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A simple model of fundamental physics
By J.A.J. van Leunen
Part two
http://www.e-physics.eu
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
3
Continuous
Quaternionic Distributions
 Quaternions
𝑎 = 𝑎0 + 𝒂
c = 𝑎𝑏 = 𝑎0 𝑏0 − 𝒂, 𝒃 +
𝑎0 𝒃 + 𝑏0 𝒂 + 𝒂 × 𝒃
 Quaternionic distributions

Two
equations
Differential equation
g = 𝛻𝑓 = 𝛻0 𝑓0 − 𝛁, 𝒇 +
𝛻0 𝒇 + 𝛁𝑏0 + 𝛁 × 𝒃
Three
kinds
𝜙 = 𝛻𝜓 = 𝑚 𝜑
{
𝑔0 = 𝛻0 𝑓0 − 𝛁, 𝒇
𝐠 = 𝛻0 𝒇 + 𝛁𝑏0 + 𝛁 × 𝒃
Differential
Coupling
Continuity
}
equation
4
Field equations
 𝜙 = 𝛻𝜓
 𝜙0 = 𝛻0 𝜓0 − 𝛁, 𝜓
 𝝓 = 𝛻0 𝜓 + 𝛁𝜓0 + 𝛁 × 𝜓
Spin of a field:
𝜮𝑓𝑖𝑒𝑙𝑑 =
𝕰 × 𝝍 𝑑𝑉
𝑉
 𝕰 ≡ 𝛻0 𝝍 + 𝜵𝜓0
 𝕭≡𝜵×𝝍
 𝝓=𝕰+𝕭
𝐸≡ 𝜙 =
𝜙0 𝜙0 + 𝝓, 𝝓
= 𝜙0 𝜙0 + 𝕰, 𝕰 + 𝕭, 𝕭 + 𝟐 𝕰, 𝕭
Is zero
?
5
QPDD’s
 Quaternionic distribution
 𝑓 = 𝑓0 + 𝒇
Scalar
field
Vector
field
 Quaternionic Probability Density Distribution
 𝜓 = 𝜓0 + 𝝍 = 𝜌0 + 𝜌0 𝒗
Density
distribution
Current density
distribution
6
Coupling equation
Differential
𝜙 = 𝛻𝜓 = 𝑚𝜑

Differential Continuity Coupling
𝜙 = 𝛻𝜓
𝛻𝜓 = 𝜙
𝛻𝜓 = 𝑚𝜑
𝜓 = 𝜑
 Integral
𝜓
2
𝑉
𝜑
2
𝑑𝑉 = 1
𝑚 = total energy
= rest mass +
kinetic energy
𝑉
𝜙
𝑉
𝑑𝑉 =
𝜓 and φ
are normalized
2
𝑑𝑉 = 𝑚2
Flat space
7
Coupling in Fourier space
𝛻𝜓 = 𝜙 = 𝑚 𝜑
ℳ𝜓 = 𝜙 = 𝑚 𝜑
𝜓|ℳ 𝜓 = 𝑚 𝜓|𝜑
ℳ = ℳ0 + 𝞛
ℳ0 𝜓0 − 𝞛, 𝝍 = 𝑚 𝜑0
ℳ0 𝝍 + 𝞛𝜓0 + 𝞛 × 𝝍 = 𝑚 𝝋
2
𝜙 𝑑𝑉 =
𝑉
ℳ𝜓
𝑉
2
𝑑 𝑉 = 𝑚2
In general 𝜓 is not an
eigenfunction of operator
ℳ.
That is only true when 𝜓
and 𝜑 are equal.
For elementary particles
they are equal
apart from their difference
in discrete symmetry.
