Features of the Hilbert Book Model

This page is renewed on 17 April 2013

The stuff from which we are made

The medium in which light propagates is space. This space can curve. The curvature is not static. So, this space moves. Its behavior can be analyzed by a kind of fluid dynamics. Let us call this method quantum fluid dynamics. It differs from conventional fluid dynamics in the medium that is treated. In conventional fluid dynamics this is a gas or a fluid. Fluid dynamics concerns density distributions and currents. In quantum fluid dynamics these are space density distributions and space current density distributions. They can be combined in quaternionic distributions, where the real part is the space density distribution and the imaginary part is the space current density distribution.

Quantum state functions are probability amplitude distributions. They can be specified as complex functions or as quaternionic functions. In the last case they fit the purpose of quantum fluid dynamics. In fact they are a special type of quaternionic distributions. The curvature of their parameter space is defined by a quaternionic distance function that has a flat parameter space. That parameter space is formed by the rational quaternions. With other words quaternionic quantum state functions describe the flow of space. Quantum state functions characterize the state of particles. Light is nothing else than oscillating space. It is constituted from the same stuff as the quantum state function of particles. Thus light is an oscillating probability amplitude distribution.

In the quaternionic format of the Dirac equation the quaternionic differential {ψ^x, ψ^y} of the quantum state function ψ acts as a drain. This drain is coupled to a source. The source is a second probability amplitude distribution φ. The coupling factor m takes the role of mass characteristic.

∇ψ^x = m ψ^y

In quaternionic format the Dirac equation is a quaternionic continuity equation. (See Wiki)

The drain compresses the local space. As a consequence in the neighborhood of the coupling the space gets curved. The Dirac equation describes what happens for the electron. Every elementary particle has its own coupling equation. Free probability amplitude distributions must oscillate. They are photons or gluons.

The coupling is characterized by four properties: coupling factor, electric charge, spin and color charge. Color charge relates to the direction of anisotropy. These properties act as sources of fields. These are known as physical fields. Their charges are located at the position of the particle and they are preserved. These rather stationary fields move with the particle and have a fundamentally different nature than the primary probability amplitude distributions.

In quantum fluid dynamics the quaternionic probability amplitude distributions act on their own parameter space. The shared parameter space of all quaternionic probability amplitude distributions comprises the whole universe. It is the arena where everything occurs. In the HBM this arena is called Palestra.

The overview of the involved objects is treated in the paper:

On the hierarchy of objects

HBM_Slides

HBM_Presentation (26Mb)

Hilbert logic

Hilbert logic slides

Hilbert logic slide comments

Deep Field Theory

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The author’s e-print archive is at

http://vixra.org/author/j_a_j_van_leunen

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Manuscript

You can download this manuscript free of charge

You may wish to buy a printed copy of the manuscript.

Abstract of the manuscript

The fundaments of quantum physics are still not well established. This book tries to find the cracks in these fundaments and explores options that were left open. This leads to unconventional solutions and a new model of physics.

In order to optimize self-consistency, the model is strictly based on the axioms of traditional quantum logic. Traditional quantum logic is lattice isomorphic to the set of closed subspaces of an infinite dimensional separable Hilbert space. It means that the separable Hilbert space can be used as the realm in which quantum physics will be modeled. However, this would result in a rather primitive model. It can easily be shown that this model cannot implement dynamics and does not provide fields.

First, the model is extended such that it can represent fields. This results in a model that can represent a static status quo of the whole universe. The most revolutionary introduction in the Hilbert Book Model is the representation of dynamics by a sequence of such static models in the form of a sequence of extended separable Hilbert spaces.

At this point the Hilbert Book Model already differs significantly from conventional physics. Conventional quantum physics does not strictly hold to the axioms of traditional quantum logic, handles fields in a different way and implements dynamics differently.

Conventional quantum physic stays with complex state functions [1]. In contrast the HBM also explores the full potential of quaternionic state functions. As a consequence the HBM offers two different views on the undercrofts of quantum physics. The complex state function offers a wave dynamics view. The quaternionic state function opens a fluid dynamics view. The fluid dynamics view is unprecedented.

Since the switch from complex to quaternionic quantum state function does not affect physical reality, the two views will both be correct

The quaternionic state functions enable the exploration of the geometry of elementary particles in which quaternionic sign flavors play an important role.

In the HBM elementary particles and physical fields are generated via the coupling of two sign flavors of the same quaternionic probability amplitude distribution (QPAD).

The quantum fluid dynamic view opens insight in the effect of the state functions on space curvature.

