Quantum Uncertainty in Curved Space-time

This study presents a novel derivation of Heisenberg’s uncertainty principle, demonstrating its natural emergence from the Planck lattice description of quantum space-time. Moreover, according to our Planck lattice framework, the dynamics of quantum space-time offer a unique theoretical approach for evaluating Heisenberg’s uncertainty principle within the context of Schwarzschild space-time. This represents an expansion of quantum uncertainty into the realm of relativity theory and gravity. Our formulation of Heisenberg’s uncertainty principle in Schwarzschild space-time offers a new understanding of Hawking radiation that relies on the thermodynamics of quantum uncertainty. Importantly, our findings indicate that the spectrum of radiation emitted by a Schwarzschild black hole is consistent with that of a blackbody, which agrees with established theories.