Bridging Linearized General Relativity and Quantum Gravity

The classical energy of gravitational waves is amplitude dependent, while the quantum energy of gravitons is frequency dependent. Applying the Bohr Correspondence Principle (BCP) to the case of gravity predicts that the classical and quantum theories should be consistent in the limit of large quantum numbers (i.e. numerous gravitons). It is found in the literature that gravitons are claimed to have a volume on the order of the wavelength cubed. However, we show that this is a violation of the BCP and is inconsistent with a formal treatment using linearized General Relativity and assuming the quantization of the gravitational field. Furthermore, using quantized gravito-electric and gravito-magnetic tensor fields, we obtain a canonical quantization of the gravitational field and an associated uncertainty principle. This formulation also leads to a gravitational version of Stefan's Law in the classical limit that quantum vacuum fluctuations of the gravitational field are negligible. Lastly, we draw a comparison between the electromagnetic and gravitational vacuum fluctuation energy in a system of gravitationally bound neutrons.