[LEAPSECS] drawing the lines

[Zefram]

Rob Seaman wrote:

>On Apr 29, 2013, at 1:25 PM, Tom Van Baak <tvb at leapsecond.com> wrote:

>> I reject the notion that UT1 is "angle" and UTC is "time".

>

>Then you reject Recommendation CCTF 6 (2012):


That Recommendation isn't consistent about maintaining a distinction
between angle and time: bullet 9 tries to separate them but then bullet
10 blithely merges them.  Also, some of its bullets (especially 6)
are actually normative recommendations, which is inconsistent with
the "... the following facts ..." rubric that introduces the list.
Looks like there are good grounds to reject that recommendation.

Ignoring that recommendation, let's look at angle vs time on its merits.
We have an instance here of a pattern I've repeatedly noticed in
intellectual activities, where one concept develops over time into
two concepts that it is useful to distinguish.  It's rather difficult
to maintain both the present distinction and the historical continuity
of both present concepts with the single precursor.  (Physical analogy:
cooling a supercritical fluid, where a distinction between liquid and gas
phases becomes relevant without the system undergoing any discontinuity.
Biological analogy: speciation.)  I think some explicit recognition of
this sort of situation helps, and we could really do with a standard
philosophical framework for analysing it.

In the present case, of course, the pre-1890s conception of time didn't
need to distinguish the passage of time from the rotation of the Earth.
Nowadays we're capable of a strict distinction, but many of our quantities
and units maintain continuity with the old view.

The historical development that most obviously fails to conform to the
modern angle/time categorisation is the development of Ephemeris Time
by reinterpreting a theory that had been formulated in terms of UT1.
In modern terms, ET is a time scale, not an angle scale: it is a
realisation of TT, by dynamical means, with its most notable flaw being
the lack of an underlying relativistic theory.  We can say that it was
a mistake to formulate Ephemeris Time in terms of the rotational "day"
concept, and the ephemeris second shouldn't have adopted the name of
the rotational "second" unit.  (Blaming the astronomers of the 1940s
for lacking a 2010s perspective is of course quite unfair.)

Pragmatically, there are a bunch of angle scales that have historically
been used as time scales, that function more or less well as time scales,
and are still used in a time-like manner as part of the definitions of
time scales, so it makes considerable sense to continue to treat them as
time scales.  I'm happy to use an inclusive definition of "time scale"
and thus say that they really are time scales, despite not directly being
measures of physical time.  Sure, the units of time and angle are being
aliased here, which isn't ideal, but accepting the implicit conversion
factor lets us get on with business.

Of course, reformulating our activities in a strictly modern way still has
value.  Given the irreversibility of the historical mistake, let's use the
second (s), with modern SI definition, as the unit of physical time, and,
radians being unhelpful, I'll use the circle (cr) as the unit of angle.
The implicit conversion factor in many of our equations is 86400 s/cr.

We could rewrite "|UT1 - UTC| <= 0.9 s" as "|UT1 * (86400 s/cr) - UTC|
<= 0.9 s".  Actually, it'd be more readable to define UT1t = UT1 * (86400
s/cr) and then write "|UT1t - UTC| <= 0.9 s".  UT1t is an actual physical
time scale (at least, it's counted in SI seconds), of a very-imperfect
dynamical nature, defined in terms of ERA.  Did that achieve something?
Actually it's got me thinking that the UT1<->ET interface wasn't so
bad after all; maybe UT1 really *was* a time scale, and the mistake
was just to describe it in angle units.  That is, in units that we've
retrospectively decided were `really' angular all along.  See how tough
the ontological bifurcation makes things?

Second attempt to be rigorous: split UTC timestamps into pure integer
UTC.d (count of days) and time quantity UTC.t (duration since midnight).
Where UTC is referenced as an angle quantity, the angle is (UTC.d + UTC.t
/ (86400 s)) * 1 cr.  The tracking bound can be expressed as "|UT1 -
(UTC.d + UTC.t / (86400 s)) * 1 cr| <= 0.9/86400 cr", or many equivalent
formulations.  This looks more as though it says something profound.
It'd still be easier to grasp by defining an intermediate unit-translated
scale, either UT1t from above or the explicitly angular form of UTC,
resulting in an expression in exactly the same form as the present
unit-aliased version.

Conclusion: let's define a set of affixes for time/angle scale names
that make explicit which units we're using, sprinkle the affixes on the
existing equations, and go on performing the same computations as before.

-zefram