Manuscript VII-H@1 · VII-H.tex · example · d20d2a9f

Example: Separated source and readout do not kill every contact

Why the same shortcuts fail in a more general response › A local action correction can have a nonlocal image · lines 1539–1558

VII-H@1#eq:propagated-action

Back to manuscript

Let $E^{R}$ be the wave retarded operator and $c$ a smooth compact function. A first-order change of the wave operator by multiplication with $c$ changes its inverse by

δ E^{R} = - E^{R} c E^{R} .

For compact tests $f, h$ , the measured change is

- \int c (y) (E^{A} f) (y) (E^{R} h) (y) d^{4} y .

The pairing is defined on smooth propagated tests and may be nonzero with separated $f, h$ . Choose $h$ and $f$ so their retarded and advanced responses are nonzero at one intermediate point; continuity permits a compact $c$ of fixed sign in a sufficiently small neighbourhood.

Displayed formulas in this passage

VII-H@1#eq:propagated-action · line 1548
$- \int c (y) (E^{A} f) (y) (E^{R} h) (y) d^{4} y .$
unlabeled · line 1543
$δ E^{R} = - E^{R} c E^{R} .$

Nearby in this section

section: A local action correction can have a nonlocal image