8
Dirac equation
Approximately
flat space
𝛻0 𝜓 + 𝛁𝛂 𝜓 = 𝑚𝛽 𝜓
 𝛂 and 𝛽 are Dirac matrices
 Spinor 𝜓
 Split
𝜓𝑅 = 𝜓𝐿∗ = 𝜓0 + 𝝍
• 𝛻0 𝜓𝑅 + 𝛁𝜓𝑅 = 𝑚𝜓𝐿
• 𝛻0 𝜓𝐿 − 𝛁𝜓𝐿 = 𝑚𝜓𝑅
 In quaternion format
• 𝛻𝜓 = 𝑚𝜓 ∗
• 𝛻 ∗ 𝜓 ∗ = 𝑚𝜓
Qpattern
QPDD
9
Dirac matrices
𝛻0 𝜓 + 𝛁𝛂 𝜓 = 𝑚𝛽 𝜓
𝛼1 ≡
0
−𝒊
𝒊
0
𝒊 ⟼ 𝜎1 ≡
0
1
1
0
𝛼2 ≡
0 𝒋
−𝒋 0
𝒋 ⟼ 𝜎2 ≡
0 −𝑖
𝑖 0
0 𝒌
𝛼3 ≡
−𝒌 0
𝒌 ⟼ 𝜎3 ≡
1 0
0 −1
0 1
𝛽≡
1 0
1 ⟼𝐼≡
1 0
0 1
10
Palestra
 Curved embedding continuum
 Represents universe
Embedded in
continuum
𝑄𝑝𝑎𝑡𝑐ℎ
Collection of
Qpatches
The Palestra is the place where everything happens
11
Sign flavors
 Coupling equation
 𝛻𝜓 𝑥 = 𝑚 𝜓 𝑦
 𝛻𝜓 𝑥 ∗ = 𝑚 𝜓 𝑦 ∗
 Coupling occurs between
pairs
 {𝜓 𝑥 , 𝜓 𝑦 }
 Colors x, y
 N, R, G, B, R, G, B, W
 Right and left handedness
 R,L
Sign flavors
𝝍⓪ 𝑁 𝐑
𝝍① 𝑅 𝐋
Imaginary
part
𝝍② 𝐺 𝐋
𝝍③ 𝐵 𝐋
𝝍④ 𝐵 𝐑
𝝍⑤ 𝐺 𝐑
𝝍⑥ 𝑅 𝐑
𝝍⑦ 𝑁 L
𝝍⓪
is the
Reference
QPDD
Discrete
symmetries
12
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.
13
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
14
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
15
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.
16
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
17
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
18
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
19
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
𝑑
𝑠 𝑑 =
𝑑
𝑑℘
0
=
0
𝑑℘
𝑑𝜏
𝑑𝜏
 𝑑 is the duration in proper time ticks. 𝜏 is the
progression parameter. It equals proper time. 𝑠 is the
coordinate time.
20
Tangent and principle normal
 We investigate constant speed curves in the imaginary Palestra.
 𝓡 is the imaginary part of ℘.

𝑑℘
𝑑𝑠
𝑻=
𝑑℘
𝐼𝑚
𝑑𝑠
𝐼𝑚
𝑑𝓡
= 𝑑𝑠
𝑑𝕽
𝑑𝑠
𝑑𝑻
𝑵 = 𝑑𝑠
𝑑𝑻
𝑑𝑠
𝑻 is the tangent unit vector. 𝑵 is the principle normal unit vector.
21
Binormal unit vector
 Since 𝑻 = 1 are 𝑵 and 𝑻 perpendicular.

𝑩=𝑻×𝑵
 𝑩 is the binormal unit vector
 The sign of T, N, and B depends on the discrete
symmetry set of the involved field
22
Path characteristics
𝑑𝑻
= 𝜅𝑵
𝑑𝑠
𝑑𝑵
= −𝜅𝑻 + 𝜏𝑩
𝑑𝑠
𝑑𝑩
= −𝜏𝑵
𝑑𝑠
𝜅 is the curvature. 𝜏 is the torque.
23
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
24
Entanglement
25
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
Φ = 𝛻𝜓 = 𝑚 𝜑
𝜓 and 𝜑 are normalized
Entanglement acts as a binding mechanism
26
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.
27
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.
28
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.
29
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.
30
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
31
Binding
32
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.
33
The effect of modularization
34
Modularization
 Modularization 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.
35
Modularization
 Elementary 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.
36
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 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.
37
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.
38
Types of physical interfaces
 Interactions 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 interactor.
 Cyclic interactions bind the corresponding modules
together.
39
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
40
Binding in sub-systems
 Let 𝜓 represent the renormalized superposition of the
involved distributions.
 𝛻𝜓 = 𝜙 = 𝑚 𝜑
 𝑉 𝜓 2 𝑑𝑉 = 𝑉 𝜑 2 𝑑𝑉 = 1
 𝑉 𝜙 2 𝑑𝑉 = 𝑚2
 𝑚 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.
41
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.
