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Equation 40 · Part 6 · The Atlas That Refuses to Close

Symbol rho_M

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

What this part means

rhoMo_M is an input to the expression that computes the quantity on the left.

Its job in the formula

rhoMo_M is an input to the expression that computes the quantity on the left.

The passage around this formula

…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)…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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