Physical phenomena emerge from the quantum fields everywhere in space. However, not only the phenomena emerge from the quantum fields, the law of the conservation of energy must have its origin from the same spatial structure. This paper describes the relations between the main law of physics and the mathematical structure of the “aggregated” quantum fields.
Physical phenomena emerge from the quantum fields everywhere in space. However, not only the phenomena emerge from the quantum fields, the law of the conservation of energy must have its origin from the same spatial structure. This paper describes the relations between the main law of physics and the mathematical structure of the “aggregated” quantum fields.
Abstract The discussion of stochasticity inherent in physical phenomena and processes occurring on our world is continued actively at present. For this purpose, various physical models and mathematical descriptions that are based most often on postulated are proposed. As a rule, stochasticity introduced in physical models phenomenologically, as well as its origin and mechanisms of emergence are not considered. However, the problem concerning the origin of stochasticity is far from being solved both in physical and mathematical aspects. In this article, the idea put forth by D.I. Blokhintsev and L.E. Ballentine concerning the emergence of stochasticity in classical and quantum field systems as a consequence of action of the surrounding stochastic background is developed. We are using the Lagrangian formalism and the categorically topological method of description for correct definition of the Lagrangian, action, the Euler–Lagrange equations, Noether currents, and generalized charges in stochastic surroundings. It is shown that Noether currents and conserved quantities become stochastic, and their probabilistic properties are determined by the background characteristics. The change in the action of the background on the observation interval determines the deviation of conserved quantities from their mean values, and the Heisenberg uncertainty relation can be treated as a manifestation of this stochasticity. As an illustration of the operability of a mathematical formulation of the stochasticity origin, we consider a classical scalar field. The proposed approach is naturally generalized to quantum fields. It can be used to obtain stochastic equations describing the behavior of material macroscopic systems in random fields and measurement processes.
Quantum fields and quantization are concepts that come from quantum physics, the most intriguing physical theory developed in the twentieth century. In our work we would like to describe in a coherent and comprehensive way basic aspects of their mathematical structure. Most of our work is devoted to the simplest kinds of quantum fields and of quantization. We will mostly discuss mathematical aspects of free quantum fields. We will consider the quantization only on linear phase spaces. The reader will see that even within such a restricted scope the subject is rich, involves many concepts and has important applications, both to quantum theory and to pure mathematics. A distinguished role in our work will be played by representations of the canonical commutation and anti-commutation relations . Let us briefly discuss the origin and the meaning of these concepts.
The Forbidden “Why?” Question — From a Single-Particle Universe to Space and Time Modern physics is extraordinarily successful at describing what happens once space, time, fields, particles, and mathematical structures are already available. But there is a more fundamental question that is rarely pursued to its logical beginning: Why is there a structure in which physical events can exist at all? This paper explores that question by considering an intentionally extreme starting point: a universe containing only a single fermionic degree of freedom. No second particle is assumed. No external detector is introduced. No Euclidean space is presupposed, and physical time is not taken as a primitive parameter. The starting point is the internal complex structure of a Dirac spinor and, in particular, the reciprocal relation between its two Weyl sectors. From the elementary relation Z+1/Z the paper investigates how reciprocal oscillation, differentiation, winding, indexing, and relational dynamics can generate distinctions that initially have no need to be interpreted as ordinary spatial or temporal structures. The central idea is that relation may precede geometry. A distinction between internally evolving sectors can generate a relational differential structure; topologically distinct winding sectors can subsequently become mutually related; and stable relations can then acquire the representation of space and time. In this view, spacetime is not introduced as the stage upon which the particle exists. It is investigated as a possible representation of stable relations generated by the underlying system. The construction connects naturally to the established CEGS–TSO framework, where compatible relational oscillations provide a route toward stable Euclidean spatial and temporal representations. The purpose here, however, is not to rederive all of TSO or quantum mechanics, but to investigate the deeper selfreferential starting point