[LEAPSECS] drift of TAI

[Zefram]

TAI has reached the grand old age of 1.6 gigaseconds.  In honour of the
occasion I shall briefly analyse the issue of its secular drift.

Like UTC, TAI serves a dual purpose, and those purposes have conflicting
requirements.  TAI serves civil society by being a global source of
regular ticks.  Civil society is in the habit of ignoring the labels
that TAI attaches to those ticks, instead applying labels derived
from Earth rotation.  (As I've previously noted, UTC is a calendar: it
correlates the cycle of the UT1 day with the cycle of the TAI second,
in much the same way that the Gregorian calendar correlates the cycle
of the solar day with the cycle of the northward equinoctal year.)

TAI also serves astronomers as a realisation of TT, and so indirectly as
a way to determine TCG and other coordinate time scales.  The standard
realisation of TT is defined as

	TT(TAI) = TAI + 32.184 s

Many sources state this equation without the "(TAI)", thus ignoring
the deviations of TAI from the true rate of TT.  This is acceptable,
for work below a certain level of precision, as long as the difference
TT-TT(TAI) remains below a corresponding magnitude.  But will it?  No.

TAI is maintained and corrected so as to keep its instantaneous rate
as close as possible to that of TAI.  This optimises it for use as a
frequency standard, including for its use as the minor cycle in the UTC
calendar.  It comes at the expense of long-term rate accuracy and direct
tracking of TT.  <ftp://ftp2.bipm.fr/pub/tai/scale/ttbipm.07> catalogues
the error: over 27 us by the end of 2007, and (more significantly)
rising at over 300 ps/day.  After a mere four millennia at the current
rate of drift, TT(TAI) will not be accurate to the precision implied by
its defining equation: once the accumulated drift has exceeded 500 us,
TT will be better approximated by TT ~ TAI + 32.185 s.	It's only a
matter of time before noon TT coincides with midnight TT(TAI)!

Unlike the situation with TAI vs UT1, the drift is not accelerating.
Indeed, as the rate of drift is inversely proportional to the
technological skill of the time laboratories, it is decelerating.  But it
is non-zero and has a consistent sign: even after years of painstakingly
tracking the drift in the TT(BIPMnn) publications, TT(TAI) continues to
diverge from TT.  Even if the rate of drift is asymptotically approaching
zero, the accumulated drift (integral of the rate) may be unbounded.

No doubt there are timekeeping systems that rely on TT(TAI) as an accurate
source of TT.  They will start to go wrong, subtly and progressively,
as TT-TT(TAI) exceeds whatever unknown bound was implicitly built
into them.  Should we be bequeathing this technological timebomb to our
grand^200-children?  Or should we keep naive expectations unshattered, by
ensuring that our broadcast time signals continue to accurately track TT?

Happy birthday TAI.

(Having been born some 601.266 Ms after TAI's birth, I'll be celebrating
my personal gigasecond in two weeks time.  If anyone's keeping track,
you can put me down as an early eschewer of solar time, for those things
where I have the choice.)

-zefram