Finding a viable theory of quantum gravity is a challenging task because it requires reconciling two fundamental theories of physics: quantum mechanics and general relativity.
Quantum mechanics describes the behavior of particles and fields at the smallest scales, such as atoms and subatomic particles, and has been tremendously successful in explaining phenomena in the realm of the very small. On the other hand, general relativity is the theory of gravity, which describes the gravitational interactions between massive objects and the curvature of spacetime. It has been successful in explaining the behavior of gravity on cosmic scales, such as the motion of planets and the bending of light around massive objects.
The difficulty arises because these two theories have different mathematical formulations and conceptual frameworks. In quantum mechanics, particles and fields are described by wave functions and probabilities, while in general relativity, gravity is described by the curvature of spacetime caused by mass and energy. The mathematical techniques and principles used in each theory are not easily compatible with each other.
Additionally, at extremely small scales, such as the Planck scale, where quantum gravitational effects become important, the curvature of spacetime becomes highly significant. This means that the classical description of gravity breaks down, and a quantum theory of gravity is required to understand the fundamental nature of spacetime and gravitational interactions in these extreme regimes.
Several approaches have been proposed in the search for a theory of quantum gravity, such as string theory, loop quantum gravity, and causal set theory, among others. Each of these approaches has its own set of challenges and open questions. They involve complex mathematical formalisms and often require novel conceptual frameworks that are still under active investigation and development.
The unification of quantum mechanics and general relativity into a consistent theory of quantum gravity remains an active area of research, and scientists continue to explore new ideas and approaches in the quest for a deeper understanding of the fundamental nature of the universe.