[LEAPSECS] Skepticism

Jonathan E. Hardis jhardis at tcs.wap.org
Thu Dec 30 23:04:52 EST 2010

On Dec 30, 2010, at 7:41 PM, Rob Seaman wrote:

> It is *hasty* to force a decision when the current definition of UTC

> is viable for centuries.

This is not being responsive. There are those who believe that the
current definition of UTC isn't viable TODAY.

> As someone else points out, it is quite possible to break

> international civil timekeeping to the point that all the King's men

> can't put it back together again.

Now, now...

Let's do a back-of-the-envelope, "what if" calculation.

First, pick a hypothetical rate for the average slowing of Earth's
rotation. For now, let's use 1.4 ms/day/century. Furthermore, let's
say that the average length of the day at the start of 2000 was 2.5 ms
longer than 86,400 s. (Adapted from: "The leap second: its history and
possible future," R. A. Nelson, D. D. McCarthy, S. Malys, J. Levine,
B. Guinot, H. F. Fliegel, R. L. Beard, and T. R. Bartholomew,
Metrologia 38, 509–529 (2001).)

This means that the total, accumulated clock error over the course of
Year X (365.25 days/year) would be: (0.91568175 + 0.0051135
(X-2000)) [seconds]

That is, in this simplified model, we would need slightly less than 1
leap second per year until 2017, at which point we would need slightly
more than 1 leap second per year. Of course, we actually haven't
needed that many leap seconds since 2000 -- but I'm sticking with the
long-term average none-the-less.

Okay. Let's presume that (1) up until the beginning of 2011 we added
leap seconds such that DUT1 was 0, (2) for the sake of early 21st
century technology, we stopped declaring leap seconds for 40 years,
until 2051, and (3) everyone was put on notice that starting in 2051
there would be two leap seconds per year (say, June and December),
each and every year, for at least 300 years.

In this model, DUT1 would be about 43 seconds in 2051. Then, after
the reimposition of leap seconds, DUT1 would decrease every year until
it reached a minimum of -22 seconds at about 2210, after which it
would then increase to about 27 seconds in 2350.

The world at large ca. 2300 would have to decide what to do next --
how many leap seconds per year, starting when. And let's give them
credit for being able to make such a decision for themselves.

The point is, there is a distinct advantage to regularity and
predictability in leap seconds -- which you could get in trade by
giving up on keeping DUT1 to less than 0.9 seconds.

- Jonathan

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