Heisenberg's principle(1) states that the product of uncertainties of position and momentum should be no less than the limit set by Planck's constant, (h) over bar /2. This is usually taken to imply that phase space structures associated with sub-Planck scales (<< (h) over bar) do not exist, or at least that they do not matter. Here I show that this common assumption is false: non-local quantum superpositions (or 'Schrodinger's cat' states) that are confined to a phase space volume characterized by the classical action A, much larger than (h) over bar, develop spotty structure on the sub-Planck scale, a = (h) over bar (2)/A. Structure saturates on this scale particularly quickly in quantum versions of classically chaotic systems-such as gases that are modelled by chaotic scattering of molecules-because their exponential sensitivity to perturbations(2) causes them to be driven into non-local 'cat' states. Most importantly, these sub-Planck scales are physically significant: a determines the sensitivity of a quantum system or environment to perturbations. Therefore, this scale controls the effectiveness of decoherence and the selection of preferred pointer states by the environment(3-8). It will also be relevant in setting limits on the sensitivity of quantum meters.
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