The theory of quantum gravity does not depend on specific physical constants like the fine structure constant or the speed of light, as these constants are typically associated with other areas of physics, such as quantum electrodynamics or special relativity.
However, there are certain fundamental constants that are relevant in the context of quantum gravity due to their significance in gravitational interactions. These include:
Newton's gravitational constant (G): This constant appears in Newton's law of gravitation and determines the strength of the gravitational force between two objects. In the context of quantum gravity, the behavior of gravitons (hypothetical particles that mediate the gravitational force) and the quantum effects of gravity are influenced by G.
Planck's constant (h): Planck's constant is a fundamental constant in quantum mechanics and describes the quantization of energy and the behavior of particles at the quantum scale. In the context of quantum gravity, the interplay between quantum mechanics and gravity becomes important, and Planck's constant sets the scale at which quantum gravitational effects are expected to become significant.
The speed of light in vacuum (c): Although the theory of quantum gravity aims to reconcile quantum mechanics with gravity, which is described by general relativity, the constant speed of light in vacuum is still relevant. This constant plays a crucial role in the structure of general relativity and serves as an important reference for the behavior of gravitational waves and the propagation of information.
It is important to note that quantum gravity is still an area of ongoing research, and the specific role of these constants and their interplay with the theory are subjects of active investigation and debate. The quest for a complete theory of quantum gravity aims to uncover the fundamental principles that underlie the behavior of gravity at the quantum level.