Manuscript XX-A@1 · XX-A.tex · definition · 3a586110

Definition: Frozen relational lapse

Complete raw and relational lapse through second order › The complete inverse relational map · lines 671–686

XX-A@1#def:rel-lapse, XX-A@1#eq:smeared

The observable scalar is

n_{s} = N_{s} \circ α_{s} .

For $f \in C_{c}^{\infty} (J \times R^{3})$ , fixed in label space, its smeared functional is

O_{f} (s) = \int f (τ, x) n_{s} (τ, x) d τ d^{3} x .

The smearing uses the fixed label density, not a fluctuating spacetime volume element.

Displayed formulas in this passage

XX-A@1#eq:smeared · line 679
$O_{f} (s) = \int f (τ, x) n_{s} (τ, x) d τ d^{3} x .$
unlabeled · line 674
$n_{s} = N_{s} \circ α_{s} .$