Buffon-Einstein Intersection Ratio: A Quantum Gravitational Probability Factor Bridging General Relativity and Quantum Mechanics License: This work is licensed under a Creative Commons Attribution of CC-By 4.0 International. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/

This paper introduces a novel approach inspired by Einstein’s thought experiments and Buffon’s needle problem, which aims to bridge General Relativity and Quantum Mechanics by developing a usable probability factor[1,2,3,4]. Through a modified Buffon Needle experiment incorporating Lorentz contraction effects and quantum uncertainty at Planck scales, we propose a theoretical framework to convert between General Relativity and Quantum Mechanical descriptions. Analyzing this in an accelerating frame, we explore quantum effects in spacetime geometry and offer potential applications in Loop Quantum Gravity, String Theory, and Quantum Computing, as well as Dark Matter, Dark Energy, and Information Paradoxes.