The challenge of unifying quantum gravity with the standard model of particle physics arises from several fundamental differences and conceptual issues between the two theories. Here are some reasons why quantum gravity has been difficult to reconcile with the standard model:
Scale and Energy: The standard model describes the behavior of elementary particles and their interactions at energy scales accessible to current particle accelerators, such as the Large Hadron Collider (LHC). On the other hand, quantum gravity becomes significant at extremely high energy scales, typically associated with the Planck scale (around 10^19 GeV), which is far beyond the reach of current experimental techniques. The disparity in energy scales between the standard model and quantum gravity makes it challenging to directly observe and test predictions of quantum gravity using current experimental methods.
Quantum Field Theory vs. General Relativity: The standard model is formulated within the framework of quantum field theory, which successfully combines quantum mechanics and special relativity to describe the behavior of particles and forces (except gravity). However, general relativity, which describes gravity as the curvature of spacetime, does not fit easily into the framework of quantum field theory. Attempts to naively quantize gravity encounter several conceptual and mathematical challenges, leading to the problem of non-renormalizability in the standard perturbative approach to quantization.
Renormalizability and Ultraviolet Divergences: In the standard model, the theory can be made mathematically consistent through the process of renormalization, which deals with the infinities that arise in quantum field theory calculations. However, when attempting to apply the same techniques to gravity, severe ultraviolet divergences (infinities related to high-energy physics) arise. These divergences indicate that gravity is non-renormalizable within the framework of standard quantum field theory.
Conceptual Differences: The standard model describes the behavior of elementary particles and their interactions within a flat, fixed background spacetime. In contrast, general relativity, which is a classical theory, describes the curvature and dynamics of spacetime itself. Unifying quantum gravity with the standard model requires reconciling these conceptual differences and developing a consistent framework that incorporates both particle interactions and the dynamical nature of spacetime.
Lack of Experimental Evidence: Another challenge in unifying quantum gravity with the standard model is the lack of direct experimental evidence for quantum gravity. Since quantum gravity effects become significant at extremely high energy scales, testing and verifying predictions of quantum gravity experimentally remain elusive. Without experimental data to guide theoretical development, progress in finding a definitive theory of quantum gravity becomes more challenging.
Due to these and other complexities, achieving a complete and consistent theory that unifies quantum gravity with the standard model remains an active area of research and one of the biggest open questions in theoretical physics. Various approaches, such as string theory, loop quantum gravity, and other quantum gravity frameworks, are being explored in the quest for a unified theory.