Quantum Mechanics and the Structure of Physical Theories

Marek Bielecki

Prislac, Thomas, Echo, AI

Appendix Q – Quantum Mechanics and GUFT: A Structural Mapping of Coherence Fields Q.1. Scope and Caution Quantum mechanics (QM) is one of the most precisely tested scientific theories in history. Standard QM and quantum field theory (QFT) correctly describe an enormous range of phenomena, from atomic spectra to semiconductor devices to superconducting qubits. We are not proposing a new physics theory or “fixing” quantum mechanics. Instead, this appendix asks a narrower, safer question: How can the core structures of quantum theory—states, coherence, entanglement, measurement, decoherence—be mapped into the GUFT framework of coherence fields (Ψ = E × T, ΔS, etc.) in a way that is faithful to physics and conceptually useful? We proceed with three strict constraints: We take standard QM/QFT (as found in textbooks and reviewed sources) as non-negotiable. We treat GUFT as a descriptive overlay: a way to talk about structure and information, not an alternative dynamics. Where we draw analogies (e.g., empathy ↔ correlation), we note they are structural, not literal or magical.

Ovidiu Cristinel Stoica

In general, a physical theory is based on some fundamental principles concerning space, time, matter, and the laws prescribing how matter is distributed in space and how it evolves in time, and even how spacetime itself changes in response to the changes of matter. The spectrum of the known theories is very diverse, since they are based on different assumptions. Some theories assume that space and time are totally independent, some that they are warped in a continuum named "spacetime", and some even that there are more dimensions than the usual 3+1. Most theories consider that space and time are continuous, but many recent theories consider them to be discrete. Most dynamical laws of fundamental Physics are deterministic, but apparently Quantum Mechanics shows that they may have an indeterministic component. Despite these distinctions between various theories, our intuition and experience tells us that they have a lot in common. In this paper I will try to capture the common features in a single mathematical structure. This is not a Theory of Everything, but only a mathematical structure which is common to most physical theories known so far. We will see that these theories can be obtained as particular cases of this structure, which I will call "world". In particular, the worlds described by the Classical Mechanics, the Theory of Relativity and the Quantum Mechanics are examples of worlds according to this definition, but also some theories attempting to unify gravity and QM, like String Theory. The purpose of this distillation is to provide a mathematical common background to both physical and metaphysical discussions about the various theories of the World.

Jaime Keller

Quantum Mechanics is a successful model to describe physical phenomena. We show that a simple set of postulates about the description of objects in Nature allows the derivation of the principles of QM, transforming this theory into a deductive approach to Physics. The main postulate is: Objects are described as energy distributions in Space–Time. 1 Quantum Mechanics from START It is universally accepted that Quantum Mechanics is a successful model to describe physical phenomena, in particular of the electronic structure of atoms, molecules and solids. As such it has been reformulated in several different forms (see for example: Nine formulations of quantum mechanics, Daniel F. Styer et al. [15]). The aim of the present paper is to show that a simple set of postulates about the description of objects in Nature allows the derivation of the principles of QM, transforming this theory into a deductive approach to Physics. In our approach the main postulate is: Objects are described as energy distributions in Space–Time. The theory is in fact a systematic mathematical analysis of this postulate and of other general considerations about action, energy–momentum and the role of the theory as a useful description of Nature. The paper also shows the fundamental and basic status of Density Functional Theory, also contained in our approach. The initial mathematical structure is a geometric (quadratic form based) union of space, time and action. In physics bundles of trajectories are used to describe the objects of nature: distribution of heights over a surface, a real object is described as a bundle of space-time trajectories, here we use a description as a bundle of action valves in space-time (energy densities in space following light-like lines). The author is fully aware that the presentation is strongly guided by the knowledge of the usual computational approach to study atoms, molecules and condensed matter electronic structure.

Jerrold L. Aronson