The unification of quantum mechanics and general relativity is considered important in modern physics for several reasons:
Understanding the fundamental nature of the universe: Quantum mechanics and general relativity are two of the most successful theories in physics, but they describe different aspects of reality. General relativity explains gravity and the behavior of objects on cosmological scales, while quantum mechanics describes the behavior of particles and forces on microscopic scales. A complete theory of everything would provide a unified description of the fundamental nature of the universe, encompassing both quantum mechanics and general relativity.
Resolving theoretical inconsistencies: At the most fundamental level, quantum mechanics and general relativity appear to be mathematically incompatible in certain extreme scenarios, such as near the centers of black holes or during the earliest moments of the Big Bang. A theory of everything would reconcile these inconsistencies and provide a consistent mathematical framework for understanding the behavior of matter, energy, and spacetime in all situations.
Explaining the origin of the universe: A theory of everything would ideally address the fundamental questions about the origin and nature of the universe, such as what happened at the Big Bang or what lies beyond black hole singularities. By unifying quantum mechanics and general relativity, we may gain insights into the nature of spacetime at the most fundamental level and the fundamental building blocks of the universe.
As for when and how we can unite these two conflicting theories, it remains an open question in physics. Currently, string theory is one of the leading candidates for a theory of everything that aims to unify quantum mechanics and general relativity. String theory suggests that particles are not point-like but tiny vibrating strings of energy, and it provides a framework for consistent quantum mechanical treatment of gravity. However, string theory is still highly speculative and has not been confirmed by experimental evidence.
Other approaches, such as loop quantum gravity and various quantum gravity models, also aim to unite quantum mechanics and general relativity. These approaches propose different mathematical frameworks and ideas for reconciling the two theories.
Ultimately, finding a successful theory of everything is a major ongoing research endeavor in theoretical physics. It may require new experimental discoveries, advancements in mathematical techniques, and a deeper understanding of the fundamental principles that govern the universe. It is challenging to predict when and how the unification will be achieved, but it remains a fascinating and important goal for physicists.