This paper proposes the Excitation Field Unification (EMU), a theoretical framework that unifies quantum mechanics and general relativity by redefining the fundamental structure of spacetime. We posit that the universe is not a continuous manifold but a discrete lattice of physical scalar oscillators (Quantum Circulation Loops). By rejecting the probabilis- tic interpretation of the wave function in favor of a realistic "physical rotation" model, we demonstrate that matter and mass emerge inevitably as topological defects (winding num- bers) within this lattice. Furthermore, we derive the wave-particle duality and the de Broglie relations as geometric consequences of pattern propagation on the lattice, without invoking the collapse of a wavefunction. This work constitutes Part I of a trilogy, focusing on the ontology of the quantum state and the origin of mass, setting the stage for the emergence of gravity (Part II) and fundamental constants (Part III).
This paper proposes the Excitation Field Unification (EMU), a theoretical framework that unifies quantum mechanics and general relativity by redefining the fundamental structure of spacetime. We posit that the universe is not a continuous manifold but a discrete lattice of physical scalar oscillators (Quantum Circulation Loops). By rejecting the probabilis- tic interpretation of the wave function in favor of a realistic "physical rotation" model, we demonstrate that matter and mass emerge inevitably as topological defects (winding num- bers) within this lattice. Furthermore, we derive the wave-particle duality and the de Broglie relations as geometric consequences of pattern propagation on the lattice, without invoking the collapse of a wavefunction. This work constitutes Part I of a trilogy, focusing on the ontology of the quantum state and the origin of mass, setting the stage for the emergence of gravity (Part II) and fundamental constants (Part III).
We present a quantum framework grounded in micro-causality and spacetime quantization, where spacetime is composed of discrete, causally ordered units rather than a continuous manifold. This intrinsic structure naturally generates fundamental quantum features—wave–particle duality, energy quantization, and the Heisenberg uncertainty principle—without invoking canonical quantization, matter-wave postulates, or harmonic-oscillator models. Consequently, this paradigm eliminates the long-standing paradoxes of wavefunction collapse, self-interference, and non-local spooky correlations in entanglement.Within this causal lattice spacetime, quantum commutation relations emerge from finite shift operators, and the uncertainty principle arises geometrically from non-commutativity at the fundamental level. Unlike standard quantum field theory (QFT), which predicts infinite vacuum energy and requires renormalization, the present framework removes zero-point energy, ultraviolet divergences, and fine-tuning. Moreover, U(1) symmetry is broken geometrically on the lattice, leading to mass generation without a Higgs mechanism.The Casimir effect is reinterpreted as a temperature-dependent imbalance in thermal radiation pressure rather than the consequence of vacuum fluctuations, predicting that the Casimir force should vary with ambient temperature. Experimental confirmation of such dependence would directly support the lattice interpretation and challenge the QFT view of vacuum energy.By unifying key quantum behaviors through discrete causal geometry, this model offers a divergence-free and physically grounded alternative to continuum-based QFT. It opens new avenues for quantum unification, cosmology, and the understanding of fundamental constants, without speculative constructs, singularities, or infinities.
This article proposes a unified theory framework encompassing a discrete topological interpretation of physical forces, wave functions, and the nature of space and time. It provides novel explanations for the collapse of wave functions, quantum entanglement, and offers insights into the origins of quantum probabilities. This article also explains the nature of mass, Higgs field, and suggests a path for unifying quantum mechanics and gravity. Elementary particles are represented as defects in discrete topological spaces. Entangled particles are directly connected to each other through a puncture in discrete space, separated by a distance of one Planck length. Wave functions are explained as mechanical stress waves within elastic discrete space. The results of the double-slit experiment are interpreted as wave functions maximizing the probability of rupture in high-stress areas of discrete space with obvious analogies to solid state mechanics. Wave-particle duality is explained as discrete topological defects causing extended distributed stress within space lattice.
The persistent challenge of unifying quantum mechanics with general relativity is often traced to a series of apparent structural tensions: complex versus real ontology, probabilistic versus deterministic dynamics, linear versus nonlinear evolution, and spectral discreteness versus geometric continuity. We argue that these tensions do not signal a fundamental incompatibility between the theories, but rather originate from surplus structure in the conventional formulation of quantum mechanics. The term unification is used in a structural sense, referring to compatibility of quantum dynamics with classical field theory rather than a modification of general relativity. Beginning from the physically indispensable requirement of matter stability, we prove that the Hamiltonian spectrum can always be shifted to become non-negative. The consequent positivity of energy enforces one-sided temporal frequency support for all physical unitary orbits. Equivalently, all scalar temporal components of physical states arise as boundary values of functions analytic in the lower half of the complex time plane, selecting the Hardy space—or, more generally, analytic tempered distributions—as the admissible solution space. In these spaces, the real and imaginary parts of the wave function are not independent; they are linked uniquely via the temporal Hilbert transform. Hence, the complex structure of quantum mechanics emerges as a representational artifact of an underlying real operator algebra. Building on our earlier work on Unified Quantum Mechanics and the Unified Real Wave Equation, we establish a rigorous proof of exact equivalence between the real-field evolution and the Schr\"odinger equation on the physical subspace. Probabilistic quantities arise naturally as quadratic invariants of analytic signals, rather than as independent postulates. We further show that quantum spectral discreteness arises from operator-theoretic confinement and boundary conditions on a smooth spacetime manifold, and does not imply any fundamental discreteness of spacetime. The resulting framework provides a real-field formulation of quantum mechanics and gravitation, with stability and causality implemented as foundational principles, and demonstrates that the Einstein field equations are compatible with a unified field-theoretic description of spacetime and matter. Extending the same analyticity principle to spacetime geometry, we propose an analytic formulation of the Einstein field equations, from which classical general relativity is recovered exactly as the real projection.
