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  • Cover De Wiskunde van de Fysieke Werkelijkheid
    De Wiskunde van de Fysieke Werkelijkheid (boek)

The Mathematics of Physical Reality

Diving deep into the crypts of physics

Hans van Leunen MSc • Boek • paperback

  • Samenvatting
    The main subject of this book is a purely mathematical model of physical reality. The book acts as a survey of the Hilbert Book Model Project. The project concerns a well-founded, purely mathematical model of physical reality. The project relies on the conviction that physical reality owns its own kind of mathematics and that this mathematics guides and restricts the extension of the foundation to more complicated levels of the structure and the behavior of physical reality. This results in a model that more and more resembles the physical reality that humans can observe. The book treats several subjects that are directly related to the main subject. The book introduces new physics and new mathematics.

    The selected approach results in a self-creating model that offers a creator’s view and a far more restricted observer’s view. Observers get their information via the dynamic field that physicists call their universe. Observers only get historic information. The creator has access to the complete model. Most physical theories only provide the observer’s view.
  • Productinformatie
    Binding : Paperback
    Distributievorm : Boek (print, druk)
    Formaat : 210mm x 297mm
    Aantal pagina's : 166
    Uitgeverij : Hans van Leunen
    ISBN : 9789463457262
    Datum publicatie : 06-2019
  • Inhoudsopgave
    1 The initiator of the project 1
    1.1 Trustworthiness 1
    1.2 The author 2
    1.3 Early encounters 3
    2 Intention 6
    3 The Hilbert Book Base Model 9
    3.1 Open questions 10
    4 Modeling dynamic fields and discrete sets 12
    4.1 Quaternionic differential calculus 13
    4.2 Field excitations 14
    5 Photons 18
    5.1 Photon structure 18
    5.2 One-dimensional pulse responses 18
    5.3 Photon integrity 19
    5.4 Light 19
    5.5 Optics 20
    6 Modular design and construction 21
    6.1 Elementary modules 21
    6.1.1 Symmetry-related charge 21
    6.2 Modular configuration 22
    6.2.1 Open question 23
    6.3 Stochastic control 23
    6.3.1 Superposition 24
    6.3.2 Open questions 25
    6.4 Benefits of modular design and construction 25
    6.4.1 Modular hierarchy 26
    6.4.2 Compound modules 26
    6.4.3 Molecules 27
    6.4.4 Consciousness and intelligence 27
    7 Dark objects and progression zigzag 29
    8 Gravity 31
    8.1 Difference between the Higgs field and the universe field 31
    8.2 A deforming field excitation 31
    8.3 Center of mass 32
    8.4 Gravitation potential 33
    8.5 Mass 35
    8.6 Hop landing generation 35
    8.6.1 Open question 36
    8.7 Inertia 36
    8.8 Symmetry-related charges 38
    8.9 Color confinement 39
    9 The concept of time 40
    9.1 Proper time 40
    9.2 Clock rates 40
    9.3 A self-creating model 40
    9.4 In the beginning 41
    10 Life of an elementary module 43
    10.1 Causality 44
    10.2 Structure hierarchy 45
    11 Relational structures 47
    11.1 Lattice 47
    11.2 Lattice types 47
    11.3 Well known lattices 49
    12 Quaternions 50
    12.1 Versions 52
    13 Quaternionic Hilbert spaces 53
    13.1 Bra's and ket's 53
    13.2 Operators 55
