Manuscript X-J-ST@1 · X-J-ST.tex · proposition · 8f0d1a36

Proposition: The instrument is not a field-acquisition map

Selectivity, orbit bounds, and non-acquisition › What is actually measured · lines 1649–1671 · proof included or linked

X-J-ST@1#prop:noacquisition

The signal instrument measures effects of the supplied finite signal register. It does not acquire $C_{2} [ϕ]$ from an unknown continuum field.

Proof. Its signal effects are

E_{F} = r I, E_{+} = (1 - r) ∣ 1 ⟩ ⟨ 1 ∣, E_{-} = (1 - r) ∣ 0 ⟩ ⟨ 0 ∣ .

Their pullbacks act on $Q$ , not on a field configuration space or a field representation. The coefficient enters only through the separately supplied preparation $τ_{σ} (ν d)$ .

No field–apparatus coupling, physical representation of the classical functional, or continuum-to-register channel has been defined.

Displayed formulas in this passage

unlabeled · line 1658
$E_{F} = r I, E_{+} = (1 - r) ∣ 1 ⟩ ⟨ 1 ∣, E_{-} = (1 - r) ∣ 0 ⟩ ⟨ 0 ∣ .$

Nearby in this section

section: What is actually measured