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Difference as the First Principle From Foundational Difference to Quantum Mechanics

Shunsuke Kato, (D-Life / FSPS Co-Creator) Ria

Published Jan 30, 2026• 0 citations
Publisher

Abstract

This volume develops a foundational perspective in which difference is treated as the minimal descriptive and generative principle underlying physical theory. Rather than postulating spacetime, particles, or dynamical laws as primitives, the collected works show how physical structure and quantum mechanics emerge naturally from relational difference itself. Difference is not introduced as a physical quantity, but as the irreducible condition that makes distinction, structure, and description possible. The volume consists of three papers that progressively build this perspective: beginning with the formulation of difference as a primitive descriptive element, advancing to the emergence of quantum mechanics from difference, and culminating in a unified foundational view of physics grounded in relational structure. These works form the conceptual groundwork underlying the FSPS framework, focusing on intuition, logical necessity, and structural coherence rather than axiomatic formalism or modification of existing physical laws. No new equations or empirical assumptions are introduced. The aim is to clarify why the mathematical and conceptual structures already used in physics take the form they do, by tracing them back to difference as a first principle.

DOI
10.5281/zenodo.18436464

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This volume develops a foundational perspective in which difference is treated as the minimal descriptive and generative principle underlying physical theory. Rather than postulating spacetime, particles, or dynamical laws as primitives, the collected works show how physical structure and quantum mechanics emerge naturally from relational difference itself. Difference is not introduced as a physical quantity, but as the irreducible condition that makes distinction, structure, and description possible. The volume consists of three papers that progressively build this perspective: beginning with the formulation of difference as a primitive descriptive element, advancing to the emergence of quantum mechanics from difference, and culminating in a unified foundational view of physics grounded in relational structure. These works form the conceptual groundwork underlying the FSPS framework, focusing on intuition, logical necessity, and structural coherence rather than axiomatic formalism or modification of existing physical laws. No new equations or empirical assumptions are introduced. The aim is to clarify why the mathematical and conceptual structures already used in physics take the form they do, by tracing them back to difference as a first principle.
This volume traces the emergence of the FS–PS (Foundational Structure / Projected Structure) distinction from an initial conceptual discomfort with the standard description of the double-slit experiment, and follows its extension toward questions of consciousness, selfhood, forgetting, and coordination. Rather than presenting a finalized physical theory, the collected texts preserve a trajectory of thought in which projection is understood as non-bijective and irreversible, and observable outcomes are treated as stabilized images of underlying difference. The work documents how a single structural insight propagates across physical and cognitive domains. The first part records the generative phase of the idea, capturing the moment at which the FS–PS distinction begins to take shape. The second part develops this distinction into a descriptive and operational framework, clarifying how projection, observation, and stabilization function across different contexts. Emphasis is placed on traceability rather than formal derivation. The volume is intended as a conceptual and phenomenological record of how FS–PS emerged as a unifying structure, complementing more formal axiomatic and technical developments within the broader FSPS framework.
This volume explains why the standard formalism of quantum mechanics is not merely successful, but structurally inevitable. Rather than proposing a new interpretation or modifying existing equations, this work derives quantum mechanics as the only stable descriptive framework compatible with the FSPS (Foundational Structure / Projected Structure) model. Within FSPS, observable physics (PS) arises as a projection from a non-geometric foundational layer (FS), and this projection necessarily introduces non-commutativity, probabilistic structure, and unitary evolution. The volume combines the axiomatic foundation of FSPS–00 v2.2 with a focused derivation showing that classical mechanics is structurally unstable under projection, while the Hilbert-space formalism of quantum mechanics represents the minimal information-preserving description. Measurement, wavefunction collapse, and probabilistic outcomes are treated not as additional physical processes but as re-projection and stabilization events within PS. No changes are made to Schrödinger dynamics, operator algebra, or experimental predictions. This work serves as a unifying explanation for why quantum mechanics has its present form, consolidating earlier FSPS-based analyses into a single, coherent account aligned with modern quantum theory.
This volume collects a set of foundational papers developed within the FSPS (Foundational Structure / Projected Structure) framework, focusing on the structural conditions that make world construction possible. Rather than introducing new physical laws or axioms, the papers address three closely related questions: why purely classical descriptions are structurally impossible, how observable worlds must be constructed through projection and stabilization, and how the concept of placement resolves long-standing interpretational ambiguities in relativity and foundational physics. The collected works emphasize conceptual necessity over formal derivation. They argue that worldhood is not given, but must be placeable, and that physical description fails when placement conditions are underspecified. Classical impossibility is treated not as a dynamical failure, but as a structural constraint arising from projection and non-bijective description. This volume is intended as an accessible conceptual entry point into FSPS-related thinking. It can be read independently of formal axiomatic developments (such as FSPS–00), while remaining fully compatible with them for readers who wish to pursue a more formal reconstruction.
This book has grown out of a one term course on quantum mechanics for third year mathematics students taught in the School of Mathematics at the University of Bristol. The genesis of quantum mechanics is in the field of physics, but from early on the infusion of new mathematics into the field has often proven fruitful (e.g. Hilbert space, matrix theory, the mathematical framework of Hamiltonian mechanics, tensor products, etc.). This course seeks to develop the mathematical framework that will equip the student for further studies in quantum mechanics while, at the same time, providing some insight into “what it means” physically.
This work presents a unified generative framework for logic, computation, and physical theories, starting from a minimal recursive structure. Rather than assuming pre-existing logical axioms, computational primitives, or physical laws, the framework derives them as emergent features of a single generative process governed by stabilization and constraint propagation. Within this model, classical logic and computation arise as stabilized regimes of recursive structure, while quantum-mechanical phenomena are interpreted as pre-stabilization behavior—patterns that have not yet resolved into invariant records at the emergent spatial level. Superposition, interference, entanglement, and measurement are described structurally, without invoking parallel-world narratives or epistemic uncertainty. Measurement is treated as constraint coupling that forces refinement until a stable record forms. The framework emphasizes pattern persistence, invariance under refinement, and dynamic resolution as organizing principles. It provides a conceptual account of quantum behavior that is consistent with standard quantum mechanics while reframing it as a consequence of generative structure rather than an axiomatic starting point. This work is foundational and conceptual in nature. It does not propose new experimental predictions or modifications to established physical theory, but aims to clarify the structural relationship between computation, logic, and physics, and to offer a coherent ontological picture underlying these domains.Contact: arthur.nogman@gmail.com