We describe a substructure for matter in which metric relations are not assumed as properties of a physical manifold, and instead the metric of general relativity is found in configurations of particle interactions. The 'state' of a particle is the set of possible configurations of surrounding particles. States are thus non-local, while particles are local. Kets are not states, or descriptions of states, but merely names for states. Ket space is a naming system constructed by an individual observer from the available information in such a way that the principle of superposition and the probability interpretation are definitional truisms, not physical laws. In this paper the treatment is developed as far as showing that the solution to the discrete equations describing the structure should be embedded into covariant continuous equations, and we remark that this leads to a requirement for four dimensions and spin in the organisation of a structure consisting solely of particle interactions, although neither dimensionality nor spin are assumed properties of particles.
We describe a substructure for matter in which metric relations are not assumed as properties of a physical manifold, and instead the metric of general relativity is found in configurations of particle interactions. The 'state' of a particle is the set of possible configurations of surrounding particles. States are thus non-local, while particles are local. Kets are not states, or descriptions of states, but merely names for states. Ket space is a naming system constructed by an individual observer from the available information in such a way that the principle of superposition and the probability interpretation are definitional truisms, not physical laws. In this paper the treatment is developed as far as showing that the solution to the discrete equations describing the structure should be embedded into covariant continuous equations, and we remark that this leads to a requirement for four dimensions and spin in the organisation of a structure consisting solely of particle interactions, although neither dimensionality nor spin are assumed properties of particles.
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical principles underlying the theory, we rigorously construct a discrete model of quantum mechanics. Kets are names, or labels which categorise states of matter but do not directly describe them. The principle of superposition is seen as a definitional truism in the categorisation of states. This resolves the measurement problem of quantum mechanics by attributing the collapse of the wave function to information. The probability interpretation has a natural meaning in which the configuration of interacting particles plays the role of a hidden variable. The model supports a form of relativistic quantum field theory which does not depend on quantisation or second quantisation from classical mechanics. Continuous laws of wave mechanics are found in a discrete metaphysic which does not involve waves. Classical law is the expected behaviour of many elementary particles. The constraints on the theory are sufficient to establish that particles are point-like entities with specific properties found in nature. Newton's first law and conservation of momentum are established from the principle of homogeneity. Maxwell's equations are derived from the simple interaction in which a Dirac particle emits or absorbs a photon. Feynman rules are calculated for the discrete theory and differ from the standard rules by the removal of the ultraviolet divergence and the use of proper loop integrals. They give finite and unambiguous results.
In this work, by summarising our recent works on the differential geometric and topological structures of quantum particles and spacetime manifolds, we discuss the possibility to classify quantum particles according to their intrinsic geometric structures associated with differentiable manifolds that are solutions to wave equations of two and three dimensions. We show that fermions of half-integer spin can be identified with differentiable manifolds which are solutions to a general two-dimensional wave equation, in particular, a two dimensional wave equation that can be derived from Dirac equation. On the other hand, bosons of integer spin can be identified with differentiable manifolds which are solutions to a general three-dimensional wave equation, in particular, a three-dimensional wave equation that can be derived from Maxwell field equations of electromagnetism. We also discuss the possibility that being restricted to three-dimensional spatial dimensions we may not be able to observe the whole geometric structure of a quantum particle but rather only the cross-section of the manifold that represents the quantum particle and the space in which we are confined. Even though not in the same context, such view of physical existence may comply with the Copenhagen interpretation of quantum mechanics which states that the properties of a physical system are not definite but can only be determined by observations.
Modern theoretical physics rests on two highly successful but conceptually distinct frameworks: quantum mechanics and general relativity. While both theories are experimentally confirmed to high precision within their respective domains, they rely on fundamentally different starting points. General relativity takes spacetime as a primitive geometric structure, whereas quantum mechanics is formulated in terms of abstract state spaces without intrinsic spacetime meaning. Most approaches to quantum gravity attempt to reconcile this tension by modifying, quantizing, or discretizing spacetime itself. Even in approaches where spacetime is said to be “emergent,” it typically remains the primary conceptual backdrop on which physical processes are defined. Despite extensive efforts, there is no consensus on whether spacetime should be regarded as fundamental or derivative. In this work, a more radical starting point is explored. Rather than modifying spacetime or its geometry, we ask whether spacetime can be excluded entirely from the fundamental layer of the theory and recovered only at a later, operational stage. The central question is not how spacetime behaves, but whether the notion of “what lies between physical objects” must be spatial or temporal at the most fundamental level. We propose a framework—referred to here as Super Relativity (SR)—based on a single pre-geometric postulate: the existence of a monotonically expanding set of possible quantum configurations, referred to as the flux. Formally, this flux is represented as a monotone, σ-finite family of capacity measures on a common configuration space (introduced in Section 2). This postulate deliberately refrains from assuming spacetime, time ordering, metric structure, causality, or dynamics. Within this pre-geometric core, two derived, dimensionless notions are introduced: utilization, describing the realization of configurations, and saturation, defined as the ratio between utilized and available configurations. A central structural element of SR is the strict separation between a core layer and an interface layer. In the core layer, all quantities are pre-geometric and dimensionless, and no reference is made to space, time, motion, energy, or interaction. Only at the interface layer are operational notions introduced, including clocks, rulers, and signal propagation. Spacetime, in this construction, is not a dynamical entity but an effective bookkeeping structure that encodes relative rates of change once a calibration to physical units is performed. Within this framework, gravitational phenomena do not originate from spacetime curvature taken as fundamental. Instead, they arise from variations in saturation that, at the interface level, manifest as uniform rescalings of physical processes. When expressed in geometric language, these rescalings reproduce the standard predictions of general relativity, including gravitational time dilation and the equivalence between gravitation and acceleration. The invariant local speed of light is not postulated but follows as a derived consequence, since both clock rates and signal propagation are affected identically by the same underlying saturation mechanism. The aim of this paper is not to introduce new empirical predictions beyond those of general relativity, nor to present a complete theory of quantum gravity. Rather, the objective is foundational: to demonstrate that the mathematical structure of general relativity can be reconstructed from a single pre-geometric postulate without assuming spacetime as part of the fundamental ontology. In this sense, SR should be understood as a reconstruction and reinterpretation of known physics, rather than as a competing dynamical theory. An extended and fully explicit formulation of the framework, including all intermediate steps, is available in a companion preprint (version V12) deposited on Zenodo. The present paper restricts itself to the minimal conceptual and mathematical structure required to establish logical consistency and to demonstrate the emergence of general-relativistic behavior at the interface level.
