A Triadic Theory of Spacetime: Essential Properties, the Double-Loop Model, and Recalculation of Established Quantum Mechanical Results

This paper presents a theoretical framework for the fundamental structure of spacetime. This theory first identifies eight essential properties that any coherent spacetime ontology must possess: absolute staticity, absolute rhythmicity, space-time inseparability, topological stability, locality, positional determinacy, scale invariance, and dynamic evolvability. To render these properties into a computable mathematical form, the "Double-Loop Structure" is introduced as an idealized mathematical model—not a hypothesized physical entity. In this model, an absolutely static loop characterizes the rest frame, an eternally periodic dynamic loop characterizes the metronome of time, and their topological entanglement (linking number L=1) characterizes the inseparability and stability of spacetime units. Without employing any standard quantum mechanical postulates, this framework is applied to recalculate three experimentally confirmed cornerstones of quantum mechanics: the blackbody radiation spectrum, the photoelectric effect, and the hydrogen spectrum. All three recalculations reproduce the established formulas exactly. The origin of quantization is traced to the essential properties of spacetime embodied in the model, rather than to ad hoc quantum hypotheses. The Double-Loop Model thus serves as a mathematically precise and physically transparent proxy for the essential structure of spacetime. (Note on AI-Assisted Computation Certain mathematical derivations and calculations in this paper were performed by an AI tool (large language model) based on the theoretical framework and postulate system provided by the author. Specifically, the AI tool contributed to: formula derivation, equation solving, integral evaluation, series summation, and recalculation verification of established quantum mechanical results. All physical insights, core assumptions, logical premises, and the theoretical framework itself were independently developed by the author. The AI tool served solely as an auxiliary instrument for mathematical derivation and computational verification, comparable in role to symbolic computation software or numerical tools routinely employed by researchers. The author has reviewed every derived result for physical plausibility, consistency with known experimental data, and logical coherence, and assumes full responsibility for all conclusions. This statement is provided in the interest of academic transparency, while clearly distinguishing between the originality of ideas and the auxiliary role of computation.)