# Re: [LEAPSECS] The real problem with leap seconds

From: M. Warner Losh <imp_at_BSDIMP.COM>
Date: Wed, 18 Jan 2006 02:42:59 -0700 (MST)

In message: <Pine.LNX.4.44.0601171508290.6977-100000_at_jupiter.obs-besancon.fr>
Francois Meyer <fmeyer_at_obs-besancon.fr> writes:
: On Mon, 16 Jan 2006, Mark Calabretta wrote:
:
: > On Fri 2006/01/13 11:17:52 -0000, Michael Deckers wrote
: > in a message to: LEAPSECS_at_ROM.USNO.NAVY.MIL
: >
: > > I must get TAI, up to an integration constant. This is correct.
: > > The integral of d( UTC ) is TAI (up to an integration constant),
: > > but this integral is UTC only where UTC is a continuous function
: > > of TAI.
: >
: > You're still not getting the point that UTC is just a representation
: > of TAI.
:
: Maybe it should be, but this is far from being
: obvious from its current definition.
:
: The actual situation corresponds to :
:
: 1. UTC and TAI share the same rate, the same
: origin, the same second. And therefore :
:
: UTC - TAI = 0

The history of UTC and TAI is complicated and tricky. You can only
say that on Jan 1, 1972, the TAI - UTC offset was fixed to be 10s.
UTC and TAI prior to 1972 did not evolve at the same rate. The UTC
seconds differed in length from the SI seconds. I'll ignore the
nomenclature differences over time as well.

: 2. UTC only differs from TAI by its definitions of
: the minute, hour and day.

This is not true prior to 1972. There were a number of frequency
offsets in UTC that weren't present in TAI. Some leap second charts
have these included in them.

: 4. the UTC minute is defined to ensure that dhms
: expressions of UTC match UT1 at .9 s; it can be
: either 59, 60 or 61 SI seconds long. This
: definition of the minute is realized
: by (positive or negative) leap seconds and
: ensures that the mean UTC day is the mean solar
: day in the long term. The UTC hour has 60 UTC
: minutes, the UTC day has 24 UTC hours.

Again, post 1972... I'm not sure what I think of this definition.

: >From that point of view, the sentence from the ITU460-6 :
:
: "[UTC] ...differs from it [TAI] from an integer of seconds"
:
:
: "representations of UTC involving minutes, hours,
: days differ from equivalent representations of TAI
: by an integral number of seconds"

After 1972, and ignoring minor variations in the realization of UTC
and TAI in any given location, this is basically true. The only ideal
difference between TAI(ideal) and UTC(ideal) is in the labeling of the
pulses that both time scales have experienced. If one were to treat
them both as fixed radix, you get the difference of 33s. Viewed
topologically as a 1-1 mapping, one could easily define subtraction so
that the difference is zero since UTC has a variable radix...

To further complicate things, TAI isn't created in realtime, but is a
paper clock that's steered to the correct time of the clocks that feed
it data. There are clocks that are steered to this paper clock, but
it is all done by hand (if the various web pages I've read are still
accurate). Different facilities realization of the TAI and UTC time
scales may differ by several nanoseconds (or more depending on a lot
of factors).

However, leaving aside those complications...

Given that UTC is a variable radix notation for labeling the pulses
that have elapsed since the epoch. TAI is a fixed radix notation for
labeling pulses that have elapsed since the epoch.

Warner
Received on Wed Jan 18 2006 - 01:46:31 PST

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