The origin of physical dynamics and the reason of existence of special relativity are explored. This endeavour is started by analysing the logic of nature. Next, only mathematics is used in order to explore the dynamics of this model of physical reality. The model that is described here annihilates the old reality and creates a new reality at each dynamic step. Hilbert space cannot treat dynamics. It contains nothing that supports dynamics. In the contrary, dynamics manages the Hilbert spaces. Like traditional quantum logic, Hilbert space cannot treat physical fields. By embedding the separable Hilbert space in a rigged Hilbert space, it can house fields by representing them as blurred sets of Hilbert vectors. The field is the convolution of the blur with a set of Dirac delta functions that represent Hilbert vectors. When the blur is differentiable, then the field is differentiable as well. The field values are attached to the Hilbert vectors. In this way traditional quantum logic can be expanded, such that it also treats fields. This extended quantum logic still cannot handle dynamics. The logic only describes a static status quo. Dynamics let nature step from one status quo to the next. It does that by letting nature transform from configuration space to Fourier space. There the fields control the difference between the past and the future status quo. The Fourier transform converts the rather complicated differentiation into a simple multiplication and since the multiplication factors are close to unity, this comes down to still simpler addition. After the confrontation in Fourier space, nature returns back to configuration space. Feynman's path integral approach exploits this fact. The up and down Fourier transforms reshuffle the Hilbert vectors. All Hilbert vectors are affected. The Hilbert vectors represent virtual or actual quanta and present themselves as shot noise.
The origin of physical dynamics and the reason of existence of special relativity are explored. This endeavour is started by analysing the logic of nature. Next, only mathematics is used in order to explore the dynamics of this model of physical reality. The model that is described here annihilates the old reality and creates a new reality at each dynamic step. Hilbert space cannot treat dynamics. It contains nothing that supports dynamics. In the contrary, dynamics manages the Hilbert spaces. Like traditional quantum logic, Hilbert space cannot treat physical fields. By embedding the separable Hilbert space in a rigged Hilbert space, it can house fields by representing them as blurred sets of Hilbert vectors. The field is the convolution of the blur with a set of Dirac delta functions that represent Hilbert vectors. When the blur is differentiable, then the field is differentiable as well. The field values are attached to the Hilbert vectors. In this way traditional quantum logic can be expanded, such that it also treats fields. This extended quantum logic still cannot handle dynamics. The logic only describes a static status quo. Dynamics let nature step from one status quo to the next. It does that by letting nature transform from configuration space to Fourier space. There the fields control the difference between the past and the future status quo. The Fourier transform converts the rather complicated differentiation into a simple multiplication and since the multiplication factors are close to unity, this comes down to still simpler addition. After the confrontation in Fourier space, nature returns back to configuration space. Feynman's path integral approach exploits this fact. The up and down Fourier transforms reshuffle the Hilbert vectors. All Hilbert vectors are affected. The Hilbert vectors represent virtual or actual quanta and present themselves as shot noise.
When physics must be based on an axiomatic foundation then the law set of traditional quantum logic is a valid candidate. However, at first sight, these axioms do not treat physical fields and they do not treat dynamics. It only prescribes the static relations that exist between quantum logical propositions that treat static subjects. These subjects are considered to be physical subjects or their properties. Amongst these propositions statements exist that describe everything that can be said about the static condition of a given physical item. Such propositions represent that item.
Quantum theory is the soul of contemporary physics. It was discovered in an adventurous way, under the urge to solve the puzzles posed by atomic spectra and blackbody radiation. But after its invention, it immediately became clear that it was not just a theory of specific physical systems: it was rather a new language of universal applicability. Already in 1928, the theory had received solid mathematical foundations by Hilbert, von Neumann, and Nordheim, and this work was brought to completion in the monumental work of von Neumann, in the form that we still study nowadays. The theory is extraordinarily successful, and its predictions have been confirmed to an astonishing level of precision in a large spectrum of experiments. However, almost 90 years after von Neumann's book, quantum theory remains mysterious. Its mathematical formulation – based on Hilbert spaces and self-adjoint operators – is far from having an intuitive interpretation. The association of physical systems to Hilbert spaces whose unit vectors represent pure states, the representation of transformations by unitary operators and of observables by self-adjoint operators – all such postulates look artificial and ad hoc . A slightly more operational approach is provided by the C * -algebraic formulation of quantum theory – still, this formulation relies on the assumption that observables form an algebra , where the physical meanings of the multiplication and the sum are far from clear. In short, the postulates of quantum theory impose mathematical structures without providing any simple reason for this choice: the mathematics of Hilbert spaces is adopted as a magic blackbox that “works well” at producing experimental predictions. However, in a satisfactory axiomatization of a physical theory the mathematical structures should emerge as a consequence of postulates that have a direct physical interpretation. By this we mean postulates referring, e.g., to primitive notions like physical system, measurement, or process, rather than notions like, e.g., Hilbert space, C * -algebra, unit vector, or selfadjoint operator. The crucial question thus remains unanswered: why quantum theory? Which are the principles at the basis of the theory? A case that is often invoked in contrast is that of Special Relativity theory, which directly follows from the simple understandable principle of relativity.