from which such structures might arise. The paper deliberately ends with open questions. In particular, it does not yet establish whether conservation of total energy follows from the winding structure itself, nor does it explain why the conversion between temporal and spatial representations introduces the physical constant c. These unresolved questions are not hidden limitations but part of the investigation: if the objective is to ask why, then unexplained constants and conservation laws cannot simply be declared fundamental and the inquiry stopped there. The result is therefore not presented as a final theory of the universe. It is a search for the beginning of physical description: an attempt to follow the chain backward from space and time toward the minimal relational structure from which they might emerge. The paper asks a simple question with unusually broad consequences: What is the minimum structure required before space and time can exist as meaningful concepts? This question points toward a deeper possibility: the underlying self-referential base of reality from which everything else may emerge. That is the forbidden “Why?” question. -------------- Please also note the sequal on the unanswered question of Lightspeed: Resolving the last Forbidden "Why" Questions: A Geometric Derivation of Lightspeed c and Energy Constancy within the Reciprocal Z + 1/Z Single-Particle Framework https://doi.org/10.5281/zenodo.23076938 -------------- For refence of TSO as a conceptual QM equivalent please read. Time–Space Oscillations: A Geometric and Deterministic Approach to Relativistic and Quantum PhenomenaZenodo DOI: 10.5281/zenodo.17534734The foundational article introducing the TSO framework and its applications to both relativistic and quantum phenomena. Time Dilation and the Nature of Gravitational and Inertial ForcesZenodo DOI: 10.5281/zenodo.17543059Explores the TSO perspective on time dilation and the interplay of inertial and gravitational forces. Time–Space Oscillations and ElectromagneticsZenodo DOI: 10.5281/zenodo.17591325Applies the TSO model to electromagnetic phenomena, revealing novel interpretations of wave propagation and field interactions. Time–Space Oscillations and Quantum Mechanics Zenodo DOI: 10.5281/zenodo.17670668Extends TSO to encompass quantum mechanical principles, including Heisenberg uncertainty, Schrödinger dynamics, path integrals, entanglement, zero-point energy, and the Quantum Zeno effect. For an overview of related work and publications, visit:https://ndl1971.github.io/time-space-oscillations/ Versions: 0.91 - Added in section 16 HOW the euclidean space emerges from the Z+1/Z relation between different winding numbers. I.e the Normalisation process out of which Euclidean space emerges. Euclidean relations emerge out of fixed spin relations. Compareable to the pauli spin states.
Presentation of the Heuristic Interpretive Model of Quantum Physics: Quantum Motion through SpaceQuantum Motion through Space — abbreviated as QMS — is a heuristic interpretive model of quantum physics that aims to provide an intelligible representation of quantum phenomena, fundamental fields, and elementary particles. It does not seek to replace the established mathematical formalisms of contemporary physics, but rather to extend their conceptual scope by proposing a physical and geometrical image of the quantum world.Starting from a fundamental postulate concerning the discrete structure of space and the dynamical role of quanta of action, the QMS model examines both historical and contemporary physical theories in order to develop a coherent interpretive framework. Within this perspective, quantum phenomena are not considered solely as mathematical structures, but also as processes that may be represented through an underlying dynamics: the motion of quanta of action through a discrete spatial substrate.This approach also has a philosophical dimension. By revisiting long-standing questions concerning the nature of space, matter, vacuum, and physical reality, QMS seeks to establish a dialogue between fundamental physics, the ontology of space, and the metaphysics of nature. The model is therefore presented as an attempt at conceptual clarification, situated at the intersection of quantum physics, relativity, gravitation, and speculative cosmology.The thesis is organized into two main parts.The first part, comprising Chapters I to IV, is devoted to the foundations and dynamics of Quantum Motion through Space. It presents the physical and philosophical assumptions of the model, before developing its interpretation of quantum propagation, particles, the wave function, mass, energy, and gravitation.The second part, comprising Chapters V and VI, explores the cosmological and ontological extension of the model. It introduces the speculative framework of Black Holes–White Mountains, together with a reflection on quantum gravity, the discrete structure of space, and the mereological issues associated with such a conception of physical reality.As a whole, this work aims to formulate a coherent, cautious, and speculative interpretive framework intended to make conceivable an underlying kinetics of quantum and cosmological phenomena, while remaining attentive to the observational and theoretical achievements of contemporary physics.