Dynamics of Quantum Vacuum Fluctuations and Their Coupling to Spacetime Curvature in Semiclassical Gravity

Article written by Nicolas Camargo Marques - 14 years old, Brazilian. This work presents a comprehensive theory connecting quantum vacuum fluctuations with the curvature of spacetime, bridging concepts from quantum field theory and general relativity. The vacuum is modeled as a fundamental field, whose tiny oscillations propagate through space and collectively give rise to classical gravitational effects. These micro-oscillations, although individually negligible, accumulate statistically to influence macroscopic phenomena such as the formation of gravitational fields around massive bodies. The theory provides a framework to understand how quantum effects can subtly modify classical gravity, suggesting that even massless or nearly light-speed particles can experience shifts due to vacuum fluctuations. By analyzing the energy density of these fluctuations, their propagation, and interactions, the model demonstrates a self-consistent connection between the quantum and classical worlds. Extensive numerical tests were carried out, ranging from subatomic particles to astrophysical objects, confirming that quantum contributions remain small but measurable under extreme conditions, and that the semiclassical approximation is robust for most practical scenarios. Conceptually, the theory explores the emergence of gravitational effects from the quantum vacuum, the potential influence on the speed of light in localized regions, and the possibility of observable temporal distortions caused by collective oscillations. This research also addresses challenges in renormalizing the vacuum energy, extending the framework to regions of strong curvature, and ensuring compatibility with multiple fields of the Standard Model. The work lays the foundation for future explorations into semiclassical gravity, the interaction of quantum fields with spacetime, and potentially testable predictions that could be observed in high-precision experiments. The document serves as a complete conceptual reference, providing a coherent narrative that explains the principles, implications, and numerical validation of the theory, making it suitable for dissemination to both academic and specialized audiences.