[LEAPSECS] the big artillery

Warner Losh imp at bsdimp.com
Sun Nov 2 14:04:17 EST 2014

On Nov 2, 2014, at 11:21 AM, Michael Deckers via LEAPSECS <leapsecs at leapsecond.com> wrote:

>  On 2014-11-01 23:31, Steve Allen wrote:
>> In the appropriate contexts there are days of Terrestrial Time,
>> International Atomic Time, Barycentric Coordinate Time, Geocentric
>> Coordinate time, GPS system time, BeiDou system time, etc.  Each of
>> those days is 86400 SI seconds in its own reference frame.
>> In other contexts there are days of Universal Time, Sidereal Time,
>> Ephemeris Time.  Each of those days is 86400 of its own kind of
>> seconds.
>   I disagree. One wants to compare all these time scales with
>   each other, and comparison requires expression in the
>   /same/ unit, not in different units.
>   For instance, the differential rate d(TAI - UT1)/d(UT1) is
>   published as LOD by the IERS as a "dimensionless" number
>   with unit ms/d. To compute this, one must be able to
>   subtract the reading of UT1 from that of TAI, and to
>   compute the difference numerically one has to convert to
>   equal units. The rate is computed correctly /only/ if
>   one assumes that a second of TAI equals a second of UT1.

This isn’t entirely true. You have to compute the length of the
different time scales to the same seconds. You can compute the
difference by comparing the clock readings at a fixed point
in time after interpolation to a common grid. This will give you the
difference in terms of the units of the common grid. If you select UT1
as the common grid, then you can also get a rate to come up
with the unit less number.

You can also compute the frequency ticking of each time scale
in terms of one or the other (or a third independent one) to compute
the frequency error of one or both of the time scales. Once you have
a frequency error (or difference), conversion of units is trivial. This is
more likely how the LOD drift number is computed. It’s how you compare
different atomic clocks to say this one is slow, that one is fast and assign
a frequency error to each one (and a similar construct to assign the
phase error of the PPS each one is producing). There are a variety
of ways to measure these differences (though UT1 something has to
involve astronomy since it is an observational time base) and compute
these numbers.

Also, UT1 were ticking in SI seconds, there would be no rate difference. :)

These are all standard techniques that we used when we built out
time library at Timing Solutions / Symmetricom based on many
different publications from NIST and the expert guidance of our
chief time scientist (Sam Stein).

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