John Cowan wrote:
> Rob Seaman scripsit:
>
>> Third result - even in the absence of lunar braking, leap jumps
>> (or equivalent clock adjustments) would remain necessary.
>
> Why is that?
>
> If the SI second were properly tuned to the mean solar day, and the
> secular slowing were eliminated, there would be no need to mess  
> about with
> the civil time scale, because the random accelerations and  
> decelerations
> would cancel out in the long run.  Of course, we'd have to tolerate  
> larger
> differences between clock time and terrestrial time, but we'd  
> expect that.
Excellent discussion.  The answer depends on how much larger the  
clock differences are, and on the meaning of the word "tolerate".  As  
Tom Van Baak said:
> My understanding is that, in addition to astronomical
> effects (lunar/solar tides), no small number of geological
> and climatological phenomena also contribute to the
> instability of the mean solar day. That all the random
> accelerations exactly cancel all the random decelerations
> in any finite time, short- or long-term, is very unlikely.
Which is to say that "proper tuning" may not even have a definition.   
It certainly is non-trivial.
Consider the historical trend (from 
http://www.ucolick.org/~sla/ 
leapsecs/dutc.html):

Detrend the data by removing the 1.7 ms/cy secular effect:

(I read the LOD from the plot every century - should repeat with the  
original data, but results should be acceptably accurate.  I'm sure  
somebody would be happy as a clam to point out any errors I may have  
made :-)
There are positive and negative excursions from "normal" that persist  
for centuries.  For the purpose of civil timekeeping, we don't care  
what geophysics causes these excursions, or even whether the rather  
evident sinusoid is real or not, but just that the residual ~ +/- 5  
ms length-of-day variations exist.
Leap seconds represent the accumulation of these daily residuals:

A very small daily residual becomes +/- 9 minute descrepancy between  
TAI and UTC over millennial time periods.  So even in the absence of  
the secular trend, the natural geophysical irascibility of the planet  
is very evident.  Leap seconds - both positive and negative, of  
course - would be needed to resync the clocks.  I count about 2200  
over 2500 years (for instance, about 500 leap seconds between the  
battle of Hastings in 1066 and the most recent eruption of Fujiyama  
in 1707).  That amounts to about one leap second per year even in the  
absence of the secular lunar effect.
Since this entire range of phase space sits within an hour's extent  
from the "mean", the ALHP is really a proposal to completely ignore  
the chore of providing time-of-day to the world.   Of course, we're  
back to the same question we've been debating with our well known  
positions all staked out – but the point is – the Moon ain't in it  
anymore.  The whipping boy for hurrying a decision to emasculate UTC  
has been the quadratic lunar term – but large numbers of leap  
seconds are seen to be needed every century, whether or not the lunar  
term is included.
Of course, on top of this long term trend are superimposed the  
decadal and seasonal effects (also from Steve Allen's page):

This +/- 1-2 ms jitter can either magnify or quiet the millennial  
effects – for relatively short periods – or equivalently can  
accelerate or retard the scheduling of leap seconds.  On the other  
hand, there is no reason to suppose that the periodicities that have  
been revealed since the time of Pericles have completely  
characterized our planet's wobbles at the long end of the spectrum.   
In particular, The LOD offset plot appears to show a baseline error  
of 0.5 or 1.0 ms.  Also, the choice of slope for detrending the  
historical data was purely a result of a phenomenological fits to the  
data in hand.  The fact that the lunar estimate, and the estimate  
born from the high precision near term data, both differ from the  
phenomenological slope could also be taken to suggest that long term  
periodicities are lurking in the data, and that even greater  
excursions from the mean are not only possible but are inevitable.
Which is all to say that not only does the secular baseline guarantee  
that we cannot tune SI seconds to match a mean solar time whose rate  
is changing, but the geophysics of the planet lead one to question  
what this even means exactly.
What to do?  What to do?
Challenge the premise of the question.
Interval time and time-of-day are simply, truly, two entirely  
different things.  Some pragmatic arrangement is going to have to be  
struck between the two.  I'd suggest that Babylonian notation be  
reserved for time-of-day (UTC) and that interval time (TAI) be  
expressed as what it is – a simple count of seconds.  But the  
details would certainly be open for discussion – if we didn't have  
to expend so much effort fending off the Absurd Leap Hour Proposal,  
again and again.
But also, we should be investing in the infrastructure needed to  
convey both quantities to the vast array of users who need one or the  
other at whatever level of precision.  Striking a "compromise" that  
eviscerates time-of-day for the imagined benefit of some interval  
time special interests is not only uncalled for - it doesn't even  
begin to address the issues.  Time-of-day is solar time and should  
always remain such.  If there are to be policy changes in the  
identification of civil time with mean solar time with Coordinated  
Universal Time - these should be driven by issues related to time-of- 
day, not force fit to match the pathologically even cadence of atomic  
clocks.
Similarly, if precision time users are having troubles dealing with  
leap seconds – we've said it before – they shouldn't select time- 
of-day as a time standard!  I mean - duh!  Why would any sane  
engineer who needs a clock regular to one in ten billion specify a  
requirement to synchronize their precious system to a clock that only  
keeps time precise to one in ten million?  Obscuring this simple fact  
by trashing UTC for the rest of us is rather – impolite.
Time-of-day is Earth orientation.  Atomic time is interval time.  One  
doesn't have anything to do with the other.
Rob Seaman
NOAO
Received on Sat Aug 05 2006 - 18:49:05 PDT