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Equation 60 · The Clock That Comes Back Wrong by Exactly Its Mass

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b\mathbf b

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bb

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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, reconstructed as the low-velocity limit of a quantity that was never central to begin with. This is exactly the contraction procedure Inönü and Wigner formalized for groups and their representations in general [ 3 ] , applied here to one specific commutator rather than asserted as a general slogan. The nonrelativistic mass superselection rule is, on this reading, the shadow a fully…
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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, reconstructed as the low-velocity limit of a quantity that was never central to begin with. This is exactly the contraction procedure Inönü and Wigner formalized for groups and their representations in general [ 3 ] , applied here to one specific commutator rather than asserted as a general slogan. The nonrelativistic mass superselection rule is, on this reading, the shadow a fully relativistic, non-superselected world casts onto its own c→\to∞\infty limit — a point developed independently in later work reconciling the rule with ordinary relativistic quantum mechanics [ 4 ] .

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