We’re pleased to share the revised preprint of our work on a discrete quantum-graph theory of spacetime (the Quantumograph). The Quantumograph is a discrete quantum graph model in which continuum field theories — including general relativity and gauge theories — emerge as effective descriptions at long wavelengths. Importantly, the discrete graph model is presented as the fundamental ontology; continuum theories arise only as approximations in a controlled scaling regime. Initial emulations and numerical checks (see our GitHub repository) qualitatively support the construction; true empirical confirmation will require implementation of the measurement protocol described in the paper, which is feasible on current QPU platforms under the conditions we specify. Key testable elements include predictions for qubit platforms (QPU and annealers), microwave/dielectric signatures, two-boundary (retrocausal) tests of causality, CHSH/Bell observables, and relations tying emergent constants to cosmological scales. Feedback and collaboration welcome.
We’re pleased to share the revised preprint of our work on a discrete quantum-graph theory of spacetime (the Quantumograph). The Quantumograph is a discrete quantum graph model in which continuum field theories — including general relativity and gauge theories — emerge as effective descriptions at long wavelengths. Importantly, the discrete graph model is presented as the fundamental ontology; continuum theories arise only as approximations in a controlled scaling regime. Initial emulations and numerical checks (see our GitHub repository) qualitatively support the construction; true empirical confirmation will require implementation of the measurement protocol described in the paper, which is feasible on current QPU platforms under the conditions we specify. Key testable elements include predictions for qubit platforms (QPU and annealers), microwave/dielectric signatures, two-boundary (retrocausal) tests of causality, CHSH/Bell observables, and relations tying emergent constants to cosmological scales. Feedback and collaboration welcome.
We’re pleased to share the revised preprint of our work on a discrete quantum-graph theory of spacetime (the Quantumograph). The Quantumograph is a discrete quantum graph model in which continuum field theories — including general relativity and gauge theories — emerge as effective descriptions at long scale. Importantly, the discrete graph model is presented as the fundamental ontology; continuum theories arise only as approximations in a controlled scaling regime. Initial emulations and numerical checks (see our GitHub repository) qualitatively support the construction; true empirical confirmation will require implementation of the measurement protocol described in the paper, which is feasible on current QPU platforms under the conditions we specify. Key testable elements include predictions for qubit platforms (QPU and annealers), microwave/dielectric signatures, two-boundary (retrocausal) tests of causality, CHSH/Bell observables, and relations tying emergent constants to cosmological scales. Feedback and collaboration welcome.
Quantum gravity is traditionally regarded as a domain of mathematical physics devoid of direct empirical access. This paper proposes an alternative research program-the Quantumograph (TQGT) (Materov 2026) - in which spacetime is ontologically identical to a finite quantum graph, while continuum notions (metric, fields, time) are strictly emergent. I argue that this program possesses excess empirical content: its central predictions are testable on existing cryogenic quantum processors, thereby relocating quantum gravity from speculation to experimental science. Philosophical analysis reveals ontological consequences: support for ontic structural realism, the constitutional finitude of the Universe, the dynamic nature of time, and two fundamental theorems on the absence of asymptotic chaos and computational reducibility. A comparison with string theory, loop quantum gravity, and the Fredkin–Wolfram–Lloyd digital-physics tradition locates the program's unique status as a falsifiable digital structuralism.
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 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.
We propose a minimal discrete model in which causality, time, spacetime geometry, and quantum measurement emerge from a single primitive concept: the node (boundary). A node is defined as an irreversible completely positive (CP) map representing interaction simultaneity—the fundamental unit where states undergo non-unitary transformation. Conventional causality is reconceptualized as a chain of such nodes connected by reversible propagation. Time is not an external parameter but the cumulative count of nodes; temporal flow velocity is proportional to node density. We demonstrate that Minkowski spacetime emerges as the continuum limit of a node network, with gravitational curvature arising from spatial gradients in node density. The quantum measurement problem dissolves naturally as nodes represent the only loci of irreversibility. We derive testable predictions for gravity-induced decoherence independent of gravitational phase shifts, offering clear falsifiability. This framework unifies gravity, quantum mechanics, thermodynamics, and temporal phenomenology through a single ontological primitive: the event itself.
Derivative Continuum: An Event-Based Framework for Quantum Mechanics and Emergent Spacetime Geometry We present a theoretical framework called Derivative Continuum, in which physical reality is composed of discrete events and their mutual complex relation amplitudes, rather than continuous fields or point particles. A reproducing kernel Hilbert space (RKHS) is constructed from a positive-definite kernel that maps the discrete event configuration into a continuous derived field Ψ(x). Within this structure: The Schrödinger equation arises from unitary evolution of event amplitudes in the RKHS projection. The Born rule is derived from the reproducing inner product, not assumed. The Einstein field equations emerge as a self-consistency condition when the kernel depends on spacetime geometry. The framework contains a single free parameter ℓ₀, a fundamental relation scale. When ℓ₀ → 0 and event density becomes infinite, standard quantum mechanics and classical general relativity are fully recovered. At finite ℓ₀, corrections appear. As a concrete example, we compute the leading deviation in the double-slit experiment: a suppression of interference visibility and a non-sinusoidal envelope distortion, both scaling as (ℓ₀/d)² where d is the slit separation. This work does not claim to replace existing theories. It offers a candidate pre-paradigm language that re-derives known results from fewer assumptions and opens a new path toward quantum gravity. Comments, criticism, and collaboration are welcome.