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Equation 31 · Part 2 · The Atlas That Refuses to Close

Symbol S

ρM=∣S∣Mc.\rho_M = \frac{|\mathbf S|}{Mc}.
SS

What this part means

S occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

S occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The scale that answer is measured against is fixed entirely by the body itself. For a system of total mass M and spin angular momentum of magnitude |S\mathbf S| — the part of JμνJ^{\mu\nu} left over once the orbital piece is subtracted — define ρM=∣S∣Mc\rho_M = \frac{|\mathbf S|}{Mc}. ρM\rho_M has units of length by inspection, angular momentum divided by momentum, and it is built from nothing but the two Poincaré-invariant labels, mass and spin, that every observer agrees on regardless of which chart they read a position off of. It will turn out to be the radius of the region within which every well-behaved chart in this atlas has to stay.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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