechanism is to provide mass to massive bosons.In the HBM that task is implemented by the coupling between the sign flavors of the space in which we live.72W-particles73W-particles are two-sided anisotropic. Thus they are multi-colored. They have electric charge e or -e.73Z-particles74Z-particles are two-sided anisotropic. Thus they are multi-colored. Their electric charge is zero.74Neutrinos75Neutrinos are fermions with charge zero. However, also corresponding bosons exist.75Color confinementThe color confinement rule forbids the generation of individual particles that have non-neutral color charge

76The Hilbert Book Model treats color confinement as a strict rule.76Color confinementColor confinement forbids the generation of individual quarks

Quarks can appear in hadrons

Color confinement blocks observation of gluons77Due to the color confinement rule no individual quarks can be generated.Thus quarks can only appear combined in hadrons.77Photons & gluons78Photons and gluons are not coupled.78Photons & 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.

79Photons and gluons are not coupled. They are not particles. They are not represented by a Qpattern.Instead photons and gluons are modulations of wave fronts that are emitted by building blocks.79Fundamental particlesDue to color confinement some elementary particles cannot be created as individualsQuarks can only be created combined in hadronsFundamental particles form a category of particles that are created in one integral actionThe color charge of fundamental particles is neutral

80Color confinement restricts quarks from appearing as individual particles.80Other subjects81Other things81Dual space distributions82Functions whose Fourier transform have the same shape are dual space distributions.82Why 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.83Question is not yet answered83ConclusionFundamentQuantum logicBook modelCorrelation vehicleMain featuresFundamentally countable QuantaEmbedded in continuum FieldsFundamentally stochastic Quantum PhysicsPalestra is curvedQuaternionic metric} Quaternionic GR84The HBM has a threefold fundament.It unifies quantum physics and gravitation.It is quaternionic physics and introduces quantum fluid dynamics.

84ConclusionContemporary physics works (QED, QCD)But cannot explain fundamental featuresOrigin of dynamicsSpace curvatureInertiaExistence of Quantum PhysicsWhat photons are85Contemporary physics cannot explain fundamental features85EndPhysics 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.

86

Contemporary physics is ill founded.86Fur Elise (by Beethoven)BeethovenYouTube Audio LibraryClassical151073.05