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ensabah6
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as a field acting over a spacetime metric (rather than encoding it in the metric) but still reproduce key GR results including time-varying phenomena?
Yes, there are formulations of GR that treat spacetime as a dynamical entity and do not rely on a fixed background structure. These formulations include loop quantum gravity and causal dynamical triangulations.
Formulating GR as background dependent allows for a more complete and consistent understanding of the theory, especially in relation to quantum mechanics. It also opens up the possibility of resolving issues such as singularities and the unification of gravity with other fundamental forces.
The traditional formulation of GR, known as the Einstein-Hilbert action, treats spacetime as a fixed background on which matter and energy interact. In contrast, a background dependent formulation treats spacetime as a dynamical entity that is influenced by matter and energy.
At the current time, there are no experimental tests that can definitively distinguish between the two formulations. However, ongoing and future experiments in quantum gravity could potentially provide evidence for one over the other.
One limitation is that the mathematical complexity of these formulations makes it difficult to make concrete predictions and perform calculations. Another limitation is that they do not yet have a complete and consistent framework for incorporating quantum mechanics, which is necessary for a complete understanding of gravity.