COMPULSORY selection; ARBiTRARY choice ..of the STANDARD set.

$$ Tom [ He between his error-bars ] Roberts ] wrote:
wrote:
[someone] might conclude that GR predicts proper clock rates
are coordinate-dependent.

But _all_ rates are coordinate dependent -- that's what we mean
by "rate". That is, the rate of K is dK/dt, and that only makes
sense for a time coordinate t. You can choose to measure this
rate using a collocated standard clock, in which case you are
really using a time coordinate determined by that clock.

That is, one cannot differentiate
with respect to readings on a clock,

$$ Tom you know GPS scientists use SEVERAL-clock's _average_ t.
$$ THERE would be NO NEED of SEVERAL-clocks, if you were RiGHT.
$$
$$ [The MORE atomic-TiCKERs ..the BETTER "clocking"-AVERAGE t].
$$ [MORE atomic-TiCs/STANDARD TiC; BETTER clocking _ACCURACY_].
$$ [Our STANDARD TiC-TOC TiME is STiLL Least-Squares-adjusted].
$$
$$ [TiME is the POiNT where the clock sits on it's WORLD-line].
$$ [TiMiNG is the *DiFFERENTiATiON* of DiSTiNGUiSHABLE POiNTs].
$$ [ -- A *MAGNiTUDE*-of-a-TiMiNG is WHAT a clock "READs" -- ].
$$
$$ COMPULSORY selection; ARBiTRARY choice.
$$ [Clock-READiNG: An UNadjusted MAGNiTUDE-of-TiMiNG counted ].
$$ [ANY "clock" is a *totally _ARBiTRARY_* human construction].
$$ [The clock-"READiNG" is ALSO a totally _ARBiTRARY _ choice].
$$
$$ [ i.e. NATURE does NOT mind if we have COHERENT STANDARDs ].
$$
$$ And the ARBiTRARiNESS is "of _CHOiCE_" not _SELECTiON_, duh.
$$ [ i.e. The CHOiCE is ARBiTRARY ..a SELECTiON is COMPULSORY].
$$
$$ You ARBiTRARiLY CHOOSE a COMPULSORY STANDARD ..then MEASURE.

-=- only with respect to some coordinate.
But you can arrange for that coordinate to
track the readings of the clock.

I don't think we are in serious disagreement here, just
terminology.

$$ [ALPHABET is ARBiTRARY but we SELECT our CHOiCE, to WRiTE].
$$
$$ And "_all_ rates" areN'T just functions-of-TiMiNG ..dimwit.

Tom [ He between his error-bars ] Roberts

COMPULSORY selection; ARBiTRARY choice ..of the STANDARD set.
NATURE doesN'T mind if we have COHERENT STANDARDs.
GR frequency shift formula. ..End of POST.