Study on Physical Mechanism of Endogenous Repulsive Force of Uncertainty Principle and Quantum Probability‑Cloud Matter Field

Abstract: Existing interpretations of the uncertainty principle in quantum mechanics are confined to mathematical statistical constraints and lack concrete physical mechanisms. This paper proposes that the probability cloud of micro‑particles possesses physical reality and constitutes an intrinsic material quantum field of particles. Based on the fundamental criteria of force‑work‑energy conservation in classical mechanics, this paper systematically demonstrates that the field‑density‑gradient effect induced by compression of probability clouds in confined spaces serves as the physical origin of endogenous quantum repulsive force at microscale. The research indicates that the position‑momentum trade‑off relation of the uncertainty principle is not merely a mathematical representation. Instead, it represents an intrinsic dynamic effect of the probability‑cloud matter field to maintain its normalized distribution and resist spatial compression. This work establishes a complete physical picture covering materiality of probability‑cloud field, field‑energy evolution and quantum repulsive‑force effect. It improves the energetic theoretical foundation for the uncertainty principle and provides new theoretical perspectives for researches on micro‑quantum repulsion effects and quantum spatial‑confinement mechanisms.