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Equation 31 · Part 7 · The Atlas That Refuses to Close

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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