Hilbert logic

On the hierarchy of objects

HBM_Slides

HBM_Presentation (26Mb)

Q-FORMULÆ

Essentials of the Hilbert Book Model

Slide presentation

Table of elementary particles

Quanta

Hilbertlogica (Dutch!)

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HBM key points

· Nature is ruled by the axioms of traditional quantum logic.

· Quantum physics can be performed in the realm of a separable Hilbert space.

· Quantum state functions are complex or quaternionic probability amplitude distributions.

· A quantum state function solves the problem raised by an over-determined set of linear equations.

· Quantum state functions link a countable set of particles via a corresponding eigenvector of the particle location operator to observable values in a continuum.

· This continuum corresponds to the shared affine versions of the parameter space of all quantum state functions.

· This space is called Palestra and it is represented by the eigenspace of an operator in the Gelfand triple of the Hilbert space.

· Nature steps universe wide from one static status quo to the next.

· This static status quo can be represented by a sandwich consisting of a separable Hilbert space, its Gelfand triple and a set of quantum state functions.

· The currents inside the static quaternionic probability amplitude distributions (QPAD’s) that are contained within the HBM pages, assure continuity and glue the Hilbert spaces together.

· Quaternionic quantum state functions transfer linear equations of motion into balance equations.

· This converts quantum wave dynamics into quantum fluid dynamics.

· A restricted version of the balance equation describes 56 elementary particles and 8 elementary waves.

· These restricted balance equations couple two probability amplitude distributions. One is the quantum state function.

· The restriction means that both probability amplitude distributions must be sign flavors of the same quaternionic distribution.

· The coupled quantum state functions compress the parameter space (Palestra) in the direct environment of the particle.

· The coupling is characterized by 4 characteristics: coupling factor, electric charge, spin, color charge.

· Apart from color charge these properties act as sources of physical fields.

· The primary coupling properties are conserved in higher order couplings.

The restricted balance equation for quantum state function ψ :

∇𝜓=m 𝜑

generates particle: { 𝜓 , 𝜑 }.

These QPAD’s are sign flavors of the same base QPAD .

∇ is the quaternionic nabla. m is the coupling strength.

For fermions 𝜑 has the sign flavor of the parameter space.

What image intensifiers reveal

At low dose rates it becomes apparent that radiation is not built from waves, but from separate quanta that move in un-sharp corridors (clouds), which may be shaped as waves.

A short film of the output of an X-ray image intensifier made at a very low dose.

Provided by Philips Healthcare

The pixel size is about 200μm
The number of pixels is about 500 * 600
The average number of X-ray quanta per pixel per frame in the mid gray area is circa 1
The range inside these picture is about 20
The direct radiance is about 5 quanta per pixel per frame
The dark regions get <<1 quanta per frame
The number of pictures is 33

Other pictures:

http://en.wikipedia.org/wiki/File:Moon_in_x-rays.gif . Low dose X-ray image of the moon.

http://www.youtube.com/watch?v=U7qZd2dG8uI ; Hail storm. Warning, this is NOT a video of an external object. It is constructed by coupling two night vision goggles. There is no input image. What is shown is cold emission of the photo cathode of the first goggle at different temperatures.

http://en.wikipedia.org/wiki/Shot_noise Very low dose photos.

The HBM states that everything in nature is constituted from quaternionic probability amplitude distributions (QPAD's). Photons and gluons are themselves free (oscillating) QPAD's. Elementary particles are constituted by the coupling of two QPAD's. QPAD's are fields. All other physical fields are derived from the couplings of QPAD's.

QPAD's describe the density distributions of carriers and the density distributions of the currents of these carriers. The density of the carriers is moving and the movement can be an oscillation. The density distribution can have the form of a wave but except for photons and gluons it does not need to oscillate.

The carriers can be interpreted to be tiny patches of the parameter space of the distributions. They represent the lowest level of objects that exist in nature. They represent locations where the owner of the QPAD can be detected. They are the objects that produce the spots in the image that is produced by an image intensifier in low radiation dose conditions. So what the observer of the intensified image sees is a hail storm of impinging carriers and no radiation wave.

It is one of the experiments that directly reveal the existence and some of the characteristics of (quaternionic) probability amplitude distributions.

Elementary particles

Elementary particles are constituted by the coupling of two Qpatterns that belong to the same generation. One of the Qpatterns is the quantum state function of the particle. The other Qpattern implements inertia. Apart from their sign flavors these constituting Qpatterns form the same quaternionic distribution. However, the sign flavor must differ and their progression must have the same direction. This results in 56 elementary particle types, 56 anti-particle types and 8 non-particle types. The coupling has a small set of observable properties: coupling strength, electric charge, color charge and spin. The coupling affects the local curvature of the involved Palestras.