It is argued that the orthodox interpretation of quantum mechanics is in conflict with the objective existence of space-time, and suggested that kets are labels which name real states of matter but do not directly describe them. Position is a relationship between particles which necessarily contains uncertainty. The principle of superposition is seen as a definitional truism in the naming of states. The description of space in quantum logic resolves the measurement problem of quantum mechanics and related paradoxes such as Schrodinger's cat by attributing the collapse of the wave function to information.
Every physical theory is constructed from observations performed within a physical frame, and this frame enters the theory at a level antecedent to its equations — in the categorical structure through which observations are organized into a formalism. This is a structural condition on physical theory as such, not a hypothesis about any particular physical phenomenon; its character is analogous to the principle of general covariance, which constrains the form of physical laws without predicting the behavior of any specific system. The condition has a precise formal consequence in the geometric setting: for any non-invariant tensor field under a frame- transformation group, the components specified in any single frame are insufficient to determine the underlying geometric object without explicit specification of the frame. This consequence has been articulated four times in the foundations of physics — in the tensor reformulation of electrodynamics, in the relativity of simultaneity, in the unification of energy and momentum, and in the geometric unification of space and time — each time by identifying a frame-dependence carried implicitly in the prevailing formalism and absorbing it into a geometric object across the class of frames. Rovelli’s (1996) relational quantum mechanics is the most explicit contempo- rary articulation of the structural condition: the frame is the physical system to which a quantum state is referred, and the relational structure is exhibited directly at the level of the measurement interaction. The condition implies that relationality must arise wherever current physics is examined at the level of its foundations — not because relationality is a fundamental feature of the physics under description, but because it is a necessary feature of any theory constructed from observations performed within physical frames, and open foundational problems are most plausibly resolved by making implicit frame-dependences explicit rather than by eliminating them.
Abstract Quantum mechanics and relativity are extraordinarily successful mathematical theories, yet their conventional physical interpretations rely on substantially different conceptual frameworks. The Theory of Space (TS) proposes a fourth dimension defined by the Planck-related interval, with interpreted as a longitudinal dimension associated with energy (cτ), rather than as the conventional Minkowski spacetime interval. This fourth dimension does not coexist continuously with the observable three spatial dimensions as a conventional four-dimensional manifold. Instead, TS proposes an oscillatory existence between observable 3D presence and a non-observable fourth-dimensional phase. Through this oscillation, the quantum system undergoes repeated dimensional projection into observable 3D, with individual eigenstates manifested probabilistically while the underlying quantum state continues to evolve. Within this framework, phenomena including measurement, the Born rule, the arrow of time, entropy, entanglement, tunneling, and Bell-type correlations acquire a common physical interpretation. Heisenberg uncertainty and non-commutativity are interpreted as consequences of physical parameters associated with different phases of the dimensional oscillation and therefore not simultaneously manifested within the same 3D instance. TS further distinguishes between the quantum system’s spatial component and its compact physical entity. Their coexistence within the complete system provides a proposed physical basis for quantum interference and phase-dependent phenomena, including the double-slit experiment and the path-integral description of quantum evolution. As an extension of the model, TS proposes that the periodic displacement and replacement of quantum space generate a pulsed inward spatial flow. This mechanism provides a possible basis for a quantized gravitational interaction and suggests that gravitational energy may be represented by a positive contribution. Related developments, including spiral spatial flows, follow naturally from the same dimensional-oscillation mechanism. The Theory of Space therefore seeks to provide a common conceptual framework for quantum, relativistic, and gravitational phenomena without replacing the established mathematical equations that successfully reproduce experimental observations. The present work develops this framework and invites critical examination of its assumptions, physical implications, and potential experimental consequences. Keywords: relativity; Lorentz transformation; quantum superposition; quantum superposition; collapse; entanglement; quantum gravity