Finding a viable theory of quantum gravity is a challenging task due to several reasons:
Unification of quantum mechanics and general relativity: Quantum mechanics describes the behavior of particles and fields on small scales, while general relativity provides a description of gravity on large scales. These two theories have been enormously successful in their respective domains, but they are fundamentally incompatible with each other. The mathematical frameworks and conceptual underpinnings of quantum mechanics and general relativity are vastly different, making their unification a non-trivial task.
Quantum gravity's high energy and small distance regimes: To fully understand gravity at the quantum level, one needs to consider extremely high energies and small distances, which are beyond the reach of current experimental capabilities. These regimes are associated with the Planck scale, where the effects of gravity become significant, and quantum gravitational phenomena are expected to manifest. Exploring the Planck scale requires novel theoretical and experimental approaches that have yet to be developed.
Lack of experimental data: Unlike other areas of physics where experimental observations play a crucial role in guiding theoretical developments, quantum gravity lacks direct experimental data. Since the energies and distances involved are currently inaccessible, researchers rely on theoretical arguments, mathematical consistency, and indirect observations to construct potential theories. This absence of empirical constraints makes it challenging to verify and refine proposed models of quantum gravity.
Complex mathematical challenges: The search for a theory of quantum gravity involves complex mathematical challenges. The mathematical frameworks of quantum mechanics and general relativity are already intricate on their own, and combining them in a consistent way requires sophisticated mathematical tools and approaches. Various techniques, such as perturbative expansions, non-perturbative methods, and approaches from string theory and loop quantum gravity, have been explored, but no definitive solution has emerged yet.
The nature of space and time: Quantum gravity also grapples with fundamental questions about the nature of space and time themselves. General relativity treats spacetime as a smooth, continuous manifold, while quantum mechanics introduces discreteness and uncertainty at the quantum level. Understanding how spacetime emerges from a more fundamental framework and reconciling the discreteness of quantum mechanics with the smoothness of general relativity is a significant conceptual challenge.
Despite these difficulties, researchers continue to explore various avenues in the quest for a theory of quantum gravity. String theory, loop quantum gravity, and other approaches provide potential frameworks for unifying gravity and quantum mechanics, but they are still under active development and subject to ongoing debate and scrutiny. Progress in this field requires advances in both theoretical understanding and experimental capabilities that can probe the Planck scale more directly.