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Equation 79 · The Atlas That Refuses to Close

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v≪cv \ll c

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vv

Symbol v

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cc

Symbol c

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What zitterbewegung adds to the atlas is a fourth, sharper illustration of the same structural point as the Pryce trade-off: x^\hat{\mathbf x} and XNW\mathbf X_{\mathrm{NW}} disagree not by a fixed offset but by a time-dependent, oscillating quantity, largest exactly where a wavepacket carries significant negative-energy content, a regime the nonrelativistic limit removes entirely. As v ≪\ll c and the wavepacket is restricted to the positive-energy subspace, the oscillating term’s amplitude falls relative to the packet’s own spatial width, and x^\hat{\mathbf x} , XNW\mathbf X_{\mathrm{NW}} , and RN\mathbf R_N converge onto one description — the same nonrelativistic recovery checked twice already,…
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What zitterbewegung adds to the atlas is a fourth, sharper illustration of the same structural point as the Pryce trade-off: x^\hat{\mathbf x} and XNW\mathbf X_{\mathrm{NW}} disagree not by a fixed offset but by a time-dependent, oscillating quantity, largest exactly where a wavepacket carries significant negative-energy content, a regime the nonrelativistic limit removes entirely. As v ≪\ll c and the wavepacket is restricted to the positive-energy subspace, the oscillating term’s amplitude falls relative to the packet’s own spatial width, and x^\hat{\mathbf x} , XNW\mathbf X_{\mathrm{NW}} , and RN\mathbf R_N converge onto one description — the same nonrelativistic recovery checked twice already, confirmed here a third time from an entirely different starting operator.

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