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∣Δx∣→∣S∣/(Mc)=ρM|\Delta\mathbf x| \to |\mathbf S|/(Mc) = \rho_M

Why this formula appears here

a shift transverse to both the spin and the relative velocity [ 13 ] . This is an exact identity of special relativity, not an approximation valid only for small v ; it holds all the way to v →\to c , at which point |Δ\Deltax\mathbf x| →\to |S\mathbf S|/(Mc) = ρM\rho_M exactly, since |S\mathbf S ×\times v\mathbf v| ≤\le |S\mathbf S|\,v saturates when the spin is perpendicular to the boost. No boosted observer, however extreme, can push a body’s own centroid further from its rest-frame value than ρM\rho_M . As u ranges over every inertial observer, Xμ(u,Σ)X^\mu(u,\Sigma) traces out a disk of exactly that radius, orthogonal to S\mathbf S — the world-tube first identified by Møller and reproduced in modern language…

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∣Δx∣→∣S∣/(Mc)=ρM|\Delta\mathbf x| \to |\mathbf S|/(Mc) = \rho_M

Equation 40 · Evolutionary Physics

The Atlas That Refuses to Close

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

a shift transverse to both the spin and the relative velocity [ 13 ] . This is an exact identity of special relativity, not an approximation valid only for small v ; it holds all the way to v →\to c , at which point |Δ\Deltax\mathbf x| →\to |S\mathbf S|/(Mc) = ρM\rho_M exactly, since |S\mathbf S ×\times v\mathbf v| ≤\le |S\mathbf S|\,v saturates when the spin is perpendicular to the boost. No boosted observer, however extreme, can push a body’s own centroid further from its rest-frame value than ρM\rho_M . As u ranges over every inertial observer, Xμ(u,Σ)X^\mu(u,\Sigma) traces out a disk of exactly that radius, orthogonal to S\mathbf S — the world-tube first identified by Møller and reproduced in modern language…

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