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Non-Cancellation of Quantum Geometry Fluctuations

Quantum vacuum fluctuations tend to be strongly anti-correlated, which reduces their observable effects. However, time dependence can upset the cancellation of these anti-correlated fluctuations and greatly enhance their effects. This form of non-cancellation is investigated for spacetime geometry fluctuations driven by the vacuum stress tensor fluctuations of the electromagnetic field. The time dependence can take the form of sinusoidal conformal metric perturbations or of time variation of the gravitational constant, both of which can arise from modifications of the gravitational action. We examine two observable quantities, luminosity fluctuations and redshift fluctuations, both of which can arise from stress tensor fluctuations. We find that both quantities can grow with increasing distance between a source and an observer. This secular growth raises the possibility of observing spacetime geometry fluctuation effects at length scales far longer than the Planck scale.