String theory and general relativity are two fundamental theories in physics that describe the behavior of the universe at different scales. While both theories have been successful in their respective domains, they are currently incompatible with each other. The main reasons for their incompatibility can be summarized as follows:
Scale: General relativity is a theory of gravity that successfully describes the behavior of spacetime on a macroscopic scale, such as the motion of planets, galaxies, and the overall structure of the universe. It is based on the concept of smooth, continuous spacetime. On the other hand, string theory is a quantum theory that attempts to describe the fundamental particles and forces at the subatomic scale. It introduces the idea that elementary particles are not point-like but instead tiny, vibrating strings. The two theories operate at vastly different scales, and reconciling them requires a unified framework that can consistently describe both macroscopic and microscopic phenomena.
Quantum Nature: General relativity is a classical theory, meaning it does not incorporate the principles of quantum mechanics. Quantum mechanics, on the other hand, is crucial for understanding the behavior of elementary particles and their interactions. String theory, being a quantum theory, naturally incorporates quantum mechanics. However, the challenge lies in bridging the gap between the classical description of gravity in general relativity and the quantum nature of string theory.
Singularities and the Big Bang: General relativity predicts the existence of singularities, points of infinite density, at the centers of black holes and at the beginning of the universe (the Big Bang). These singularities pose a problem when trying to apply the principles of quantum mechanics to these extreme conditions. String theory, in its current form, has not resolved the issue of singularities and how to treat them within a quantum framework.
Background Independence: General relativity is a background-independent theory, meaning the geometry of spacetime is dynamic and can be influenced by matter and energy. In string theory, on the other hand, the theory is often formulated on fixed background geometries. This difference in the treatment of spacetime poses challenges in finding a consistent way to incorporate both theories.
It's important to note that while these are some of the main challenges in reconciling string theory and general relativity, ongoing research and developments in theoretical physics may provide new insights and potential resolutions to these issues in the future.