    13.2.1 Operator construction 57
    13.3 Non-separable Hilbert space 57
    14 Quaternionic differential calculus 59
    14.1 Field equations 59
    14.2 Fields 62
    14.3 Field equations 62
    15 Line, surface and volume integrals 68
    15.1 Line integrals 68
    15.2 Surface integrals 68
    15.3 Using volume integrals to determine the symmetry-related charges 69
    15.4 Symmetry flavor 71
    15.5 Derivation of physical laws 72
    16 Polar coordinates 74
    17 Lorentz transform 76
    17.1 The transform 76
    17.2 Minkowski metric 77
    17.3 Schwarzschild metric 77
    18 Black holes 79
    18.1 Geometry 79
    18.2 The border of the black hole 79
    18.3 An alternative explanation 80
    19 Mixed fields 81
    19.1 Open questions 83
    19.2 The envelops of black holes 84
    19.3 The Bekenstein bound 85
    20 Material penetrating field 86
    20.1 Field equations 86
    20.2 Pointing vector 87
    21 Action 88
    22 Dirac equation 92
    22.1 The Dirac equation in original format 92
    22.2 Dirac’s formulation 93
    22.3 Relativistic formulation 94
    22.4 A better choice 95
    22.5 The Dirac nabla 97
    23 Low dose rate imaging 98
    23.1 Intensified image perception 98
    24 Human perception 99
    24.1 Information encoding 99
    24.2 Blur 101
    24.3 Detective quantum efficiency 102
    24.4 Quantum Physics 102
    25 How the brain works 104
    25.1 Preprocessing 104
    25.2 Processing 104
    25.3 Image intensification 104
    25.4 Imaging quality characteristics 105
    25.5 The vision of noisy images 105
    25.6 Information association 106
    25.7 Noise filter 106
    25.8 Reasoning 106
    25.9 Other species 107
    25.10 Humans 107
    25.11 Science 107
    25.12 Physical reality 107
    25.13 Theories 108
    25.14 Inventions of the human mind 108
    25.15 History 109
    25.16 Dreams 109
    25.17 Addendum 109
    26 Physical creation story 111
    26.1 Motivation 111
    26.2 Justification 112
    26.3 Creation 112
    26.4 Dynamics 114
    26.5 Modularity 116
    26.6 Illusion 117
    26.7 Cause 117
    26.8 Begin to end 117
    26.9 Lessons 118
    27 Story of a war against software complexity 120
    27.1 Summary 120
    27.2 Prelude 120
    27.3 Analysis 120
    27.4 Setting 121
    27.5 History 121
    27.6 Strategy 122
    27.7 Approach 122
    27.8 What happened 122
    27.9 Attack 123
    27.10 Set-back 123
    27.11 Remnants 124
    27.12 Goal 124
    27.13 Lessons 124
    27.14 Conclusions 125
    27.15 Way out 126
    27.16 Discussion 126
    28 Managing the software generation process 128
    28.1.1 Introduction 128
    28.2 Managing complexity 128
    28.2.1 Breaking level 128
    28.2.2 Measure of complexity 128
    28.2.3 Extreme complexity 129
    28.3 The modular approach 130
    28.3.1 Modularization 130
    28.3.2 Modular system design 131
    28.3.3 Interfaces 131
    28.3.4 Proper modules 133
    28.3.5 Properties and Actions 133
    28.3.6 Costs of modularization 133
    28.3.7 Abuse 134
    28.3.8 Modularization success cases 135
    28.3.9 Requirements for success 135
    28.3.10 Difficulties posed by modularization 136
    28.3.11 Diversity 136
    28.3.12 Hardware versus software 138
    28.3.13 Coupling the market and the design and creation of software modules and interfaces 141
    28.3.14 A fully-fledged software components industry 143
    28.3.15 Code 151
    29 References 152

