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t∼1/(Λ Δx2)t \sim 1/(\Lambda\, \Delta x^2)

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Reading a decoherence time off this table only requires the exponent above: a superposition separated by Δ\Delta x decays with a characteristic time t ∼\sim 1/(Λ\Lambda\, Δ\Delta x2x^2) . Take the largest grain delocalized over roughly its own diameter, Δ\Delta x ≈\approx 10^{-3} centimetres, and the numbers in the first column turn into times measured in seconds only in the single, almost pathologically clean case of the cosmic background radiation acting alone — about one second. Every other row is not a slower version of the same story; it is a different order of magnitude of story entirely. Ordinary air brings that same superposition down to roughly 10^{-30} seconds, and a superposition…

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tt

Symbol t

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Δx2\Delta x^2

Symbol Δ x^2

Δ x2x^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

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t∼1/(Λ Δx2)t \sim 1/(\Lambda\, \Delta x^2)

Equation 11 · Evolutionary Physics

Decoherence: The Quiet Selection That Makes the World Look Solid

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Reading a decoherence time off this table only requires the exponent above: a superposition separated by Δ\Delta x decays with a characteristic time t ∼\sim 1/(Λ\Lambda\, Δ\Delta x2x^2) . Take the largest grain delocalized over roughly its own diameter, Δ\Delta x ≈\approx 10^{-3} centimetres, and the numbers in the first column turn into times measured in seconds only in the single, almost pathologically clean case of the cosmic background radiation acting alone — about one second. Every other row is not a slower version of the same story; it is a different order of magnitude of story entirely. Ordinary air brings that same superposition down to roughly 10^{-30} seconds, and a superposition…

Meanings in this article

  • Λ\Lambda: what Joos and Zeh call the localization rate: a single number.
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