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Equation 59 · Part 3 · The Clock That Comes Back Wrong by Exactly Its Mass

Symbol b

⟨H⟩ℏc2 b⋅v=Mℏ b⋅v+⟨HNR⟩ℏc2 b⋅v.\frac{\langle H\rangle}{\hbar c^2}\,\mathbf b\cdot\mathbf v=\frac{M}{\hbar}\,\mathbf b\cdot\mathbf v+\frac{\langle H_{\rm NR}\rangle}{\hbar c^2}\,\mathbf b\cdot\mathbf v.
bb

What this part means

b occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

b occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

…a system at rest as H=Mc2c^2+HNRH_{\rm NR} , separating the rest energy from whatever nonrelativistic energy — kinetic, internal — sits on top of it. The relativistic loop phase becomes ⟨H⟩ℏc2 b⋅v=Mℏ b⋅v+⟨HNR⟩ℏc2 b⋅v\frac{\langle H\rangle}{\hbar c^2}\,\mathbf b\cdot\mathbf v=\frac{M}{\hbar}\,\mathbf b\cdot\mathbf v+\frac{\langle H_{\rm NR}\rangle}{\hbar c^2}\,\mathbf b\cdot\mathbf v. Holding b\mathbf b , v\mathbf v , M , and ⟨\langle HNRH_{\rm NR}⟩\rangle fixed and sending c→\to∞\infty , the second term vanishes and the first survives unchanged, converting a state-dependent relativistic phase into a fixed, universal constant multiplying every vector in the fixed- M sector — Bargmann’s central charge,…

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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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