Fitting gravity into the framework of quantum mechanics has been a long-standing challenge in theoretical physics. The main difficulty arises from the fundamental differences between the two theories and their mathematical descriptions.
Quantum mechanics successfully describes the behavior of particles on small scales, such as atoms and subatomic particles. It is based on the principles of superposition and uncertainty, where particles can exist in multiple states simultaneously and their properties are described by probabilities. The mathematics of quantum mechanics is formulated in terms of wave functions and operators.
On the other hand, gravity is described by Einstein's general theory of relativity, which provides a geometric description of gravity as the curvature of spacetime caused by mass and energy. General relativity is a classical theory that works well in the macroscopic regime, such as the motion of planets and galaxies. It does not incorporate the principles of quantum mechanics.
The challenge lies in reconciling the probabilistic, wave-like nature of quantum mechanics with the smooth, deterministic nature of general relativity. This task requires developing a theory of quantum gravity, which would provide a consistent framework for describing the quantum behavior of spacetime itself.
Several approaches have been proposed to tackle this problem, such as string theory, loop quantum gravity, and causal dynamical triangulations, among others. These approaches attempt to extend or modify either quantum mechanics or general relativity to accommodate both theories simultaneously.
However, finding a complete and satisfactory theory of quantum gravity is still an active area of research, and it remains one of the greatest unsolved problems in theoretical physics. It is a highly complex and challenging task due to the lack of experimental data at the Planck scale, where both quantum effects and gravity are expected to be important.