Qpatterns that belong to the same generation have the same shape. The difference between the coupling partners resides in the discrete symmetry sets. Thus the properties of the coupled pair are completely determined by the sign flavors of the partners.

HYPOTHESIS: If the quaternionic quantum state function of an elementary particle couples to a local piece of the reference integral two-stage QPAD, then the particle is a fermion, otherwise it is a boson. For anti-particles the quaternionic conjugate of the reference integral two-stage QPAD must be used. Non-coupled Qpatterns are bosons.

The coupling of two Qpatterns is controlled by a coupling equation

∇ψ=m φ

This equation is equivalent to a quaternionic differential continuity equation.

∇ψ=ϕ

And it is equivalent to a quaternionic differential equation.

ϕ=∇ψ

Here ∇ is the quaternionic nabla. ψ, φ and ϕ are Qpatterns that belong to the same generation.

Photons and gluons belong to a generation that does not couple.

In the standard model the eight gluons are constructed from superpositions of these six base gluons.

Coupling Qpatterns

Qpatterns are not static. Instead they oscillate. The interpretation of this oscillation is that on the average the Qpattern keeps its location and it keeps its size. Thus an outbound move must be followed by an inbound move. The zero order temporal frequency of this oscillation is set by the progression step. In this light coupling means the synchronization of the involved Qpatterns. The sharp distance function takes care of the slower part of the dynamics. The synchronization can involve oscillations that are in-phase and oscillations that are in anti-phase. These criterions may act isotropic or they may hold in one or two dimensions.

The coupling uses pairs of two sign flavors. Thus the coupling equation runs:

Corresponding anti-particles obey

The anti-phase couplings must use different sign flavors. In the figure below acts as the reference sign flavor.

Eight sign flavors
(discrete symmetries)
Colors N,R,G,B,R ̅,G ̅,B ̅, W
Right or Left handedness R,L

Figure 1: Sign flavors

Elementary particle properties

Spin

Spin relates to the fact whether the coupled Qpattern is the reference Qpattern. Each generation has its own reference Qpattern.

Electric charge

Electric charge depends on the difference and direction of the base vectors for the Qpattern pair. Each sign difference stands for one third of a full electric charge. Further it depends on the fact whether the handedness changes. If the handedness changes then the sign of the count is changed as well.

Color charge

The color charge of the reference Qpattern is white. The corresponding anti-color is black. The color charge of the coupled pair is determined by the color of its members.

Mass

Mass is related to the number of involved Qpatches.

Samples

With these ingredients we can look for agreements with the standard model.

Leptons and quarks

According to the Standard Model both leptons and quarks comprise three generations. Neutrinos will be treated separately.

Pair	s-type	e-charge	c-charge	Handedness	SM Name
	fermion	-1		LR	electron
	Anti-fermion	+1		RL	positron
	fermion	-1/3		LR	down-quark
	Anti-fermion	+1/3		RL	Anti-down-quark
	fermion	-1/3		LR	down-quark
	Anti-fermion	+1/3		RL	Anti-down-quark
	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
	fermion	+2/3		RR	up-quark
	Anti-fermion	-2/3		LL	Anti-up-quark
	fermion	+2/3		RR	up-quark
	Anti-fermion	-2/3		LL	Anti-up-quark

The generations contain the muon and tau generations of the electrons, the charm and top versions of the up-quark and the strange and bottom versions of the down-quark.

W-particles

W-particles have indiscernible color mix. and are each other’s anti-particle.

Pair	s-type	e-charge	c-charge	Handedness	SM Name
	boson	-1		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

Z-candidates

Z-particles have indiscernible color mix.

Pair	s-type	e-charge	c-charge	Handedness	SM Name
	boson	0		LL
	boson	0		LL
	boson	0		RR
	boson	0		RR

Neutrinos

Neutrinos are fermions and have zero electric charge. They are leptons, but they seem to belong to a separate low-weight family of (three) generations. They couple to a Qpattern that has the same sign-flavor. They have a small rest mass.

Other particles

When we include photons, gluons and neutrinos, then apart from their generations we can identify 35 particle types that conform to corresponding SM particles. A multitude of pairs do not conform to an SM-particle. They are all bosons. Some are neutral and others have electric charge. They all have rest mass.

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[1] The HBM uses the name state function for the quantum state of an object or system rather than the usual term wave function because the state function may characterize flow behavior as well as wave behavior.

[2] The notion of “sign flavor” is used because for elementary particles “flavor” already has a different meaning.

[1] The notion of “sign flavor” is used because for elementary particles “flavor” already has a different meaning.