2011/08/26 by T. G. Downes, Downes, T. G., G. J. Milburn +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #gr-qc #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1108.5220
arxiv created 2012/11/05 · arxiv updated 2012/11/07
Here we describe the quantum limit to measurement of the classical gravitational field. Specifically, we write down the optimal quantum Cramer-Rao lower bound, for any single parameter describing a metric for spacetime. The standard time-energy and Heisenberg uncertainty relations are shown to be special cases of the uncertainty relation for the spacetime metric. Four key examples are given, describing quantum limited estimation for: acceleration, black holes, gravitational waves and cosmology. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly spacetime independent derivation. The result is an uncertainty relation applicable to all causal spacetime manifolds.