The Hilbert Book Mode l

The Hilbert Book Model A simple model of fundamental physics By J.A.J. van Leunen Part two http://www.e-physics.eu

Quaternionic physics How to use Quaternionic Distributions and Quaternionic Probability Density Distributions

The HBM is a quaternionic model • The 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 model • This can only be done properly in the right circumstances

Continuous Quaternionic Distributions • Quaternions c = • Quaternionic distributions • Differentialequation Two equations { Three kinds Differential Coupling Continuity } equation

Field equations • = Spin of a field: Is zero ?

QPDD’s • Quaternionic distribution • Quaternionic Probability Density Distribution Scalar field Vector field Density distribution Density distribution Current density distribution Current density distribution

Coupling equation • Differential • Integral and φ are normalized = total energy = rest mass + kinetic energy Flat space

Coupling in Fourierspace • 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.

Dirac equation Approximately flat space • and are Dirac matrices • Spinor • Split • In quaternion format Qpattern QPDD

Dirac matrices

Palestra • Curved embedding continuum • Represents universe The Palestra is the place where everything happens Embedded in continuum Collection of Qpatches

Sign flavors L • Coupling equation • Coupling occurs between pairs • Colors x, y • , W • Right and left handedness • R,L Sign flavors Imaginary part is the Reference QPDD Discrete symmetries

Bundles of sign flavors • Mostly 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.

Reference sign flavor • The 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

Space Hypotheses • Our 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

Constituents of the Palestra • Elementary 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.

Fermions and bosons • One 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 bosons

Alternative of the Higgs mechanism • The 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

Palestra and particle movement path • The 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

Duration • At any point in the Palestra and in any direction a path can be started • Also Qpatches that represent particles follow such paths • In the Palestra the “length” of the quaternionic path is the coordinate time duration • is the duration in proper time ticks. is the progression parameter. It equals proper time. is the coordinate time.

Tangent and principle normal • We investigate constant speed curves in the imaginary Palestra. • is the imaginary part of. is the tangent unit vector. is the principle normal unit vector.

Binormalunit vector • Since are and perpendicular. • is the binormal unit vector • The sign of T, N, and B depends on the discrete symmetry set of the involved field

Path characteristics is the curvature. is the torque.

Constant speed path • Since 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 curve • The 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 steps • The major step // tantrix • The intermediate step // principal normal • The minor step // binormal The signs of these sub-steps are determined by the sign flavor

Composites Entanglement

Entanglement • The correlation mechanism manages entanglement • At 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 normalized • Entanglement acts as a binding mechanism

Binding • The 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.

Geoditches • In 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.

Pauli principle • If 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.

Non-locality • Action at a distance cannot be caused via information transfer • Non-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.

Focus • If 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 gets at least partly broken • After that the separated particles and the resulting entangled system act as separate swarms

Composites Binding

Binding mechanism • When 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 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.

Composites The effect of modularization

Modularization • Modularization is a very powerful influencer. • Together with the corresponding encapsulation it reduces the relational complexityof the ensemble of objects on which modularization works. • The encapsulation keeps most relations internalto 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.

Modularization • Elementary particles can be considered as the lowest level of modules. • All composites are higher level modules. • Modularization uses resources efficiently. • When sufficient resourcesin the form of reusable modules are present, then modularization can reach enormous heights. • On earth it was capable to generate intelligent species.

Complexity • Potential 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 complexityof 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 complexityis the ratio of the number of actual relations divided by the number of potential relations.

Relations and interfaces • Modules 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.

Types of physical interfaces • Interactions run via (relevant) relations. • Inboundinteractions 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.

Modular systems • Modular (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

Binding in sub-systems • Let represent the renormalized superposition of the involved distributions. • is the total energy of the sub-system • The binding factor is the total energy of the sub-system minus the sum of the total energies of the separate constituents.

Random versus intelligent design • At 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.

Quanta The noise of low dose imaging Low dose X-ray imaging Film of cold cathode emission

Gamma quantanoise Low dose X-ray image of the moon

Shot noise

Large scale physics Large scale fluid dynamics

Physical fields-1 harmonic • SHF wave modulations • Photon • Gluon • Energy quanta • SHF wave potentials • Electromagnetic field • Gravitation field }

Physical fields-2 • Fields from step stone distributions • Scalar step stone density distribution & Vector hop density distribution • Quaternionic quantum state function • QPDD • Quaternionic Probability Density Distributions • Quaternionic distributions • Charges are preserved

Inertia-1 • Inertia is implemented via the embedding continuum • The embedding continuum is formed by a curved background field that forms our living space

Omnipresent Background Field • All particles emit a contribution to the omnipresentbackground field • The largest contribution to the omnipresent background field is delivered by the set of most distant particles

The Hilbert Book Mode l