Classical and quantum gravity
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Classical and Quantum Gravity: A Comprehensive Overview
Introduction to Classical and Quantum Gravity
Classical gravity, as described by Einstein's General Relativity, views gravity as the curvature of spacetime caused by mass and energy. Quantum gravity, on the other hand, seeks to describe gravity according to the principles of quantum mechanics. The interplay between these two frameworks has been a significant area of research, with various theories and models proposed to bridge the gap.
Irreversibility in Classical-Quantum Coupling
One of the fundamental challenges in coupling classical gravity with quantum matter is the inherent irreversibility of such interactions. When gravity is treated as a classical field interacting with quantum systems, it leads to a violation of one or more fundamental principles of quantum theory or general relativity. Specifically, it has been shown that if gravity remains classical, the interaction between matter and the gravitational field must be fundamentally irreversible . This irreversibility is a critical aspect that any consistent theory must address.
Discrepancies in Gravitational Potential
The relationship between classical and quantum gravity is further complicated by discrepancies in the gravitational potential. Studies have shown that the gravitational potential derived from quantum scattering amplitudes does not align with the classical results predicted by the Schwarzschild solution of general relativity . This indicates that quantum corrections to gravity may not simply be a straightforward extension of classical theories.
The Necessity of Quantum Gravity
Given the difficulties in quantizing general relativity, some researchers argue that gravity might be fundamentally classical. However, theoretical arguments against mixed classical-quantum models are strong, suggesting that a purely classical description of gravity may not be sufficient. Experimental tests exploiting the nonlinearity of classical-quantum coupling are being explored to settle this question .
Postquantum Theories and Stochastic Dynamics
A consistent theory of classical gravity coupled with quantum field theory has been proposed, which modifies the dynamical laws of quantum mechanics. This theory is fundamentally stochastic, involving probabilistic jumps in spacetime and the quantum field, and does not require the measurement postulate of quantum mechanics. Such a framework suggests that the interaction of quantum degrees of freedom with classical spacetime inherently causes wave-function collapse .
Fractional Operators in Quantum Gravity
Another approach involves the use of fractional operators in the formulation of quantum gravity. These theories modify the kinetic operator of the graviton using fractional derivatives or a covariant fractional d'Alembertian. While these models can be unitary and infrared-finite, they face challenges in achieving both unitarity and renormalizability simultaneously .
Classical-Quantum Duality
The concept of classical-quantum duality extends to the Planck scale, where classical gravity and quantum mechanics intersect. This duality is universal and reveals that the boundaries of classical and quantum domains blur near the Planck scale. The duality also provides insights into the global properties of spacetime, such as the Schwarzschild-Kruskal manifold .
Quantum Field Theory Perspective
Viewing gravity as a quantum field theory highlights its similarities with other fundamental interactions. Like strong interactions, gravity can be seen as a low-energy effective field theory related to a nonlinearly realized symmetry. This perspective opens the possibility of finding a UV complete quantum field theoretic description of gravity .
Emergence of Classical Spacetime
Classical spacetime can emerge from quantum gravity through specific models, such as the quantum FRW cosmological model. In these models, the quantum back reaction of matter fields can lead to equations that are equivalent to classical Einstein equations, demonstrating a pathway from quantum to classical descriptions of gravity .
Global Flows and Renormalization
Non-perturbative renormalization group methods have been used to study four-dimensional quantum gravity, revealing a global phase diagram. This diagram shows a smooth transition from a non-Gaussian ultraviolet fixed point to a classical infrared fixed point, indicating that the theory is ultraviolet complete and smoothly deforms into classical gravity in the infrared limit .
Unification of Classical and Quantum Gravity
The unification of classical and quantum gravity involves promoting classical variables to quantum operators, covering various curvatures and coherent states. This approach aims to unify the classical and quantum realms without speculative aspects, providing a coherent framework for understanding gravity across different scales .
Conclusion
The interplay between classical and quantum gravity remains a complex and rich field of study. Various models and theories offer insights into how these two frameworks can be reconciled, each addressing different aspects of the fundamental challenges involved. As research progresses, experimental tests and theoretical advancements will continue to shape our understanding of gravity in both classical and quantum domains.
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