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Equation 11 · Part 5 · Decoherence: The Quiet Selection That Makes the World Look Solid

superscript

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

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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