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Equation 5 · Part 2 · The Bit Comes Back Before the Bearing

Symbol g

∣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).
gg

What this part means

an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis.

Its job in the formula

g is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

g is an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis.

The passage around this formula

…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 carries units of action (joule-seconds), so gJ^\hat J/ℏ\hbar is dimensionless, as an exponent must be. Nothing about this setup is exotic — a large-spin coherent state…

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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

These citations provide research context; check each source for the exact claim it supports.