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Equation 5 · Part 4 · The Bit Comes Back Before the Bearing

Symbol pi

∣ψ(g)⟩=e−igJ^/ℏ ∣ψ(0)⟩,g∈[0,2π).|\psi(g)\rangle = e^{-ig\hat J/\hbar}\,|\psi(0)\rangle, \qquad g \in [0,2\pi).
π\pi

What this part means

pi is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

pi is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Into this old hole go two systems. The first, A , is a two-dimensional qubit prepared in an arbitrary, unknown state and coupled to nothing the hole’s own symmetries track — a spectator, chosen so that its recovery is the cleanest possible test of the Hayden-Preskill mechanism on its own terms. The second, C , is a compass: a physical carrier prepared in a state |ψ(g)\psi(g)⟩\rangle that transforms under a one-parameter group of rotations generated by a Hermitian charge J^\hat J , the same charge the hole’s own angular momentum is built from, ∣ψ(g)⟩=e−igJ^/ℏ ∣ψ(0)⟩,g∈[0,2π)|\psi(g)\rangle = e^{-ig\hat J/\hbar}\,|\psi(0)\rangle, \qquad g \in [0,2\pi). g is an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis. J^\hat J…

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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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