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Equation 23 · Every Crystal Has Its Own Speed of Light

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3×1043\times10^{4}

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superscript

superscript

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Between those extremes sit two families with a gap between them. Engineered quantum simulators — cold-atom lattices, trapped-ion chains, Rydberg-atom arrays — cluster between 10^{-3} and 3×\times10^{-2} metres per second, because their dynamics run on tunnelling and spin-exchange rates measured in kilohertz, multiplied by lattice spacings measured in hundreds of nanometres. Natural crystals run several orders faster: longitudinal sound in ordinary crystalline silicon travels at 8.433 kilometres per second [ 12 ] ; the spin excitations of the near-ideal one-dimensional antiferromagnet potassium copper fluoride, with a measured exchange energy of 33.5 millielectronvolts, propagate at roughly…
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Between those extremes sit two families with a gap between them. Engineered quantum simulators — cold-atom lattices, trapped-ion chains, Rydberg-atom arrays — cluster between 10^{-3} and 3×\times10^{-2} metres per second, because their dynamics run on tunnelling and spin-exchange rates measured in kilohertz, multiplied by lattice spacings measured in hundreds of nanometres. Natural crystals run several orders faster: longitudinal sound in ordinary crystalline silicon travels at 8.433 kilometres per second [ 12 ] ; the spin excitations of the near-ideal one-dimensional antiferromagnet potassium copper fluoride, with a measured exchange energy of 33.5 millielectronvolts, propagate at roughly 3×\times10^{4} metres per second [ 11 ] ; and a nine-transmon superconducting circuit — a lattice of qubits wired on a chip rather than atoms trapped in light — shows the same information cone in a purely electronic system, its speed a dimensionless slope in wiring distance converted through the chip’s own pitch rather than a velocity in the ordinary sense [ 14 ] . No platform measured so far sits between about 3×\times10^{-2} and 2×\times10^{2} metres per second, and the paper is careful about what that gap means: not a forbidden band, but a statement about what has been built, since nothing yet measured is both slow enough to watch atom by atom and fast enough to fill it.

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