subscript

The passage around this formula

None of this says a relativistic particle’s position is meaningless. It says the specific combination this atlas has been building — a sharp operator, exact eigenstates, and strictly causal free-particle dynamics — cannot be jointly realized by any chart above, Newton–Wigner included. The theorem applies to $\mathbf X_{\mathrm{NW}}$ exactly as it applies to $\hat{\mathbf x}$ , since commuting components buy nothing against Hegerfeldt’s argument; the argument never uses the commutator structure, only positivity of energy and the existence of a bounded region with zero amplitude outside it.

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