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Equation 1 · Part 9 · How Fast Can a Horizon Learn Which Path You Took?

Denominator: sqrt 2

∣Ψ(0)⟩=∣0⟩+∣1⟩2⊗∣hin⟩.|\Psi(0)\rangle= \frac{|0\rangle+|1\rangle}{\sqrt 2}\otimes|h_{\rm in}\rangle .
2\sqrt 2

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

sqrt 2 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

Begin with an equal superposition of two localized alternatives, ∣Ψ(0)⟩=∣0⟩+∣1⟩2⊗∣hin⟩|\Psi(0)\rangle= \frac{|0\rangle+|1\rangle}{\sqrt 2}\otimes|h_{\rm in}\rangle . The labels zero and one denote paths, not energy eigenstates. After the system’s long-range field interacts with the inaccessible degrees of freedom, an idealized final pure state has the form

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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