← All parts of this equation

Equation 11 · Part 2 · The Bit Comes Back Before the Bearing

Symbol U_in

V Uin(g)  =  [Urad(g)⊗Urem(g)] V.V\,U_{\mathrm{in}}(g) \;=\; \big[U_{\mathrm{rad}}(g)\otimes U_{\mathrm{rem}}(g)\big]\,V.
UinU_{\mathrm{in}}

What this part means

UiU_in is part of the quantity the equation computes from the expression on the right.

Its job in the formula

UiU_in is part of the quantity the equation computes from the expression on the right.

The passage around this formula

The hole’s evaporation is modeled, as it is throughout this line of work, as an isometry V from the interior-plus-infalling-system Hilbert space to a radiation-plus-remaining-interior Hilbert space. What makes the conservation law bite is that V must commute with the group action on both sides: V Uin(g)  =  [Urad(g)⊗Urem(g)] VV\,U_{\mathrm{in}}(g) \;=\; \big[U_{\mathrm{rad}}(g)\otimes U_{\mathrm{rem}}(g)\big]\,V. Every symbol here is a unitary representation of the same rotation on a different Hilbert space — dimensionless linear operators, none of them observables in their own right. The equation says the hole’s internal dynamics cannot tell which way “up” was chosen before the compass fell in: rotate the input, and the output rotates the same way, split between radiation and remainder.…

Read this part in the article →

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 →

See this notation across published equations →

Sources cited in the surrounding passage

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