[LEAPSECS] epoch of TAI, and TAI vis a vis GPS

Wed Mar 4 02:17:06 EST 2015

On 2015-03-03 09:23 PM, Steve Allen wrote:
> On Wed 2015-03-04T00:04:10 +0000, Tony Finch hath writ:
>> They have different epochs:
>>
>> TAI: 1958-01-01 T 00:00:00 Z
>> PTP: 1970-01-01 T 00:00:00 Z
>> GPS: 1980-01-06 T 00:00:00 Z

Using ISO 8601 style date and time representation on the TAI timescale 
and on the UTC timescale before 1972-01-01T00:00:00Z (UTC) is dangerous 
without qualification or explanation.

The "Z" implies its on the UTC timescale. It is controversial when the 
term "UTC" came into use. It is controversial if the UTC timescale 
existed prior to 1972-01-01T00:00:00Z (UTC), and if it did, exactly what 
it is..

"TAI: 1958-01-01 T 00:00:00 Z"  - By preceding it with "TAI" we guess 
you mean the TAI timescale if we ignore the Z.
1958-01-01T00:00:00 (TAI) is the origin of the TAI timescale, as per 
ITU-R Rec 460.
Using pure Gregorian calendar counting method, 1958-01-01T00:00:00 (TAI) 
is exactly (1972-1958 = 14 years * 365 = 5110 days + 3 leap year days = 
5113 days * 86400 seconds = 441763200 seconds) before 
1972-01-01T00:00:00 (TAI).

"PTP: 1970-01-01 T 00:00:00 Z" - The PTP Epoch is defined as 
1970-01-01T00:00:00 (TAI) *on the TAI timescale*. Using pure Gregorian 
calendar counting method, 1970-01-01T00:00:00 (TAI) is exactly 
(1972-1970 = 2 years * 365 = 730 days + 0 leap year days = 730 days * 
86400 seconds = 63072000 seconds) before 1972-01-01T00:00:00 (TAI).

"GPS: 1980-01-06 T 00:00:00 Z" - The GPS Epoch is properly and firmly on 
the UTC timescale, after 1972-01-01T00:00:00Z (UTC). There's no 
controversy there. The GPS Epoch is 1980-01-06T00:00:00Z (UTC) = 
1980-01-06T00:00:19 (TAI). From there they count in uninterrupted weeks.

Meantime (always fun to use that expression in a discussion of 
timescales :-) ), POSIX "the epoch" is stated as "January 1, 1970 
Coordinated Universal Time (UTC)". It is controversial if UTC existed 
before 1972. So, to get to that date from 1972-01-01T00:00:00Z (UTC) = 
1972-01-01T00:00:10 (TAI) we need to constuct some proleptic timescale 
before 1972-01-01T00:00:00Z (UTC). I'm not sure what we'd like to call 
this proleptic timescale, lets call it "POSIX" for now. Using Gregorian 
calendar counting, 1970-01-01T00:00:00 (POSIX) is (1972-1970 = 2 years * 
365 = 730 days + 0 leap year days = 730 days * 86400 seconds = 63072000 
seconds) before 1972-01-01T00:00:00Z (UTC).

Similarly for NTP. RFC 5905 states ".. the prime epoch, or base date of 
era 0, is 0 h 1 January 1900 UTC". Again, lets call this proleptic 
timescale "NTP". So, 1900-01-01T00:00:00 (NTP) is (1972 - 1900  = 72 
years * 365 = 26280 days + 17 leap year days = 26297 days * 86400 
seconds = 2272060800 seconds) before 1972-01-01T00:00:00Z (UTC).

Our "POSIX" timescale overlaps our "NTP" timescale - they exist on the 
same timescale proleptic to 1972-01-01T00:00:00Z (UTC) using the the 
Gregorian calendar counting method. I got flamed for calling it 
"proleptic UTC". What should it be called? After all its used all the 
time, shouldn't we have a name for it?

> Getting meaninglessly pedantic, in Survey Review v19 #143 p7 (1967)
> A.R. Robins had been talking with Sadler and Smith and with that
> information in hand he wrote that atomic time was identical to UT2 at
> 1958-01-01 T 20:00:00 Z
ITU-R Rec 460 says "TAI .. from the origin 1 January 1958 (adopted by 
the CGPM 1971)".

In 'Metrologia - leap second: its history and possible future' - 
http://www.cl.cam.ac.uk/~mgk25/time/metrologia-leapsecond.pdf - we read:
"In conformity with the recommendations of IAU Commissions 4 and 31 in 
1967, the CCDS [80] defined the origin so that TAI would be in 
approximate agreement with UT2 on 1 January 1958, 0 h UT2. The 14th CGPM 
approved the establishment of TAI in 1971."

As I interpret this, while there were previous historic uses of 
"1958-01-01" as an epoch for various things, including LORAN and early 
development atomic timescales, TAI didn't officially exist until 1971, 
and by adopting 1958-01-01T00:00:00 (TAI) as the TAI origin they 
acknowledged those precedents and made the definition specific and 
official on the TAI timescale. Whatever the values or accuracies may 
have been for previous "1958-01-01" epochs, this act established the 
modern version accurately tied to the TAI timescale.

Is that how you see it?

>
> This, of course, disagrees with Guinot's memoir, but the various
> realizations of UT2 then differed by centiseconds and the different
> versions of atomic time were subsequently realigned by milliseconds.
> And that date of 1958-01-01 was decided ex post facto at the 1959
> August meetings where the US and UK decided to try coordinating their
> broadcast time signals using cesium.  So there really isn't an epoch
> for TAI.
Seems to me there is, as above.

>
> On Tue 2015-03-03T14:31:13 -0800, Hal Murray hath writ:
>> Since GPS time is a fixed offset from TAI, it's easy to convert.
> I believe that BIPM would disagree because of the different kinds of
> steering at the nanosecond level.  The stance of the BIPM was expressed in
> http://www.bipm.org/cc/CCTF/Allowed/18/CCTF_09-27_note_on_UTC-ITU-R.pdf
> where TAI "should not be considered as an alternative time reference."
>
> Without the assent of the BIPM it is hard for there to be an agreed
> upon name for real-time versions of time scales that are trying to
> track the value of TAI (which will not actually be available until the
> next issue of Circular T).
Well, really, UTC is a dissemination of TAI encoded with the UTC Leap 
Second counting scheme - you need only convert from UTC to TAI, which is 
easy if (a big if) you have the Leap Second information and apply it 
properly.

-Brooks

>
> --
> Steve Allen                 <sla at ucolick.org>                WGS-84 (GPS)
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