42
The noise of low dose imaging
Low dose X-ray imaging
Film of cold cathode emission
43
Gamma quanta noise
Low dose X-ray image of the moon
44
Shot noise
45
Large scale fluid dynamics
46
Physical fields-1
 SHF wave modulations
 Photon
𝛻𝜓 = 0
 Gluon
𝛻2𝜓 = 0
}

harmonic
𝛻𝜓 = 𝑚𝜑
Energy quanta
𝑛𝑖 𝑒𝑖 𝜓𝑖
𝑖
𝑒𝑖 = ±𝑒
 SHF wave potentials
 Electromagnetic field
 Gravitation field
𝑛𝑖 𝑚𝑖 𝜑 𝑖
𝑖
47
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
𝛻𝜓 = 𝑚𝜑
48
Inertia-1
 Inertia is implemented via the embedding
continuum
 The embedding continuum is formed by a
curved background field that forms our
living space
49
Omnipresent Background Field
All 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 particles
50
Inertia-2
Potential fields of
distant particles
 Φ0 =
𝑉
𝜓 dV
In a uniform background:
𝜓 = 𝜌0 𝑟 ; 𝜌0 is constant
Everywhere present
background field
𝜌0
 Φ0 =
𝐺=
𝑉
−𝑐 2 Φ
𝜌0 𝒗
𝑟
dV = 𝜌0
1
𝑉
𝑟
dV = 2π𝑅2 𝜌0
(Dennis Sciama, The Origin of Inertia)
; 𝚽 = Φ0 𝒗
𝑐
 𝕰 = 𝛻𝟎 𝚽 + 𝛁Φ0 = 𝚽 + 𝛁Φ0 = Φ0 𝒗
𝑐
𝚽=
𝑉
𝑐𝑟
dV = Φ 𝒗
𝑐
+ 𝛁Φ0
51
Inertia-3
 Φ0 is a scalar background field
 𝜱 is a vector background field
 𝐺 is gravitational constant
 𝕰 = Φ0 𝒗 𝑐 + 𝛁Φ0
 𝕰 ≈ Φ0 𝒗
= 𝐺𝒗
 Acceleration goes together with an extra field 𝕰
 This field counteracts the acceleration
𝑐
52
Inertia-4
 Starting from coupling equation
 𝛻𝜓 = 𝑚𝜑
 𝜓 = χ + χ0 𝒗
 χ represents particle at rest
 𝜓0 = χ0
Small
 𝝍 = χ + χ0 𝒗
 𝛻0 𝝍 = χ0 𝒗 = 𝑚𝝋 − 𝜵𝜓0 − 𝜵× 𝝍
 𝕰 ≡ 𝛻0 𝝍 + 𝜵𝜓0
Represents influence
of distant particles
53
Continuity equation
 Balance equation
 Total change within V
= flow into V + production inside V


𝑑
𝑑𝜏 𝑉
𝜌0 𝑑𝑉 =
𝛻𝜌
𝑉 0 0
𝑑𝑉 =
𝒗
𝒏𝜌0
𝑆
𝑐
𝑉
𝑑𝑆 +
𝛁, 𝝆 𝑑𝑉 +
𝑠
𝑉 0
𝑠
𝑉 0
𝑑𝑉
𝑑𝑉
Gauss
 𝝆 = 𝜌0 𝒗/𝑐
 𝜌 = 𝜌0 + 𝝆
 𝑠 = 𝛻𝜌
 𝑠0 = 2𝛻0 𝜌0 − 𝒗 𝑞 , 𝛁𝜌0 − 𝛁, 𝒗 𝜌0
 𝒔 = 𝛻0 𝒗 + 𝛁𝜌0 +𝜌0 𝛁 × 𝒗 − 𝒗 × 𝛁𝜌0
54
Inversion surfaces


𝑑
𝑑𝜏 𝑉
𝑉
𝜌 𝑑𝑉 +
𝛻 𝜌 𝑑𝑉 =
 The criterion
𝑆
𝑉
𝒏𝜌 𝑑𝑆 =
𝑉
𝑠 𝑑𝑉
𝑠 𝑑𝑉
𝑆
𝒏𝜌 𝑑𝑆=0 divides universe in
compartments
Inversion surface
55
Compartments
universe
Huge
BH
Black holes
Huge BH ⇔ s tart of new episode
BH ⇔ densest packaging
Merge
Compartments
Never ending story
56
History of Cosmology
 Black hole represents natal state of compartment
