Classically, a gauge potential was merely a convenient device for generating a corresponding gauge field. Quantum-mechanically, a gauge potential lays claim to independent status as a further feature of the physical situation. But whether this is a local or a global feature is not made any clearer by the variety of mathematical structures used to represent it. I argue that in the theory of electromagnetism (or a non-Abelian generalization) that describes quantum particles subject to a classical interaction, the gauge potential is best understood as a feature of the physical situation whose global character is most naturally represented by the holonomies of closed curves in space-time.
Abstract A central problem in the interpretation of non‐relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable.
This document concerns the discovery of the grand structure of physical reality in terms of mathematical constructs and mechanisms. The grand structure emerges from simple foundations and leads via spaces that show an increasing complexity to a system of Hilbert spaces that will be called Hilbert repository. This structure acts as a powerful storage medium that physical reality applies to store and retrieve prepared data. The repository can easily capture the dynamic geometric data of all objects that will ever exist in our universe. It can also archive the universe as a dynamic manifold and all other physical fields that play in the lifetime of the universe. This enables physical reality to prepare data in a creation episode in which no running time exists and play the story of all archived objects during a running episode in which a flowing time indicates the progression of that life story as an ongoing embedding process. The investigation concerns a hierarchy of spaces that show increasing degrees of complexity. Finding more complicated spaces is not a big problem. This turns out to be quite simple. The move to a more complicated platform appears always accompanied by several significant restrictions and understanding where these limitations come from is a much bigger problem. Today's mathematics is only just able to explain the restrictions of the Hilbert space. This no longer applies to the system of Hilbert spaces, which in this document is called the Hilbert repository. Current math cannot explain the restrictions and the extra features of the Hilbert repository. This fact will particularly interest those who are curious about the structure and behavior of physical reality. The approach is quite different from the usual path and provides other insights. The usual way tries to deduce new insights from what we know about classical physics. That path appears to be blocked. The story makes it clear that only mathematics cannot provide a complete picture of reality, while experiments alone also cannot expose physical reality. The combination of mathematics and experimentation produces the best results. The behavior of fields plays an important role in most theories. Basic physical fields are dynamic fields like our universe and the fields that are raised by electric charges. These fields are dynamic continuums. Most physical theories treat these fields by applying gravitational theories or by Maxwell equations. Mathematically these fields can be represented by quaternionic fields. Dedicated normal operators in quaternionic non-separable Hilbert spaces can represent these quaternionic fields in their continuum eigenspaces. Quaternionic functions can describe these fields. Quaternionic differential and integral calculus can describe the behavior of these fields and the interaction of these fields with countable sets of quaternions. All quaternionic fields obey the same quaternionic differential equations. The basic fields differ in their start and boundary conditions. The paper introduces the concept of the Hilbert repository. It is part of a hierarchy of structures that mark increasingly complicated realizations of a purely mathematical model that describes and explains most features of observable physical reality. That model is the Hilbert Book Model. Many of the subjects that are treated in this document cannot be found in standard textbooks. The paper treats the mathematical and experimental underpinning of the Hilbert Book Model.