New perspectives on quantum gravity: Striking parallels between QED and quantized linear GR

The classical energy of electromagnetic and gravitational waves depends on amplitude, while the quantum energy of photons and gravitons depends on frequency. This discrepancy suggests a paradox, but the Bohr Correspondence Principle (BCP) ensures that classical and quantum descriptions align in the limit of large quantum numbers. To demonstrate this, we follow the same approach as Quantum Electrodynamics (QED) by quantizing the linearized gravitational wave perturbation and introducing quantized gravito-electric and gravito-magnetic tensor fields. This quantum formulation reduces to the classical Isaacson power formula in the limit of large graviton number. Also, just as Stefan's Law is obtained from QED in the classical limit of negligible quantum vacuum fluctuations, likewise a gravitational version of Stefan's Law emerges in the same limit. Furthermore, we construct a canonical quantization of the linearized gravitational field and show that it leads to a canonical field-mode uncertainty relation for the quantized gravitational field. Finally, the framework predicts novel phenomena, including applications to gravitationally bound neutrons ("gravitational atoms"), gravitational versions of the Schwinger and Casimir effects, and a formal description of "quantum space-time foam."