The equations of quantum physics, specifically quantum mechanics, and those of quantum gravity are related in the sense that they both describe the behavior of particles and fields at the microscopic level. However, the specific equations used in quantum mechanics and quantum gravity are different due to the distinct nature of the phenomena they address.
Quantum mechanics provides a framework for describing the behavior of particles and their interactions, including the wave-particle duality and probabilistic nature of quantum systems. The equations of quantum mechanics, such as the Schrödinger equation or the equations of quantum field theory, describe the evolution of quantum states and the probabilities of different measurement outcomes.
On the other hand, quantum gravity aims to describe the behavior of gravitational interactions at the quantum level. The goal of quantum gravity is to develop a theory that combines quantum mechanics with general relativity, which is the theory of gravity on large scales. However, a consistent and mathematically rigorous theory of quantum gravity is still an active area of research, and there is no widely accepted framework for it.
Various approaches to quantum gravity, such as string theory, loop quantum gravity, and causal set theory, propose different mathematical formulations and equations to address the quantum nature of gravity. These approaches involve modifying or extending the equations of general relativity to incorporate quantum effects.
In summary, while both quantum mechanics and quantum gravity deal with the behavior of particles and fields at a microscopic level, they have distinct mathematical frameworks and equations. Quantum gravity seeks to extend our understanding of gravity by incorporating quantum principles, but a complete and unified theory of quantum gravity is still an ongoing research endeavor.