A Unified Conceptual Foundation for Relativity and Quantum Mechanics

N. Glenn Gratke

Karim P. Y. Thébault

This Element explores the formal and conceptual foundations of phase space formulations of classical and quantum mechanics. It provides an overview of the core mathematical and physical content of Hamiltonian mechanics, stochastic phase space mechanics, contact Hamiltonian mechanics, and open and closed quantum mechanics on phase space. The formal material is unified via three interpretative themes relating to structured possibility spaces, Liouville's theorem and its failure, and the classical and quantum notions of open and closed systems. This Element book is intended for researchers and graduate students in the philosophy and foundations of physics with an interest in the conceptual foundations of physical theory.

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

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.

Joginder Singh Galsin

João Pedro Barra

The persistent tension between Quantum Mechanics and General Relativity is commonly framed as the need for a deeper theory capable of unifying both within a single ontological structure. In this work, a different strategy is adopted. Rather than pursuing direct unification, we propose a triadic conceptual framework that emphasizes organization prior to unification, treating Quantum Mechanics and General Relativity as complementary descriptions of a single physical system operating under distinct epistemic commitments. Within this framework, each theory is assigned a specific functional role, and a third element—a principle of coherence—is introduced to clarify how these roles may be consistently related without reduction. Approaches grounded in information theory and quantum information are highlighted as natural candidates for articulating this coherence interface, given their ability to mediate between operational descriptions and structural constraints. It is argued that several well-known conflicts between the quantum and relativistic frameworks can be reinterpreted as tensions arising from mismatched levels of description rather than fundamental physical inconsistencies. The proposed approach is structural and organizational in nature, aiming to provide a conceptual map for existing and future work in the foundations of physics.