Manuscript III-B@1 · III-B-v1.tex · section · d2c98f62

The clock record is not a classical relational lapse

Permitted manipulations and non-identifications › The clock record is not a classical relational lapse · lines 2238–2270

Back to manuscript

The coordinate $T$ , the finite pointer

T_{C} = k \sum t_{k} P_{k},

the history map $κ$ , a harmonic relational scalar, a slice-harmonic rod prescription, a relational lapse, and a density ramp have different domains and definitions.

Em02-E and the original-rod XX records retain their separate backgrounds and classical constructions CheungLapse,CheungClockSeparation. No comparison map identifies them with the finite clock here.

Even the same scalar coordinate does not determine a lapse. For the comparison metrics

g_{N} = - c^{2} N^{2} d T^{2} + h,

with constant $N = 1$ or $N = 2$ , the same scalar $T$ is harmonic, but

- g_{N}^{- 1} (d T, d T) = \frac{1}{c ^{2} N ^{2}}

differs. The principal construction fixes $N = 1$ ; this comparison does not change that input.

For our chosen static history events, $t_{k} - t_{j}$ is their geometric proper-time interval. That equality uses the supplied metric and event map. It is not inferred from the code probabilities.

Displayed formulas in this passage

unlabeled · line 2241
$T_{C} = k \sum t_{k} P_{k},$
unlabeled · line 2255
$g_{N} = - c^{2} N^{2} d T^{2} + h,$
unlabeled · line 2260
$- g_{N}^{- 1} (d T, d T) = \frac{1}{c ^{2} N ^{2}}$