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Equation 3 · Part 7 · How Fast Can a Horizon Learn Which Path You Took?

subscript

ν(T)=⟨h0(T)∣h1(T)⟩,V(T)=∣ν(T)∣.\nu(T)=\langle h_0(T)|h_1(T)\rangle, \qquad V(T)=|\nu(T)|.
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

Tracing out the field multiplies the off-diagonal element of the path density matrix by the conditional-state overlap ν(T)=⟨h0(T)∣h1(T)⟩,V(T)=∣ν(T)∣\nu(T)=\langle h_0(T)|h_1(T)\rangle, \qquad V(T)=|\nu(T)|. Under balanced arms and otherwise ideal readout, V is the remaining fringe visibility. That statement belongs to ordinary complementarity, not black-hole mysticism. Englert derived a quantitative visibility–which-way bound for a two-path interferometer, and atom-interferometer experiments later measured visibility and distinguishability independently in agreement with the relation [ 11 , 12 ] .

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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.

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Sources cited in the article section

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