The objects that occur in nature can be categorized in several levels. In this collection every level except the first level is built from lower level objects. This collection represents a simple model of nature. The model exploits the possibilities that mathematical concepts provide. Also typical physical ingredients will be used. The paper splits the hierarchy of objects in a logic model and a geometric model. These two hierarchies partly overlap. The underlying Hilbert Book Model is a simple self-consistent model of physics that is strictly based on quantum logic. This paper refines quantum logic to Hilbert logic such that it more directly resembles its lattice isomorphic companion, which is a separable Hilbert space. The HBM extends these static sub-models into a dynamic model that consists of an ordered sequence of the static sub-models. The paper is founded on three starting points: • A sub-model in the form of traditional quantum logic that represents a static status quo. • A correlation vehicle that establishes cohesion between subsequent members of a sequence of such sub-models. • The cosmological principle. Further it uses a small set of hypotheses. It turns out that the cosmological principle is already a corollary of the first two points. The paper explains or indicates the explanation of all features of fundamental physics that are encountered in the discussed hierarchy which ranges from propositions about physical objects until composites of elementary particles. Amongst them are the cosmological principle, the existence of quantum physics, the existence of a maximum speed of information transfer, the existence of physical fields, the origin of curvature, the origin of inertia, the dynamics of gravity, the existence of elementary particles, the existence of generations of elementary particles and the existence of the Pauli principle.
The Hilbert book test model is a purely mathematical test model that starts from a solid foundation from which the whole model can be derived by using trustworthy mathematical methods. What is known about physical reality is used as a guidance, but the model is not claimed to be a proper reflection of physical reality. The mathematical toolkit still contains holes. These holes will be encountered during the development of the model and suggestions are made how those gaps can be filled. Some new insights are obtained and some new mathematical methods are introduced. The selected foundation is interpreted as part of a recipe for modular construction and that recipe is applied throughout the development of the model. This development is an ongoing project. The main law of physics appears to be a commandment: “Thou shalt construct in a modular way”. The paper reveals the possible origin of several physical concepts. This paper shows that it is possible to discover a mathematical structure that is suitable as an extensible foundation. However, without adding extra mechanisms that ensure dynamic coherence, the structure does not provide the full functionality of reality. These extra mechanisms apply stochastic processes, which generate the locations of the elementary modules that populate the model. All discrete items in universe are configured from dynamic geometric locations. These items are stored in a repository that covers a history part, the current static status quo, and a future part. The elementary modules float over the static framework of the repository. Dedicated mechanisms ensure the coherent behavior of these elementary modules. Fields exist that describe these elementary modules. An encapsulating repository supports these fields. Both repositories are formed by quaternionic Hilbert spaces. The model offers two interesting views. The first view is the creator’s view and offers free access to all dynamic geometric data that are stored in the eigenspaces of operators. The second view is the observer’s view. The observers are modules that travel with the vane, which represents the static status quo. The observers only perceive information that comes from the past and that is carried by the field that embeds them. This view sees the model as a spacetime based structure that stores its dynamic geometric data with a Minkowski signature.
This chapter presents the origins of quantum mechanics. The story of how people hit on the highly non-intuitive world picture of quantum mechanics, in which the physical state of a system is represented by an element in an abstract linear space and its observable properties by operators in the space, is fascinating and exceedingly complicated. The much greater change from the classical world picture of Newtonian mechanics and general relativity to the quantum world picture came in many steps taken by many people, often against the better judgment of participants. There are three major elements in the story. The first is the experimental evidence that the energy of an isolated system can only assume special discrete or quantized values. The second is the idea that the energy is proportional to the frequency of a wave function associated with the system. The third is the connection between the de Broglie relation and energy quantization through the mathematical result that a wave equation with fixed boundary conditions allows only discrete quantized values of the frequency of oscillation of the wave function (as in the fundamental and harmonics of the vibration of a violin string).
The Feynman path integral is an essential part of our mathematical description of fundamental nature at small scales. However, what it seems to say about the world is very much at odds with our classical intu-itions, and exactly why nature requires us to describe her in this way is currently unknown. We will describe here a possibility according to which the path integral may be the spacetime manifestation of objects existing in a lower-dimensional analog of spacetime until they give rise to the emergence of spacetime objects under a process that is currently labeled a ‘Quantum Measure-ment’. This idea is based on a mathematical distinction which at present does not appear to be widely appreci-ated.