The incompatibility between the theory of relativity and quantum mechanics arises due to fundamental conceptual differences and mathematical inconsistencies between the two theories. While both theories are highly successful in their respective domains of applicability, they describe the behavior of the universe at different scales and under different conditions, leading to conflicts when trying to unify them into a single, coherent framework.
One of the key differences is the nature of spacetime. In general relativity, spacetime is described as a smooth, continuous four-dimensional manifold that can be curved by the presence of mass and energy. On the other hand, quantum mechanics treats spacetime as a fixed background and focuses on the behavior of elementary particles and their interactions.
Additionally, there is a discrepancy in the mathematical formalism used in the two theories. Quantum mechanics employs wave functions and probabilities to describe the behavior of particles, whereas general relativity is based on the geometry of spacetime described by Einstein's field equations.
Attempts to reconcile the two theories have been made, such as the development of quantum field theory (QFT) on curved spacetime, which combines aspects of both theories. However, a complete and consistent theory of quantum gravity that fully incorporates both general relativity and quantum mechanics remains elusive. This has been a major challenge in theoretical physics, and various approaches, such as string theory, loop quantum gravity, and other quantum gravity models, have been proposed, but none has yet been conclusively proven.
Ultimately, the resolution of the conflict between general relativity and quantum mechanics requires a deeper understanding of the fundamental nature of space, time, and gravity at the quantum level, which is an ongoing area of research in theoretical physics.