General relativity and quantum theory are two fundamental theories in physics that describe the behavior of the universe at different scales. General relativity, formulated by Albert Einstein, provides a framework for understanding gravity and the behavior of massive objects on a large scale, such as planets, stars, and galaxies. On the other hand, quantum theory deals with the behavior of particles at the microscopic level, encompassing phenomena like particle interactions and the fundamental forces of nature.
The main reason why general relativity and quantum theory have not been successfully combined into a single unified theory is that they have different mathematical formulations and conceptual foundations that are difficult to reconcile. These differences arise due to the nature of space, time, and the fundamental quantities they describe.
General relativity describes gravity as the curvature of spacetime caused by massive objects. It is formulated in terms of smooth, continuous spacetime and is a deterministic theory, meaning that it predicts outcomes with certainty given the initial conditions. On the other hand, quantum theory describes the behavior of particles and their interactions using probabilistic mathematics. It introduces discrete quantities, such as energy levels and particle properties, and involves uncertainty in measurements due to the Heisenberg uncertainty principle.
Attempts to merge general relativity with quantum theory have encountered significant theoretical challenges. The mathematical techniques used in general relativity, such as differential geometry, do not readily incorporate the probabilistic and discrete nature of quantum theory. Additionally, the extreme conditions that arise in scenarios like the early universe or black holes, where both quantum effects and strong gravitational fields are important, pose theoretical difficulties.
Developing a theory that unifies general relativity and quantum theory, often referred to as "quantum gravity," is an ongoing area of research and remains one of the biggest challenges in theoretical physics. Various approaches, such as string theory, loop quantum gravity, and others, have been proposed in the quest for a unified theory, but a complete and experimentally verified solution has not yet been achieved.