Heuristic Approach to Quantum Gravity in Terms of Incremental Curvature of Spacetime

Abstract Physicists since Einstein have pondered how gravitation and quantum mechanics could be connected fundamentally given widely differing scales and mathematical formalism. Gravitational bending of light in null geodesics around an isolated point mass, curved incrementally to Compton’s wavelength is proposed to associate semi-classical particle interactions with quantum wave phenomena. Although a basic methodology rather than a full quantum theory of gravity, this path leads to a simple expression of gravity at the quantum level in terms of constants ℏ, c, and G, with mass as the source of gravitational curvature. When taken further to the Planck scale, quantized spacetime curvature is the square of the inverse Planck length which is a constant and the canonical inner boundary of spacetime. This elementary thought experiment of spacetime curvature taken to the Planck limit arrives at the ultimate state where quantum gravity existed in the very early universe. This state may also exist at the smallest scales in the current universe as curvature entanglement at nearly undetectable low energy due to the relative strength of gravity.