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
I take non-locality to be the Michaelson Morley experiment of the early 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: i. If we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. ii. There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime.If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: Matter not only curves spacetime, but “creates” spacetime.We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity.This quantum creation of spacetime consists in: i. Fully non-local entangled coherent quantum variables.ii. The onset of locality via decoherence. iii. A metric in Hilbert Space among entangled quantum variables by the sub-additive von Neumann Entropy between pairs of variables. iv. Mapping from metric distances in Hilbert Space to metric distances in classical spacetime by episodic actualization events.v. Discrete spacetime is the relations among these discrete actualization events. vi. “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously.vii. The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. viii. The arrow of time history of these events is recorded in the very structure of the spacetime constructed. ix. Actual Time is a succession of two or more actual events.The theory inevitably yields a UV cut-off of a new type. The cut-off is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition.This quantum creation of spacetime modifies general relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity.Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed.Possible observational and experimental tests based on: i. the existence of Sub- Planckian photons, ii. knee and ankle discontinuities in the high energy gamma ray spectrum, and iii. possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use.The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
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.
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
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.
We provide a mechanism by which, from a background-independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model of spacetime, our ansatz is that the microscopic dynamics can be chosen so that (i) the model has a low-energy limit which reproduces the nonrelativistic classical dynamics of a system of N particles in flat spacetime, (ii) there is a minimum length, and (iii) some of the particles are in a thermal bath or otherwise evolve stochastically. We then construct simple functions of the degrees of freedom of the theory and show that their probability distributions evolve according to the Schr\"odinger equation. The nonlocal hidden variables required to satisfy the conditions of Bell's theorem are the links in the fundamental graph that connect nodes adjacent in the graph but distant in the approximate metric of the low-energy limit. In the presence of these links, distant stochastic fluctuations are transferred into universal quantum fluctuations.