If classicality emerges from quantum mechanics via decoherence (Zurek, Joos), a 'classical' gravitational field is already an approximation that cannot carry the precision required to violate uncertainty relations.
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Uncertainty relations(as used in physics and philosophy of science)
Rules in quantum physics stating that you cannot know certain pairs of properties (like a particle's position and speed) with perfect precision at the same time—the more accurately you measure one, the less you can know about the other.
Zurek, Joos(as cited physicists)
Wojciech Zurek and Erich Joos are physicists who developed the modern theory of decoherence, explaining how the quantum world becomes the 'normal' classical world we observe.
decoherence(Used to describe why macroscopic superpositions are not directly observed, and assessed here for whether it resolves the measurement problem.)
A quantum mechanical process in which differently localised states of a measuring apparatus couple to different states of the surrounding environment, entangling the composite system and suppressing interference between branches.