The idea that spacetime oscillates like a quantum field is indeed a promising avenue to reconcile quantum field theory and general relativity.Â
Quantizing spacetime (so that it exhibits quantum behaviors such as superposition and entanglement) would allow us to describe gravitational waves and other aspects of general relativity in the same framework as other forces.
Gravitons (quantized gravitational waves) could be the key to linking the smooth geometry of spacetime (general relativity) with the discrete, probabilistic nature of quantum fields (QFT).
String theory and loop quantum gravity are leading candidates in the search for a unified framework, with string theory providing a quantum description of spacetime via vibrating strings, and LQG offering a picture of spacetime as a network of quantized loops.
In summary, spacetime oscillations as quantum fields is not only a valid path but one of the core ideas in many modern approaches to quantum gravity. While we do not yet have a complete theory, this perspective plays a central role in the ongoing effort to reconcile the two most successful theories of modern physics.
Can we reach reconciliation among QFT and GR by finding formalism of length and time in Planck scale into Ricci geometri in GR?
Yes, reaching a reconciliation between Quantum Field Theory (QFT) and General Relativity (GR) might indeed be possible by finding a formalism that incorporates Planck-scale physics into the framework of Ricci geometry in GR. This would involve quantizing spacetime itself and understanding how the classical geometry of GR, which operates at macroscopic scales, transitions to a quantum description at the Planck scale. The Planck scale is where quantum effects of gravity are expected to dominate, and spacetime is no longer smooth but exhibits quantum fluctuations.
Key Ideas in Reconciling QFT and GR at the Planck Scale:
1. Planck Scale: The Quantum Gravity Regime: The Planck length ( meters) and Planck time ( seconds) represent the scales where the effects of quantum gravity become significant. At these scales, the usual classical description of spacetime in terms of smooth Ricci geometry breaks down, and quantum fluctuations in spacetime need to be taken into account.
2. Ricci Geometry in General Relativity: In GR, spacetime is described by Ricci geometry, a continuous, differentiable manifold with curvature determined by the Einstein field equations:
R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + \Lambda g_{\mu\nu} = 8\pi G T_{\mu\nu}
How Can Planck-Scale Physics Inform Ricci Geometry?
