Equation 11 · Part 2 · Decoherence: The Quiet Selection That Makes the World Look Solid

Symbol Lambda

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

\Lambda

What this part means

what Joos and Zeh call the localization rate: a single number.

Its job in the formula

Lambda is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol LambdaArticle meaning

Where the article explains it

$\left[-\Lambda (x - x')^2 t\right]$ Here $\Lambda$ is what Joos and Zeh call the localization rate: a single number, with units of inverse length squared per unit time, built from the scattering cross-section of the object, the flux and momentum of whatever is doing the scattering, and nothing else [ 7 ] .

The passage around this formula

Reading a decoherence time off this table only requires the exponent above: a superposition separated by $\Delta$ x decays with a characteristic time t $\sim$ 1/( $\Lambda$ \, $\Delta$ $x^2$ ) . Take the largest grain delocalized over roughly its own diameter, $\Delta$ 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

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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