We introduce a pregeometry employing uniform spaces over the denumerable set X of spacetime events. The discrete uniformity D_X over X is used to obtain a pregeometric model of macroscopic spacetime neighborhoods. We then use a uniformity base generated by a topological group structure over X to provide a pregeometric model of microscopic spacetime neighborhoods. Accordingly, quantum non-separability as it pertains to non-locality is understood pregeometrically as a contrast between microscopic spacetime neighborhoods and macroscopic spacetime neighborhoods. A nexus between this pregeometry and conventional spacetime physics is implied per the metric induced by D_X. A metric over the topological group Z2 x ... x Z2 is so generated. Implications for quantum gravity are enumerated.
We introduce a pregeometry employing uniform spaces over the denumerable set X of spacetime events. The discrete uniformity D_X over X is used to obtain a pregeometric model of macroscopic spacetime neighborhoods. We then use a uniformity base generated by a topological group structure over X to provide a pregeometric model of microscopic spacetime neighborhoods. Accordingly, quantum non-separability as it pertains to non-locality is understood pregeometrically as a contrast between microscopic spacetime neighborhoods and macroscopic spacetime neighborhoods. A nexus between this pregeometry and conventional spacetime physics is implied per the metric induced by D_X. A metric over the topological group Z2 x ... x Z2 is so generated. Implications for quantum gravity are enumerated.
We introduce a pregeometry employing uniform spaces over the denumerable set X of spacetime events. The discrete uniformity D_X over X is used to obtain a pregeometric model of macroscopic spacetime neighborhoods. We then use a uniformity base generated by a topological group structure over X to provide a pregeometric model of microscopic spacetime neighborhoods. Accordingly, quantum non-separability as it pertains to non-locality is understood pregeometrically as a contrast between microscopic spacetime neighborhoods and macroscopic spacetime neighborhoods. A nexus between this pregeometry and conventional spacetime physics is implied per the metric induced by D_X. A metric over the topological group Z2 x ... x Z2 is so generated. Implications for quantum gravity are enumerated.
This paper reinterprets quantum entanglement from a pregeometric perspective in which connectivity precedes distance, metric, and continuous space. At the lowest layer, objects are represented solely by sets of relations. It is assumed that the addition of physical interaction to a two-element relation generates an elementary length, while three- and four-element relations generate elementary area and volume, respectively. Macroscopic distance, area, and space are interpreted as emergent quantities obtained by coarse-graining or integrating large ensembles of these elementary relations. A complete four-element connection is represented by the tetrahedral graph K₄ and interpreted as a fundamental object. The line graph L(K₄) is the octahedral graph, providing a natural mathematical model of a relational space generated from the connections of tetrahedral objects. Octahedral geometry contains three mutually orthogonal directions together with the normalized diagonal directions (x±y)/√2, and is geometrically compatible with the 45° measurement configuration associated with maximal CHSH violation. This paper does not claim to derive the quantum correlation E(a,b)=−cosθ. Rather, it presents a discrete geometry compatible with the known CHSH geometry and interprets quantum entanglement as a possible observable manifestation of a connectivity layer underlying ordinary spacetime. Rotation and phase coupling are further introduced as candidate dynamical ingredients for a future derivation of the angular correlation law. The model suggests that Bell nonlocality need not represent propagation across pre-existing space, but may instead expose the relational structure from which spatial distance itself emerges. Keywords: quantum entanglement, pregeometry, tetrahedron, octahedron, line graph, emergent space, CHSH, phase, rotation, fine-structure constant
We develop a pregeometric reconstruction framework in which quantum theory, entanglement structure, gauge symmetry, locality, Lorentzian spacetime geometry, gravitation, and effective physical constants emerge from recursively stabilized coherent relational organization. The framework begins from a primitive relational substrate consisting of compositional accessibility processes endowed with complex coherent transport amplitudes. No background spacetime manifold, metric geometry, particle ontology, or external classical time parameter is assumed fundamentally. The central proposal is that coherent compositional structure is more fundamental than spacetime geometry. Hilbert organization emerges from consistency requirements on coherent relational composition. Observable physical sectors arise through projection stabilization: a dynamical stability-selection process acting on coherent relational transport. Decoherence partitions coherent accessibility structure into approximately factorizable sectors, producing emergent locality and classical persistence. Gauge symmetry emerges naturally as redundancy in coherent transport representation. Lorentzian geometry arises statistically from stabilized accessibility organization, while gravitation appears as thermodynamic relaxation of projected coherent geometry. The framework is formulated as a reconstruction program rather than a completed unified theory. Its aim is not to replace existing physics at the phenomenological level, but to explain why physical reality organizes itself through Hilbert structure, gauge redundancy, locality, relativistic spacetime, and thermodynamic gravitational dynamics. Particular emphasis is placed on the possibility that quantum nonseparability is more fundamental than spacetime locality.