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2 Intention
Theoretical physics still contains unresolved subjects. These deficiencies of the theory are caused by the way that physics was developed and by the attitude of the physicists that designed the current theory. Scientists take great care to secure the trustworthiness of their work, which ends in the publication of the results. They take measures to prevent that their publications get intermingled with badly prepared publications or even worse, with descriptions of fantasies. For that reason, they invented the scientific method [7]. In applied physics, the scientific method founds on observations. Applied physics flourishes because the descriptions of observations help to explore these findings, especially when formulas extend the usability of the observations beyond direct observation. In theoretical physics, this is not always possible because not all aspects of physical reality are observable. The only way of resolving this blockade is to start from a proper foundation that can be extended via trustworthy methods that rely on deduction. This approach can only be successful if the deduction process is guided and restricted such that the extensions of the foundation still describe physical reality. Thus, if a mathematical deduction is applied, then mathematics must guide and restrict this process such that a mathematically consistent extension of the model is again a valid model of physical reality. After a series of development steps, this approach must lead to a structure and behavior of the model that more and more conforms to the reality that we can observe.
This guidance and restriction are not self-evident. On the other hand, we know that when we investigate deeper, the structure becomes simpler and easier comprehensible. So, finally, we come to a fundamental structure that can be considered as a suitable foundation. The way back to more complicated levels of the structure cannot be selected freely. Mathematics must pose restrictions onto the extension of the fundamental structure. This happens to be true for a foundation that was discovered about eighty years ago by two scholars. They called their discovery quantum logic [8]. The scholar duo selected the name of this relational structure because its relational structure resembled closely the relational structure of the already known classical logic. Garrett Birkhoff was an expert in relational structures. These are sets that precisely define what relations are tolerated between the elements of the set. Mathematicians call these relational structures lattices, and they classified quantum logic as an orthomodular lattice [9]. John von Neumann was a broadly oriented scientist that together with others was searching for a platform that was suitable for the modeling of quantum mechanical systems. He long doubted between two modeling platforms. One was a projective geometry, and the other was a Hilbert space [10] [11] [12].Finally, he selected Hilbert spaces. In their introductory paper, the duo showed that quantum logic emerges into a separable Hilbert space. The set of closed subspaces inside a separable Hilbert space has exactly the relational structure of an orthomodular lattice. The union of these subspaces equals the Hilbert space. A separable Hilbert space applies an underlying vector space [13], and between every pair of vectors, it defines an inner product [14]. This inner product can only apply numbers that are taken from an associative division ring [15] [16]. In a division ring, every non-zero member owns a unique inverse. Only three suitable division rings exist. These are the real numbers, the complex numbers, and the quaternions. Depending on their dimension these number systems exist in several versions that differ in the way that Cartesian and polar coordinate systems sequence their members [17] [18].
In the Hilbert space, operators exist that can map the Hilbert space onto itself. In this way, the operator can map some vectors along themselves. The inner product of a normalized vector with such a map produces an eigenvalue. This turns the vector into an eigenvector. Together the eigenvalues of an operator form its eigenspace. This story indicates that mathematics guides and restricts the extension of the selected foundation into more complicated levels of the structure. It shows that the scholar duo started a promising development project.
However, this initial development was not pursued much further. Axiomatic models of physical reality are not popular. Most physicists mistrust this approach. Probably these physicists consider it naïve to suspect that an axiomatic foundation can be discovered that like the way that a seed evolves in a certain type of plant, will evolve into the model of the physical reality that we can observe.
Most quantum physicists decided to take another route that much more followed the line of the physical version of the scientific method. As could be suspected this route gets hampered by the fact that not every facet of physical reality can be verified by suitable experiments.
Mainstream quantum physics took the route [20] of quantum field theory [21], which diversified into quantum electrodynamics [22] and quantum chromodynamics [23]. It bases on the principle of least action [24], the Lagrangian equation [25] and the path integral [26] However, none of these theories apply a proper foundation.
In contrast, the Hilbert Book Model Project intends to provide a purely and self-consistent mathematical model of physical reality [1] [20]. It uses the orthomodular lattice as its axiomatic foundation and applies some general characteristics of reality as guiding lines. An important ingredient is the modular design of most of the discrete objects that exist in the universe. Another difference is that the Hilbert Book Model relies on the control of coherence and binding by stochastic processes that own a characteristic function instead of the weak and strong forces and the force carriers that QFT, QED, and QCD apply [21] [22] [23].
Crucial to the Hilbert Book Model is that reality applies quaternionic Hilbert spaces as structured read-only archives of the dynamic geometric data of the discrete objects that exist in the model. The model stores these data before they can be accessed by observers. This fact makes it possible to interpret the model as the creator of the universe. The classification of modules as observers introduces two different views; the creator’s view and the observer’s view. Time reversal is only possible in the creator’s view. It cannot be perceived by observers because observers must travel with the scanning time window. ×