Manuscript Em03-D@1 · Em03-D-v1.tex · corollary · 450d878a

Corollary: Inherited Hawking prediction

The local Hawking-packet correspondence theorem · lines 1617–1644 · proof included or linked

Em03-D@1#cor:baseline

In the Unruh system state,

(ω_{U} \otimes σ_{R, ϵ}) [Θ_{ϵ} (I \otimes O_{ϵ})] - \frac{1}{2} [1 + e^{- ϑ^{2} (2 ν_{h} + 1) /4}] \leq ϵ_{local}

with $C = 1$ .

The exact local prediction is

\frac{1}{2} [1 + c_{ϵ} e^{- ∥ k (f_{ϵ}) ∥_{U}^{2} /2}] .

Proof. Use (eq:Hawkingbaseline) and Theorem thm:main. The exact formula follows by applying the Unruh characteristic function to (eq:inducedeffect).

Displayed formulas in this passage

unlabeled · line 1620
$(ω_{U} \otimes σ_{R, ϵ}) [Θ_{ϵ} (I \otimes O_{ϵ})] - \frac{1}{2} [1 + e^{- ϑ^{2} (2 ν_{h} + 1) /4}] \leq ϵ_{local}$
unlabeled · line 1632
$\frac{1}{2} [1 + c_{ϵ} e^{- ∥ k (f_{ϵ}) ∥_{U}^{2} /2}] .$