Quantum gravity is a challenge for field theories from "summary" of The Quantum Theory of Fields by Steven Weinberg,Weinberg S
The problem of quantum gravity is that it is not just a small modification of familiar quantum field theory. Gravity is not even a field theory, in the usual sense. The gravitational field is the spacetime metric itself, not a set of fields defined at each point in spacetime. This means that the metric is subject to quantum fluctuations, which are not well understood. One might try to treat the metric as a field on a fixed flat background spacetime, but this approach is inherently inconsistent because the metric determines the geometry of spacetime itself. One might also try to quantize gravity by treating the metric as an operator on a Hilbert space of wave functions, but this leads to severe mathematical and conceptual problems. The problem is not just technical. The very nature of spacetime is called into question by quantum gravity. In the framework of general relativity, spacetime is a smooth manifold that can be curved by matter and energy. In quantum theory, however, spacetime is expected to be fundamentally uncertain and fluctuating. These two pictures of spacetime are difficult to reconcile, and resolving this conflict is at the heart of the problem of quantum gravity. The challenge of quantum gravity is to find a consistent and mathematically rigorous quantum theory of the gravitational field that is compatible with the principles of quantum mechanics and general relativity. Various approaches to quantum gravity have been proposed, such as string theory, loop quantum gravity, and causal dynamical triangulations. Each of these approaches has its own strengths and weaknesses, and none has yet been fully successful in providing a complete and satisfactory theory of quantum gravity. Progress has been made in understanding certain aspects of quantum gravity, such as the behavior of black holes and the structure of spacetime at very small scales. Despite these advances, the problem of quantum gravity remains unsolved, and it is likely to be one of the most challenging and profound questions in theoretical physics for the foreseeable future. The quest for a unified theory of quantum gravity continues to be a source of inspiration and frustration for physicists, as they grapple with the complexities and uncertainties of this fundamental aspect of the universe.
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