 Black holes suck all mass from their compartment
 An instable passivized huge black hole represents start
of new episode of its compartment
 Driving force is enormous mass present outside
compartment ⇒ expansion
 Whole universe is affine space
 Result is never ending story
57
Gravitation
 The Palestra is a curved space
 𝒫𝑏𝑙𝑢𝑟𝑟𝑒𝑑 = ℘𝑠ℎ𝑎𝑟𝑝 ∘ 𝒮𝑠𝑝𝑟𝑒𝑎𝑑
𝜈
 𝑑𝑠 𝑥 = 𝑑𝑠 𝑥 𝑒𝜈 = 𝑑℘ =
 𝑞 𝜇 is quaternion
c dτ
dr
𝜕℘
𝑑𝑥𝜇 = 𝑞 𝜇 𝑥 𝑑𝑥𝜇
𝜇=0…3 𝜕𝑥𝜇
16 partial derivatives
 𝑐 2 𝑑𝑡 2 = 𝑑𝑠 𝑑𝑠 ∗ = 𝑑𝑥02 + 𝑑𝑥12 +𝑑𝑥22 +𝑑𝑥32
 𝑑𝑥02 = 𝑑𝜏 2 = 𝑐 2 𝑑𝑡 2 − 𝑑𝑥12 −𝑑𝑥22 −𝑑𝑥32
 ∆𝑠𝑓𝑙𝑎𝑡 = ∆𝑥0 + 𝒊 ∆𝑥1 + 𝒋 ∆𝑥2 + 𝒌 ∆𝑥3
 ∆𝑠℘ = 𝑞 0 ∆𝑥0 + 𝑞1 ∆𝑥1 + 𝑞 2 ∆𝑥2 + 𝑞 3 ∆𝑥3
Pythagoras
Minkowski
Flat space
Curved space
58
Metric
 𝑑℘ is a quaternionic metric
 It is a linear combination of 16 partial derivatives
 𝑑℘ =
𝜕℘
𝑑𝑥𝜇
𝜕𝑥
𝜇=0…3 𝜇
=
𝜈=0,…3
= 𝑞 𝜇 𝑥 𝑑𝑥𝜇
𝜕℘𝜈
𝑒𝜈
𝑑𝑥𝜇 =
𝜕𝑥𝜇
𝜇=0…3
𝜇
𝑒𝜈 𝑞𝜈 𝑑𝑥𝜇
𝜈=0,…3
𝜇=0…3
 Avoids the need for tensors
59
The primary building blocks
60
Sign flavors
 Coupling equation
 𝛻𝜓 𝑥 = 𝑚 𝜓 𝑦
 𝛻𝜓 𝑥 ∗ = 𝑚 𝜓 𝑦 ∗
 Coupling occurs between
pairs
 {𝜓 𝑥 , 𝜓 𝑦 }
 Colors x, y
 N, R, G, B, R, G, B, W
 Right and left handedness
 R,L
Sign flavors
𝝍⓪ 𝑁 𝐑
𝝍① 𝑅 𝐋
Imaginary
part
𝝍② 𝐺 𝐋
𝝍③ 𝐵 𝐋
𝝍④ 𝐵 𝐑
𝝍⑤ 𝐺 𝐑
𝝍⑥ 𝑅 𝐑
𝝍⑦ 𝑁 L
𝝍⓪
is the
Reference
QPDD
Discrete
symmetries
61
Spin
 HYPOTHESIS : Spin relates to the fact whether the
coupled QPDD is the reference Qpattern 𝝍⓪ .
 Each generation has its own reference QPDD.
 Fermions couple to the reference QPDD 𝝍⓪ .
 Fermions have half integer spin.
 Bosons have integer spin.
 The spin of a composite equals the sum of the spins of
its components.
62
Sign of spin
 The micro-path can be walked in two directions
 This determines the sign of spin
63
Electric charge
 HYPOTHESIS : 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.
64
Color charge
 HYPOTHESIS : 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.
65
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 𝐸.
Any internal kinetic energy is included in 𝐸.
The same mass rule holds for composite particles.
The fields of the composite particles are dynamic
superpositions of the fields of their components.
