[LEAPSECS] drawing the lines

[Redman, Russell]

I just gave a presentation at the "Requirements for UTC" colloquium that discussed the terminology for timekeeping.  ITU-R already has a well-developed vobaulary defined in its glossary (TF.686-2), and I am proposing some changes to help clarify a few of the terms that are now ambiguous. 


> -----Original Message-----

> From: leapsecs-bounces at leapsecond.com 

> [mailto:leapsecs-bounces at leapsecond.com] On Behalf Of Tony Finch

> Sent: Thursday, June 06, 2013 12:45 PM

> To: Leap Second Discussion List

> Subject: Re: [LEAPSECS] drawing the lines

> 

> Zefram <zefram at fysh.org> wrote:

> 

> > 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?

> 

> The way I like to think about it is a bit Platonic: there are various

> theoretical timescales which are the perfectly uniform proper 

> time of some

> body, e.g. what TT aims for; then there are the somewhat muddy


I think the existing term you are looking for is "coordinate time", which these days must be defined using general relativity.  That should stand as a warning that the definition is fussy and getting it right requires input from a real general relativist (i.e. not me), but in essence it defines a smoothly varying time coordinate that approximates Newtonian time for slowly moving observers on the Earth's surface.  A coordinate time is nominally represented by a real number with some origin (epoch or zero point, depending on how you want to think of it).

UTC and TAI share a common coordinate time, which for reasons that are historical has not previously received its own name.  I am proposing to call it "reference coordinate time" to make it more clear that the concept of the coordinate time is different from the concept of the time-scale that is used to measure it.  On this, I think we are on the same wavelength.


> realisations of timescales which approach the ideal more or 

> less closely

> depending on the effort we make, e.g. TAI, or some lab's 

> atomic time, or

> what my clock says; big spinning rocks in space make fairly adequate

> clocks and some of them have a lot of historical importance, and for

> several reasons we put a lot of effort into measuring their 

> motion very

> precisely, e.g. UT1; but the more you concentrate on measuring precise

> position, the less your activity is about getting a uniform 

> measurement of

> time.

> 

> UTC is not a timescale or an angular measurement, but an 

> inconvenient way

> of labelling the seconds of an atomic timescale to get a bad 

> approximation

> of an angle.


One of the nifty things about separating the coordinate time from the time-scale is that you get to see explicitly how the units of the coordinate relate to the units of the time scale.  A time-like interval will normally be measured in SI seconds, with the conversion from coordinate time to SI seconds handled in the metric.  It is easy to forget that the metric is a necessary part of the definition.  In a region of time containing gravitational fields, it is usually NOT true that one "second" of coordinate time is the same as one second of proper time for a "stationary" clock (with quotes because any relativist will have conniptions at the number of new terms I just introduced).  For reference coordinate time, elapsed coordinate time will only be the same as proper time for clocks embedded on the rotating geoid.

Angular coordinates are different of course, and it is a matter of historical interest that the mean Sun used to take an hour of time to move an "hour" of angle across the sky.  It gets worse when discussing seconds, which can mean a second of arc, a second of angular time, a second of coordinate time, or a second of proper time according to a local clock.  In principle, though, the metric takes care of the conversion once you get your definitions right.  It is perfectly acceptable to measure angles in time-like units.

The concept of a time-scale is also pretty elastic, so that almost anything that changes with time can be used to define a time-scale.  The underlying coordinate time can be measure in any units convenient to the measurement.  The voltage across the capacitor in a timing circuit makes a perfectly good time-scale measured in volts.  If you want to convert that to a proper time measured in SI seconds, you can, but it may not be worth the bother.  

In the same way, the rotation angle of the Earth can be used to define a coordinate time and a corresponding time-scale.  It is in this sense that UT1 is an angle that we choose for some purposes to use as a coordinate time with a corresp[onding time-scale.  It is convenient, but occasionally confusing, to use time units to measure UT1.  Since UT1 is not currently the center of the controversy, I have not bothered to invent separate names for UT1 as a coordinate time versus as a time-scale, but it would be sensible to keep in mind the distinction between the two concepts "UT1 coordinate time" and "UT1 time-scale".

I do not want to reproduce here the paper I am writing for the colloquium, but suffice to say that UTC is a time-scale that uses reference coordinate time as its underlying coordinate time (so is measureable with atomic clocks), and is synchronized with the (unpredictable) rotation of the Earth using leap seconds to provide an approximation of UT1 such that the difference |UT1 - UTC| is bounded and is good enough for some very important purposes.  It is NOT good enough for some other very important purposes, for which a time-scale like TAI that uniformly has 60 seconds per minute would be better suited. 

UTC is a good tool to use for celestial navigation and to coordinate civil times, but a poor tool to predict planetary ephemerides or to synchronize systom clocks in the computers running global reservation systems, for which it would be better a uniform time-scale like TT or TAI.  Time-scales are tools, and we need to use the tools appropriate for the problem at hand.  

Cheers,
Russell O. Redman