On 2014-11-03 01:58, Warner Losh wrote:
A common grid is an artificial construct that measurements from
different clocks can be interpolated to. The top of second (or other
phase) measurements place place the top of second in time. Interpolating
to a grid places the time of each time scale at a fixed point on the grid
so they can be compared by simple subtraction. The interpolation causes
the local measurement device’s time scale to subtract out, and gives
phase measurements at a specific time.
For example, if UTC top of second for second 1 comes in at local time scale
1.1 and 2.1 and the UT1 PPS for second 1 comes in at 0.95 and 1.96[*], you
can interpolate a phase at time 1.0 on the local time scale for each of these
clocks and know the phase difference at 1.0. Do this for 1.0, 2.0, etc and you
can make phase and frequency statements about UTC and UT1.
[*] I know this is absurdly large, it should be 1.950000001 or so)
Is this required? In the general case it is, but in specific other cases it may
not be absolutely required. It also generalizes to clocks whose frequency
may not be 1Hz.
This method also assumes that the local time scale (oscillator) is more stable
than
the acceptable error over the interpolation period, since all physical
oscillators are
imperfect.
Thank you for the explanation! So a grid works as a kind of laboratory
time scale to be used as a reference during measurements.
You also replied to my statement:
UT1 is a timescale that ticks 1 SI second when the Earth Rotation Angle
increases by exactly (2·π rad)/86 636.546 949 141 027 072,
Which it rarely does for any length of time.
On the contrary, the fixed angular speed d(ERA)/d(UT1) is a
defining property of UT1, and it is an "auxiliary defining
constant" in the IAU 2009 system of constants.
Michael Deckers.
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