COMPULSORY standard; ARBiTRARY units.

[1] Sam [ -worms ] Wormley wrote:
$$ "It takes an infinite amount of time ..at which point,..".

$$ [ VELOCiTY is ANY VECTOR/duration but SPEED is ANY PATH/duration ]:
o o o o
X o Q vector
o o o projection
A - - - VELOCiTY vector - - B - - - - - C
o o o
P o Y
o o o o
ANY path ..trajectory.
$$ Any VELOCiTY vector can ONLY be "MEASURED" ..in RETROSPECT.
$$ [ Radar gun VELOCiTY vector, ONLY in "SECOND-hand" RETROSPECT ].
$$
$$ [Vector VELOCiTY, (A-B)/t, is iNDEPENDANT of path SPEED, (A~B)/t].
$$ NOTE: Any *OTHER iMAGiNARY* velocity, BETWEEN any OTHER TWO points
$$ (each located on the SAME path) will indicate a DiFFERENT velocity
$$ vector, albeit (even though) THAT SAME *path* clearly doN'T CHANGE.
$$ [i.e. Note, velocities X-Y and P-Q are vectors on the SAME PATH].
$$
$$ Momentum UNcertainty varies iNVERSELY with the PATH's STRAiGHTNESS.

$$ You need BOTH velocity vector END-POiNT positions at ONCE.
$$ The VELOCiTY is ALWAYs known _ONLY_ in retrospect, so 'dv'
$$ caN'T EVER be known, at ONCE (i.e. ..at ANY *DURATiON* t).

$$ Atomic giga-frequency counters ..of REAL time.
The BEST atomic clock is SiMPLY a GiGA-frequency-COUNTER.!!
And, even the VERY best ATOMiC clocks CANNOT be SYNCRONiZED
TOGETHER, at once, on any GR or any OTHER sort of Ph.Tivity
TiME-line (i.e. WORLD-line), in ANY SPACE-time-continuum.!!

$$ All "clocks" are simply various FREQUENCY-COUNTERs used
even since very early on in PRE-history (to wit, period
tally-marks ..on excavated sticks & bones), to "TRY-to"
*CLOCK* ..the "REAL TiME".!! NOT to mention SUN & MOON.

However, a sort of TiME-AVERAGED simultaneity is achievable
..all having to compensate (REset) for design mysteries.!!

$$ DELTA v, (dv), caN'T *HAPPEN* ..all at ONCE.
$$ Simultaneity happens AT ONCE; EveryTHiNG else needs TiMiNG.
$$ And, *REAL* TiME is why *SHOP (LAB)* TiME has *ERROR* bars.

$$ ANY clock MOViNG ..or MOVED any LOWER ..will run FASTER.!!
$$ ANY clock MOViNG ..or MOVED any HiGHER, will run SLOWER.!!
$$ ANY clock's HORiZONTAL "SLOW transport", is UP transport.
$$ ANY clock moving OUT [ HORZ ] on a turn table", moves UP.

$$ ANY clock VARiES in ALTiTUDE for ANY horizontal TRANsPORT.

$$ Three VELOCiTY vector END-POiNT positions REQUiRED, for dv.
$$ Three VELOCiTY vector END-POiNTs (3 positions) define a dv.
$$ [GR Tivity CRACKED-pots: NOTE 'dt' caN'T HAPPEN ..at ONCE].


[2] Delta t (dt), PERiOD.
$$ A COMPULSORY selection of ARBiTRARY choices.
$$ [That COMPULSORY standard ..of ARBiTRARY units].

$$ Tom [ He between his error-bars ] Roberts ] 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,
$$ "One *CAN* differentiate ..[DiFFERENT] readings on a clock".
$$ "One *CANNOT* differentiate [ONE reading] on a clock" ..duh.
$$ ["*CANNOT* differentiate [DiFFERENT] readings [at ONCE]" duh.]

$$ [The MORE atomic-TiCKERs ..the BETTER "clocking"-AVERAGE t].
$$ [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].
$$ [ -- A *MAGNiTUDE*-of-a-timing is WHAT a clock "READs" -- ].
$$
$$ No CLOCK-READiNG can exhibit ONE *DURATiON*, at ONCE, dooOP.
$$ [A CLOCK-READiNG can exhibit ONLY ONE *tic COUNT*, at ONCE].
$$ [One MUST "differentiate" BETWEEN *READiNGs*, of the clock].
$$
$$ TiME is ANALOG but FREQUENCY is DiGiTAL.. dimwit.
$$
$$ COMPULSORY selection; ARBiTRARY choice.
$$ [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 wants GR to have COHERENT GUESS iSS 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.

But you can arrange for that coordinate to
track the readings of the clock.
$$ [i.e. "..to COUNT tics".]
$$ [ ALPHABET is ARBiTRARY but we SELECT one CHOiCE ..to WRiTE ].

Tom [ He between his error-bars ] Roberts ].

$$ That COMPULSORY standard ..of ARBiTRARY units.
COMPULSORY selection & ARBiTRARY choices; ..The STANDARD set.
Time is analog; Frequency, digital.
Delta t (dt), PERiOD. End (2) edited RePOSTs.

In brian a m stuckless writes:

[1] Sam [ -worms ] Wormley wrote:
$$ "It takes an infinite amount of time ..at which point,..".
...


$$ [ You do NOT need to be MiSUNDERSTOOD. Seek MEDiCAL help NOW.!! ].

NoOne wrote:

In brian a m stuckless writes:

[1] Sam [ -worms ] Wormley wrote:
$$ "It takes an infinite amount of time ..at which point,..".
...


$$ [ You do NOT need to be MiSUNDERSTOOD. Seek MEDiCAL help NOW.!! ].

For what, to be cured of his artistic abilities and habits?

I suppose you've got all the answers.

http://cosmic.lifeform.org