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Equation 5 · Part 1 · The Bit Comes Back Before the Bearing

Symbol psi

∣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).
ψ\psi

What this part means

psi is part of the quantity the equation computes from the expression on the right.

Its job in the formula

psi is part of the quantity the equation computes from the expression on the right.

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 function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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