Yes, there is something missing in quantum field theory that drives the search for quantum gravity. Quantum field theory, which successfully describes the behavior of particles and their interactions within the framework of quantum mechanics, is a non-gravitational theory. It does not incorporate the gravitational force, which is described by Einstein's theory of general relativity.
General relativity provides a classical description of gravity, treating it as the curvature of spacetime caused by the presence of matter and energy. However, when we try to combine general relativity with quantum field theory, we encounter significant theoretical challenges. The mathematics of general relativity and quantum field theory do not easily merge, leading to various conceptual and technical difficulties.
Quantum gravity is the ongoing effort to develop a consistent theory that incorporates both quantum mechanics and general relativity. It aims to describe the behavior of gravity at the quantum level, where the discrete and probabilistic nature of quantum mechanics becomes important.
The search for quantum gravity is driven by the desire to understand the fundamental nature of the universe at the most fundamental level and to reconcile the principles of quantum mechanics with those of general relativity. Such a theory would be crucial for understanding the behavior of the universe at extremely small scales, such as the Planck scale, where the effects of gravity and quantum mechanics are expected to become significant.
Several approaches to quantum gravity have been proposed, such as string theory, loop quantum gravity, and causal set theory, among others. However, finding a complete and consistent theory of quantum gravity remains an active area of research, and it is an ongoing challenge in theoretical physics.