Spacetime As An Agreement
Year: 2026
Type: preprint
Abstract: Spacetime as an Agreement: Native Continuation and Manifest Geometry examines one of the most fundamental questions in physics: what physically establishes the relations that we measure as space and time, and what carries the propagation of light? The paper revisits the historical development of relativity through the contributions of Hendrik Lorentz, Henri Poincaré, Albert Einstein and Hermann Minkowski. It examines the transition from the luminiferous ether as an attempted physical explanation of propagation to the geometrical structure of spacetime, questioning whether mathematical invariance alone establishes the physical origin of the processes being described. Drawing upon Einstein's 1920 Leiden address on ether and relativity and his 1954 correspondence with Michele Besso, the investigation examines Einstein's own recognition of the physical qualities of space and his expressed uncertainty about whether continuous field structures could ultimately provide the foundation of physics. The investigation then develops the distinction between native physical continuation and the measurable geometrical structures that emerge through manifestation in Pattern Field Theory (PFT). Principal contributions include: The Spacetime Agreement: Examines the historical transition from explanations based on a physical propagation medium to the invariant geometrical relations of Special and General Relativity, identifying the distinction between mathematical description and physical construction. Einstein's Physical Foundations: Investigates Einstein's 1920 assertion that space without ether is inconceivable within General Relativity, together with his explicit restriction against treating that ether as an ordinary mechanical medium. Einstein's Later Doubts: Examines Einstein's 1954 letter to Michele Besso, in which he acknowledged the possibility that continuous field structures might be insufficient as the ultimate foundation of physics, including his gravitational theory. Lost in Translation?: Provides a comparative linguistic examination of original German statements by Minkowski and Einstein, established English translations, and independent translations by James Johan Sebastian Allen. Swedish, a closely related Germanic language, serves as an intermediate language of comprehension, revealing distinctions in terminology, emphasis and physical interpretation. Geometrical Invariance: Examines the invariant spacetime interval, the metric tensor and the mathematical relationship between coordinate descriptions, distinguishing geometrical consistency from the physical processes responsible for observable relations. The Problem of Time: Establishes the distinction between native successor ordering and measured duration. PFT begins with Identity, Relation and Continuation, while time enters downstream as a Mensural measurement assigned to physical transitions. Native Continuation: Develops the ordering of admissible relational configurations through successor dependencies, identity inheritance and persistence, independently of a primitive temporal coordinate. The Emergence of Spatial Geometry: Examines the relationship between native lateral routing, inherited depth continuation and three-dimensional manifested geometry, with spatial separation and dimensionality expressed through Mensural assignments. The Manifestation Boundary: Distinguishes the physical construction of relational states from the measured quantities of velocity, acceleration, force, distance and duration used to describe their observable behaviour. Geometry, Infinity and Representation: Examines how bounded coordinate representations can describe mathematically unbounded domains, distinguishing the limits of a representation from the physical limits of the system represented. Recurrence and Geometrical Closure: Demonstrates that the return of a manifested trajectory to an observed position does not imply recurrence of the complete inherited physical configuration. Geometrical closure and native recurrence are therefore distinct mathematical and physical conditions. A Common Foundation for Gravitation and Quantum Fields: Connects the investigation to the PFT recovery of General Relativity and Quantum Field Structure, examining how both continuum descriptions relate to native Transport, admissible continuation and downstream Mensural measurement. The paper places particular emphasis on the difference between describing physical observations and establishing the processes from which those observations arise. A geometrical representation may reproduce experimentally established relationships without independently identifying their underlying physical construction. Within Pattern Field Theory, native Transport and relational continuation precede the assignment of spatial coordinates and measured duration. Physical identities inherit relations through admissible successive configurations, while observers obtain measurable distances, temporal intervals and geometrical descriptions through manifestation and Mensural mapping. The central conclusion is that the physical origin of spacetime must be examined through the processes responsible for continuation and manifestation, rather than inferred solely from the many times repeated mathematical successes of spacetime geometry that lack a description and derivation of spacetime itself. Something that bothered Einstein then and even later in life. By connecting the historical foundations of relativity with the relational architecture of Pattern Field Theory, this work establishes a unified conceptual treatment of physical succession, measured time, spatial geometry, recurrence and the continuum structures used in gravitation and quantum field theory. This complements the connected papers: Recovering General Relativity in Pattern Field Theory, Recovering Quantum Field Structure in Pattern Field Theory and Toward the Origin of Quantum Probability, addressing the foundational relationship between physical Transport (Gravity) and the geometrical and probabilistic descriptions constructed from it. James Johan Sebastian AllenPattern Field Theoryhttps://patternfieldtheory.com/https://zenodo.org/communities/pft...............................Update note - 8 November 2026 This updated edition of Spacetime as an Agreement: Native Continuation and Manifest Geometry incorporates historical, mathematical, and structural refinements. The update includes: Revised translations and closer examination of Einstein's 1920 Leiden address, his 1954 letter to Michele Besso, and Minkowski's original German terminology. Expanded historical analysis of Felix Pirani and Richard Feynman's contributions to the 1957 Chapel Hill Conference, particularly the physical measurement of gravitational-wave energy transfer. Clarification of native continuation, geometrical closure, and Mensural measurement, including the distinction between physical succession, biological cycles, mechanical-clock operation, and numerical time. Explicit identification of General Relativity and quantum field theory as downstream descriptions within Pattern Field Theory's native Transport architecture. Added references to the relevant PFT derivations and recovery papers covering dimensional construction, gravitation, metric geometry, curvature, and quantum field structure. Editorial corrections, improved terminology, and consolidated references. The central finding remains: native physical continuation establishes the relationships subsequently represented through spacetime geometry and measured duration.
Author: Allen, James Johan Sebastian
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225323511