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Equation 31 · Part 4 · The Atlas That Refuses to Close

Symbol c

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

What this part means

c occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

c occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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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