Canonical Uncertainty Relations for Madelung Variables in Curved Spacetime

• URL: http://arxiv.org/abs/2604.04784v1
• Date: Mon, 06 Apr 2026 15:54:59 GMT
• Title: Canonical Uncertainty Relations for Madelung Variables in Curved Spacetime
• Abstract summary: We derive exact uncertainty principles that depend on spacetime geometry through the lapse function $N$ and spatial metric $_ij$.<n>These relations reveal how gravitational fields modulate quantum fluctuations and provide first-principles constraints for scalar field dark matter models and quantum gravity.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density $n$ and phase $θ$ variables and their conjugate momenta, we derive exact uncertainty principles that depend on spacetime geometry through the lapse function $N$ and spatial metric $γ_{ij}$. These relations reveal how gravitational fields modulate quantum fluctuations and provide first-principles constraints for scalar field dark matter models and stochastic quantum gravity.

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