The need for a theory that merges quantum mechanics and general relativity arises from the fact that these two theories, despite being incredibly successful in their respective domains, appear to be incompatible with each other under certain conditions.
Quantum mechanics is the theory that describes the behavior of particles at the microscopic scale, such as atoms and subatomic particles. It provides a probabilistic description of these particles, where their properties are represented by wave functions. Quantum mechanics has been extensively tested and has accurately predicted the behavior of particles in countless experiments.
On the other hand, general relativity is the theory of gravity and describes the behavior of massive objects, such as planets, stars, and galaxies. It formulates gravity as the curvature of spacetime caused by massive objects. General relativity has also been remarkably successful in predicting the behavior of massive objects and has passed numerous experimental tests.
However, when attempting to describe phenomena that involve both the microscopic realm, where quantum mechanics reigns supreme, and the macroscopic realm governed by general relativity, the two theories clash. For instance, when trying to describe the behavior of matter in extremely strong gravitational fields or the early moments of the universe, we encounter situations where the effects of both quantum mechanics and general relativity become significant, and their combined description is necessary.
One of the primary challenges in merging these theories lies in their fundamentally different mathematical frameworks and conceptual underpinnings. Quantum mechanics relies on probabilistic wave functions and operates within a flat spacetime background, while general relativity describes the curvature of spacetime and uses deterministic equations.
Efforts to reconcile quantum mechanics and general relativity have led to various approaches, such as string theory, loop quantum gravity, and other quantum gravity approaches. These theories aim to provide a consistent framework that incorporates both quantum mechanics and general relativity, resolving the incompatibilities that arise at the fundamental level.
Regarding the idea of spacetime simply being the field where particles reside and incompatible with a unified theory, it's an interesting perspective. However, it's worth noting that unifying these two theories is not merely about finding a common arena but rather about resolving the fundamental conflicts that arise between their mathematical descriptions and predictions. It involves understanding how gravity emerges from quantum phenomena or how quantum effects can manifest in gravitational systems.
Ultimately, the development of a theory that successfully merges quantum mechanics and general relativity would not only provide a more complete understanding of the fundamental laws of nature but also have significant implications for our understanding of the early universe, black holes, and other phenomena where both quantum and gravitational effects play a crucial role.