📝 SummarXiv

Abstract

Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory of quantum spacetime becomes the key problem about quantum gravity. This paper is the solution to this problem. The starting point of this paper is very simple -- physical variant with higher-order variability (see the below discussion). Based on this simple starting point, a microscopic theory for quantum spacetime is developed, including its matrix representation for quantum states, its time evolution, its geometry quantization, its generalized symmetry, its canonical quantization, and the uncertainty principle, black hole, AdS/CFT correspondence, scattering amplitudes of gravitons... The result leads to a great unification of matter and spacetime -- the particles constitute the basic blocks of spacetime and spacetime is really a multi-particle system that is made of matter. As a result, this work would help researchers to understand the mysteries in quantum gravity.