Finding a viable theory of quantum gravity is a challenging task for several reasons. Here are some of the key difficulties associated with this endeavor:
Unification of General Relativity and Quantum Mechanics: General relativity describes gravity as the curvature of spacetime, while quantum mechanics deals with the behavior of particles and fields at the microscopic level. These two theories have been incredibly successful in their respective domains, but they are fundamentally incompatible with each other. Quantum gravity aims to reconcile these two frameworks into a single consistent theory, which is no easy task.
High Energy and Small Scales: Quantum gravity becomes crucial in extreme conditions such as the early universe, black holes, or the very beginning of the Big Bang. At such high energies and small scales, both quantum effects and gravitational effects become important. Understanding the nature of spacetime and gravity in these extreme regimes requires a theory that goes beyond what we currently have.
Lack of Empirical Data: Our current experimental capabilities are limited when it comes to probing the quantum gravitational regime directly. The energy scales at which quantum gravity effects become significant are far beyond the reach of current particle accelerators. Consequently, we lack direct empirical evidence to guide us towards a theory of quantum gravity. This makes it challenging to test and validate potential theories, as they often rely on mathematical consistency and theoretical elegance.
Non-Renormalizability: Renormalization is a technique in quantum field theory that allows physicists to deal with infinities that arise in certain calculations. However, when applying this technique to the combination of general relativity and quantum field theory, the resulting theory appears to be non-renormalizable. This poses a fundamental challenge because non-renormalizability leads to inconsistencies and makes it difficult to extract meaningful predictions.
Lack of a Unified Framework: Various approaches have been proposed to tackle quantum gravity, such as string theory, loop quantum gravity, and causal dynamical triangulation, among others. However, these approaches often have different assumptions, mathematical formalisms, and predictions. There is currently no consensus or overarching framework that unifies all these different approaches into a single theory of quantum gravity.
It's important to note that progress has been made in various directions, and researchers continue to explore different avenues in the quest for a theory of quantum gravity. However, the complexity and fundamental nature of the problem make it one of the most challenging puzzles in modern theoretical physics.