Equation 64 · The Clock That Comes Back Wrong by Exactly Its Mass
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Symbol c
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Holding , , M , and fixed and sending c , 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 , , M , and fixed and sending c , 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 limit — a point developed independently in later work reconciling the rule with ordinary relativistic quantum mechanics [ 4 ] .
Sources cited in the surrounding passage
- [3] On the Contraction of Groups and Their Representations ↗
- [4] On Galilei Invariance in Quantum Mechanics and the Bargmann Superselection Rule ↗
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