= Colella–Overhauser–Werner experiment
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The Colella–Overhauser–Werner experiment observed a gravitationally induced relative <quantum phase> in a <neutron interferometer>. The 1975 primary report identifies the measured signal as a phase shift caused by the interaction of neutron matter waves with Earth's gravitational field.<Observation of Gravitationally Induced Quantum Interference by R. Colella and others>[Physical Review Letters 34 (1975), p. 1472, abstract]{ref}
An idealized two-path model explains the sensitivity. If equal-speed horizontal segments of length $L$ are separated vertically by $h$, their <gravitational potential energy> difference is $mgh$ and their common traversal time is approximately $L/v$. The corresponding phase-difference magnitude is
$$
|\Delta\phi|\simeq\frac{mghL}{\hbar v}=\frac{mgA}{\hbar v},\qquad A=hL.
$$
The sign depends on path orientation and phase convention. Recombination converts this difference into <matter-wave interference>, making a tiny potential-energy difference measurable through phase accumulation. The rectangular equal-speed expression is a leading explanatory model, not a complete precision correction for real crystal diffraction, bending and rotation effects.
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