Equation 5 · The Oldest Quantum-Gravity Experiment Is a Neutron Falling
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the inertial piece. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
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where is the n -th negative zero of the Airy function — 2.338, 4.088, 5.521, 6.787, and so on — and the mass has been split deliberately into a gravitational piece , which sets how hard the potential pulls, and an inertial piece , which sets how the wavefunction spreads in response. Nesvizhevsky and collaborators’ 2005 refinement of the original measurement, using a position-sensitive track detector to scan the standing-wave density directly above the mirror rather than only the transmitted flux, pinned down the characteristic length scale = 5.87 micrometres and reported the same Airy-zero ladder to several figures [ 2 ] . Feed that length scale and the lowest…
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where is the n -th negative zero of the Airy function — 2.338, 4.088, 5.521, 6.787, and so on — and the mass has been split deliberately into a gravitational piece , which sets how hard the potential pulls, and an inertial piece , which sets how the wavefunction spreads in response. Nesvizhevsky and collaborators’ 2005 refinement of the original measurement, using a position-sensitive track detector to scan the standing-wave density directly above the mirror rather than only the transmitted flux, pinned down the characteristic length scale = 5.87 micrometres and reported the same Airy-zero ladder to several figures [ 2 ] . Feed that length scale and the lowest Airy zero into the formula above and the ground state comes out to 1.407 picoelectronvolts — a fantastically small number by nuclear or even atomic standards, corresponding to the neutron’s classical turning point at 13.7 micrometres, the hundredth-of-a-millimetre height the whole system lives at.
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