66
Computing total energy
 Let 𝜓 represent the quantum state function of the
particle
 𝛻𝜓 = 𝜙 = 𝑚 𝜑
 𝑉 𝜓 2 𝑑𝑉 = 𝑉 𝜑 2 𝑑𝑉 = 1
 𝑉 𝛻𝜓 2 𝑑𝑉 = 𝑉 𝜙 2 𝑑𝑉 = 𝑚2
 𝑚 is the total energy of the particle
67
Leptons
Pair
s-type
e-charge c-charge
{𝜓 ⑦ , 𝜓 ⓪ }
fermion
-1
{𝜓 ⓪ , 𝜓 ⑦ }
Antifermion
+1
Handed
ness
SM Name
N
LR
electron
W
RL
positron
68
Quarks
Pair
s-type
e-charge
c-charge
Handedness
SM Name
{𝜓 ① , 𝜓 ⓪ }
fermion
-1/3
R
LR
down-quark
{𝜓 ⑥ , 𝜓 ⑦ }
Anti-fermion
+1/3
R
RL
Anti-down-quark
{𝜓 ② , 𝜓 ⓪ }
fermion
-1/3
G
LR
down-quark
{𝜓 ⑤ , 𝜓 ⑦ }
Anti-fermion
+1/3
G
RL
Anti-down-quark
{𝜓 ③ , 𝜓 ⓪ }
fermion
-1/3
B
LR
down-quark
{𝜓 ④ , 𝜓 ⑦ }
Anti-fermion
+1/3
B
RL
Anti-down-quark
{𝜓 ④ , 𝜓 ⓪ }
fermion
+2/3
B
RR
up-quark
{𝜓 ③ , 𝜓 ⑦ }
Anti-fermion
-2/3
B
LL
Anti-up-quark
{𝜓 ⑤ , 𝜓 ⓪ }
fermion
+2/3
G
RR
up-quark
{𝜓 ② , 𝜓 ⑦ }
Anti-fermion
-2/3
G
LL
Anti-up-quark
{𝜓 ⑥ , 𝜓 ⓪ }
fermion
+2/3
R
RR
up-quark
{𝜓 ① , 𝜓 ⑦ }
Anti-fermion
-2/3
R
LL
Anti-up-quark
69
Reverse quarks
Pair
s-type
e-charge
c-charge
Handedness
SM Name
{𝜓 ⓪ , 𝜓 ① }
fermion
+1/3
R
RL
down-r-quark
{𝜓 ⑦ , 𝜓 ⑥ }
Anti-fermion
-1/3
R
LR
Anti-down-r-quark
{𝜓 ⓪ , 𝜓 ② }
fermion
+1/3
G
RL
down-r-quark
{𝜓 ⑦ , 𝜓 ⑤ }
Anti-fermion
-1/3
G
LR
Anti-down-r-quark
{𝜓 ⓪ , 𝜓 ③ }
fermion
+1/3
B
RL
down-r-quark
{𝜓 ⑦ , 𝜓 ④ }
Anti-fermion
-1/3
B
LR
Anti-down-r_quark
{𝜓 ⓪ , 𝜓 ④ }
fermion
-2/3
B
RR
up-r-quark
{𝜓 ⑦ , 𝜓 ③ }
Anti-fermion
+2/3
B
LL
Anti-up-r-quark
{𝜓 ⓪ , 𝜓 ⑤ }
fermion
-2/3
G
RR
up-r-quark
{𝜓 ⑦ , 𝜓 ② }
Anti-fermion
+2/3
G
LL
Anti-up-r-quark
{𝜓 ⓪ , 𝜓 ⑥ }
fermion
-2/3
R
RR
up-r-quark
{𝜓 ⑦ , 𝜓 ① }
Anti-fermion
+2/3
R
LL
Anti-up-r-quark
70
Massive Bosons
 Fermions 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.
