The Fractal Quantum Gravity

Abstract

Based on the smallest physical constant of the product of space interval, time interval, and energy, the fractal quantum gravity (FQG) theory has demonstrated that every particle or physical system consists of these smallest units in fractal structures. The general relativity is an approximation of the FQG equation when the quantum effect is negligible, while the quantum theory is an approximation of the FQG equation when the interaction between space, time, and energy is very weak or negligible. The stationary-action principle can be derived from the FQG equation. The mass range of possibly existing elementary particles and an accelerating expansion evolution model of the universe can be obtained through the FQG equation. This FQG equation satisfied almost all the requirements of a quantum gravity theory and there is no free constant needed in the FQG theory. It looks promising that the FQG theory may offer a novel way to calculate all the free constants in the Standard Model of particle physics and general relativity.