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Equation 41 · Part 4 · The Atlas That Refuses to Close

multiplication

∣S×v∣≤∣S∣ v|\mathbf S \times \mathbf v| \le |\mathbf S|\,v
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

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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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.