71
Higgs 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
72
W-particles
{𝜓 ⑥ , 𝜓 ① }
boson
-1
RR
RL
𝑊−
{𝜓 ① , 𝜓 ⑥ }
Anti-boson
+1
RR
LR
𝑊+
{𝜓 ⑥ , 𝜓 ② }
boson
-1
RG
RL
𝑊−
{𝜓 ② , 𝜓 ⑥ }
Anti-boson
+1
GR
LR
𝑊+
{𝜓 ⑥ , 𝜓 ③ }
boson
-1
RB
RL
𝑊−
{𝜓 ③ , 𝜓 ⑥ }
Anti-boson
+1
BR
LR
𝑊+
{𝜓 ⑤ , 𝜓 ① }
boson
-1
GG
RL
𝑊−
{𝜓 ① , 𝜓 ⑤ }
Anti-boson
+1
GG
LR
𝑊+
{𝜓 ⑤ , 𝜓 ② }
boson
-1
GG
RL
𝑊−
{𝜓 ② , 𝜓 ⑤ }
Anti-boson
+1
GG
LR
𝑊+
{𝜓⑤ , 𝜓③ }
boson
-1
GB
RL
𝑊−
{𝜓 ③ , 𝜓 ⑤ }
Anti-boson
+1
BG
LR
𝑊+
{𝜓 ④ , 𝜓 ① }
boson
-1
BR
RL
𝑊−
{𝜓 ① , 𝜓 ④ }
Anti-boson
+1
RB
LR
𝑊+
{𝜓 ④ , 𝜓 ② }
boson
-1
BG
RL
𝑊−
{𝜓 ② , 𝜓 ④ }
Anti-boson
+1
GB
LR
𝑊+
{𝜓 ④ , 𝜓 ③ }
boson
-1
BB
RL
𝑊−
{𝜓 ③ , 𝜓 ④ }
Anti-boson
+1
BB
LR
𝑊+
73
Z-particles
Pair
s-type
e-charge
c-charge
Handedness
SM Name
{𝜓 ② , 𝜓 ① }
boson
0
GR
LL
Z
{𝜓 ⑤ , 𝜓 ⑥ }
Anti-boson
0
GR
RR
Z
{𝜓 ③ , 𝜓 ① }
boson
0
BR
LL
Z
{𝜓 ④ , 𝜓 ⑥ }
Anti-boson
0
RB
RR
Z
{𝜓 ③ , 𝜓 ② }
boson
0
BR
LL
Z
{𝜓 ④ , 𝜓 ⑤ }
Anti-boson
0
RB
RR
Z
{𝜓 ① , 𝜓 ② }
boson
0
RG
LL
Z
{𝜓 ⑥ , 𝜓 ⑤ }
Anti-boson
0
RG
RR
Z
{𝜓 ① , 𝜓 ③ }
boson
0
RB
LL
Z
{𝜓 ⑥ , 𝜓 ④ }
Anti-boson
0
RB
RR
Z
{𝜓 ② , 𝜓 ③ }
boson
0
RB
LL
Z
{𝜓 ⑤ , 𝜓 ④ }
Anti-boson
0
RB
RR
Z
74
Neutrinos
type
s-type
e-charge
c-charge
Handedness
SM Name
{𝜓 ⑦ , 𝜓 ⑦ }
fermion
0
NN
RR
neutrino
{𝜓 ⓪ , 𝜓 ⓪ }
Anti-fermion
0
WW
LL
neutrino
{𝜓 ⑥ , 𝜓 ⑥ }
boson?
0
RR
RR
neutrino
{𝜓 ① , 𝜓 ① }
Anti- boson?
0
RR
LL
neutrino
{𝜓 ⑤ , 𝜓 ⑤ }
boson?
0
GG
RR
neutrino
{𝜓 ② , 𝜓 ② }
Anti- boson?
0
GG
LL
neutrino
{𝜓 ④ , 𝜓 ④ }
boson?
0
BB
RR
neutrino
{𝜓 ③ , 𝜓 ③ }
Anti- boson?
0
BB
LL
neutrino
75
Color confinement
The color confinement rule forbids the
generation of individual particles that
have non-neutral color charge
76
Color confinement
 Color confinement forbids the generation of
individual quarks
 Quarks can appear in hadrons
 Color confinement blocks observation of
gluons
77
Photons & gluons
type
s-type
e-charge
c-charge
Handedness
SM Name
{𝜓 ⑦ }
boson
0
N
R
photon
{𝜓 ⓪ }
boson
0
W
L
photon
{𝜓 ⑥ }
boson
0
R
R
gluon
{𝜓 ① }
boson
0
R
L
gluon
{𝜓 ⑤ }
boson
0
G
R
gluon
{𝜓 ② }
boson
0
G
L
gluon
{𝜓 ④ }
boson
0
B
R
gluon
{𝜓 ③ }
boson
0
B
L
gluon
78
Photons & gluons
 Photons 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.
79
Fundamental particles
 Due 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
80
81
Dual space distributions
 A subset of the (quaternionic) distributions have the




same shape in configuration space and in the linear
canonical conjugated space.
We call them dual space distributions
These 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, ∆p = ∆q in the Heisenberg’s uncertainty relation.
82
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.
83
Conclusion
 Fundament
 Quantum logic
 Book model
 Correlation vehicle
 Main features
 Fundamentally countable ⇛ Quanta
 Embedded in continuum ⇛ Fields
 Fundamentally stochastic ⇛ Quantum Physics
 Palestra is curved
⇛ Quaternionic “GR”
 Quaternionic metric
}
84
Conclusion
 Contemporary physics works (QED, QCD)
 But cannot explain fundamental features
 Origin of dynamics
 Space curvature
 Inertia
 Existence of Quantum Physics
 What photons are
85
End
 Physics 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