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Description
A quantum object is extended by virtue of uncertainty. When subjected to gravity, different parts of its wave function experience distinct local relativistic effects, leading to tidal and interference phenomena absent in the classical limit. These effects can be incorporated into a geometric extension of classical spacetime. For states that are quantum correlated in at least two directions, a complete description of motion requires a non-Riemannian geometry whose form is controlled by the state's entropy and purity. A specific implication of this framework is the appearance of quantum parameters in the time-dilation law in addition to the usual dependence on velocity and gravitational potential. The new methods imply specific squeezing rates that optimize a quantum clock.