# [tz] When will physics make 32-bit signed leap-second counts obsolete?

Steve Allen sla at ucolick.org
Thu Sep 27 17:14:41 UTC 2018

```On Thu 2018-09-27T08:45:23-0700 Paul Eggert hath writ:
> A while ago I vaguely remember a prediction on this list of when the TZif
> file format will become obsolete because we have accumulated 2**31 total
> leap seconds if we continue to just add leap seconds as needed to keep UTC
> roughly in sync with TAI. To some extent this is just a playful prediction,
> as the format will undoubtedly become obsolete for other reasons long before
> then, but it's still fun to predict. Unfortunately I don't remember the
> details, and a quick Google search didn't find it. Does anyone else remember
> this? If not, I'll have to recalculate.
>
> The topic has just come up again on the tzdist-bis mailing list, which is
> why I'm thinking about it again. See <https://mailarchive.ietf.org/arch/msg/tzdist-bis/Q7OVmd60wydqcJahS3QRNHwtXHM>.

Extrapolating predictions of Delta T is something that should only be
undertaken by the bravest of souls.  For visual examples of various
different efforts I recommend viewing
https://www.ucolick.org/~sla/leapsecs/deltat.html
and even moreso
https://www.ucolick.org/~sla/leapsecs/year2100.html

Most of the predictions suppose a roughly linear increase of LOD, thus
a roughly parabolic increase of Delta T.  The few seconds of offset
between Ephemeris Time, Atomic Time, and Universal Time right now are
pretty much irrelevant, but strictly speaking the parabolic formula is

CalendarYearOfParticularDeltaT = 1820 + 100 * sqrt((DeltaT + 20) / decel)

where decel is expressed in second/century/century

A reasonable value for decel is 32 s/cy/cy, and extreme values for
decel are 25 and 42, so

decel=25    year=930000
decel=32    year=820000
decel=42    year=720000

It is hubris beyond measure to suppose that any calendar or timekeeping
system will survive more than 1000 years.

--
Steve Allen                    <sla at ucolick.org>              WGS-84 (GPS)
UCO/Lick Observatory--ISB 260  Natural Sciences II, Room 165  Lat  +36.99855
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```