We propose a novel operator-based formulation of quantum gravity grounded in two foundational principles: a discrete causal lattice and algebraic microcausality. Departing from traditional continuum approaches and wavefunction-based quantum mechanics, this framework models spacetime and matter as emergent phenomena arising from the algebraic structure of displacement operators. In this first part of a two-part series, we construct the foundational framework and demonstrate how key features of quantum mechanics—such as the uncertainty principle, de Broglie relations, and entanglement—emerge naturally without invoking wavefunctions, path integrals, or metric-based geometry. Operator non-commutativity on the causal lattice gives rise to a self-consistent quantum structure with natural ultraviolet finiteness, intrinsic time directionality, and a microcausal interpretation of measurement. This foundational part lays the groundwork for gravitational dynamics, cosmology, and the grand unification principles of gravity and the Standard Model to be explored in the sequel to quantum gravity part II.
Addressing the fundamental metaphysical question of the origin of Being, this paper takes de Broglie’s classical wave mechanics (1924) as its scientific foundation and constructs a self‑consistent interpretive framework of information ontology. It establishes three core axioms: information as the primordial ground, relations prior to entities, and global conservation of information. On this basis, the paper further derives the origin of spatiotemporal dimensions from the laws of information interaction: each basic flip configuration of information corresponds to the generation of a spatial dimension; after three‑dimensional topological closure is completed, the inevitably produced “pending redundant information” that cannot be synchronously and self‑consistently integrated gives rise to the dimension of time within its queuing sequence. Spacetime is therefore not an a priori container but the first compensatory stratum of structure through which information moves toward self‑consistent expression. Subsequently, by means of de Broglie’s phase field, the paper deduces the entire evolutionary chain from pure information distinctions and primordial phase oscillation to the emergence of material hierarchies and quantum‑observation interactions. It argues that quantum measurement and wave‑function collapse are essentially topological remappings and information‑coupling consolidations of heterogeneous phase fields; gravitation and cosmic expansion can be reduced to macroscopic effects of phase gradients. Throughout the text, physical references are strictly limited to de Broglie’s classical wave mechanics, without introducing non‑standard physical models. This study supplements fundamental physical philosophy with a relational‑ontology approach and provides a unified information‑theoretic metaphysical interpretation for foundational problems such as wave–particle duality, the origin of spacetime, and the nature of gravity.
This paper proposes a theoretical framework—Relational Theory—based on dynamic relational networks, in which discrete spacetime serves as the fundamental ontology, while continuous geometry and gravity emerge as macroscopic statistical phenomena. This framework unifies the description of matter, spacetime, and gravity, aiming to bridge the theoretical divide between quantum field theory and general relativity, while providing a discrete spacetime physical substrate for the orthodox prob abilistic interpretation of quantum mechanics. The fundamental ontology of the universe is defined as the evolution of a dynamic relational network, where nodes represent fundamental quantum units of space, edges correspond to adjacency relations between units, and matter manifests as complex probability amplitude excitation modes propagating on the network. The framework is built upon two foundational axioms: the matter field undergoes unitary evolution driven by the graph Lapla cian operator, and the network topology dynamically reconfigures in response to the matter energy density, with links undergoing continuous generation and decay, while matter evolution exhibits the discrete alternating character of “annihilation here, creation there.”Under the mean-field continuum limit, the two axioms respectively evolve into a Schr¨odinger equation describing matter propagation in curved space and a link density equation characterizing the response of spacetime geometry to matter distribution. These two sets of equations form a self-consistent feedback mechanism in which matter and spacetime geometry mutually constrain each other. The study demonstrates that grav ity is not a fundamental interaction, but rather a statistical emergent entropic force driven by the inhomogeneous spatial distribution of network link density.This paper further proposes a dynamic relational network interpretation, circumventing the collapse paradox of the Copenhagen interpreta tion, the universe-splitting problem of the many-worlds interpretation, and the non-locality dilemma of hidden variable theories. It provides an underlying topological explanation for wave function evo lution, the measurement problem, and the origin of quantum probability. The laws of black hole thermodynamics and the fundamentals of the holographic principle can all be reasonably explained within this microscopic topological framework. The paper systematically verifies the mathematical self-consistency of the model, distinguishes rigorously derived conclusions from conjectures awaiting verification, and demonstrates the feasible pathways for numerical simulation tests and astronomical observational corroboration.