The Causal Set hypothesis for Quantum Gravity asserts that the smooth Lorentzian spacetime manifold of General Relativity is only an approximation to a fundamental microscopic discrete structure: a locally-finite partially-ordered set. The points of this set are akin to the point-events of the spacetime manifold, and the order-relations among these points are akin to the causal-relations among these point-events. The local-finiteness condition implies a fundamental discreteness and provides an important [conformal] factor needed for the continuum approximations. In this dissertation, we address two aspects toward the formulation of a quantum dynamics for causal sets. The first aspect concerns the dynamics of a zero-mass classical scalar field on a background causal set, Poisson-sampled from an Alexandrov interval in (1 + 1)-dimensional Minkowski spacetime. Our numerical simulations suggest that actions can be defined for such a scalar field, expressed solely in terms of the causal set and the scalar field, which approximates the corresponding classical action on the continuum Minkowski spacetime. This result may help us describe matter and gauge fields in a local and Lorentz-invariant way on a causal set, a discrete structure now being considered as the arena for spacetime physics. More importantly, it may help us formulate an action for the causal set itself, which would be used in a sum-over-histories approach to describe the quantum dynamics of causal sets. The second aspect concerns Quantum Measure Theory, a new approach to quantum dynamics inspired by the sum-over-histories approach, which is better suited to formulating the dynamics of causal sets and of other alternative structures for spacetime. To better understand the mathematical structure underlying this new approach, we derive some algebraic identities involving the sum-rules of the Quantum Measure and its generalizations. We conclude with a discussion on possible applications and open problems concerning these aspects.
In the following we undertake to describe how macroscopic spacetime (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of cellular networks and random graphs . One of our main themes is the development of the concept of physical (proto)points or lumps as densely entangled subcomplexes of the network and their respective web, establishing something like (proto)causality . It may perhaps be said that certain parts of our programme are realizations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this two-storey concept of quantum spacetime can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic spacetime causality!
The conceptual difficulties of Quantum Mechanics—manifesting as paradoxes of locality, causality, and realism—arise from the fundamental assumption that spacetime is a contin- uous, metric geometry. We propose an alternative framework: The Quantum Loom, which models the vacuum as a discrete, incompressible superfluid network of Planck-scale nodes. By integrating the ER=EPR conjecture with Superfluid Vacuum Theory, we demonstrate that ”Metric Locality” is an emergent approximation, while fundamental reality is governed by ”Topological Connectivity.” In this paper, we apply this framework to resolve eight major foundational paradoxes. We show that ”Temporal Paradoxes” (Wheeler’s Delayed Choice, Quantum Eraser) are re- solved by viewing entanglement as global tension on a closed topological circuit. ”Interaction Paradoxes” (Hardy, Elitzur-Vaidman, Klein) are explained by the non-local interaction of strain fields and dielectric breakdown of the vacuum lattice. Finally, ”Observer Paradoxes” (Wigner’s Friend, Quantum Zeno, and Schr¨odinger’s Cat) are demystified as phase transi- tions: macroscopic superposition is strictly limited by the Topological Jamming density of the network, forcing massive systems to ”flash freeze” into definite states. This model recov- ers objective realism without abandoning non-locality, suggesting that the ”spooky” features of quantum mechanics are simply the hydrodynamics of a pre-stressed vacuum web.