# [tz] What's "right"?

John Sauter John_Sauter at systemeyescomputerstore.com
Sun Nov 15 23:21:23 UTC 2020

```On Sun, 2020-11-15 at 22:31 +0000, Michael H Deckers wrote:
>
>      I think the view that different time scales are just relabelings
>      of the point of a time line is fundamentally flawed. I consider
>      a time scale to be the temporal part of a coordinate system for
>      4-dimensional spacetime; changing the coordinate system, even
>      if it is only for one coordinate, does not mean relabeling
>      the coordinate.
>
>         Yes, there are many people and several authors which
>         understand the term, time scale, in other meanings
>         (eg, ISO 8601). And a geological time scale is probably
>         not (yet?) part of a coordinate system.
>
>      At any rate, the values of (such) time scales are points on the
>      time line, which offers the well known operations (adding a time
>      value to a time point, determining the difference between two
>      time points, etc). These are operations on physical quantities,
>      and cannot be done with labels. Different time scales must take
>      their values on the same time line (at least when their values
>      are to be comparable).
>
>      Points on the time line can be denoted in many different ways:
>      with many calendars, many time units for time of day and time
>      since an epoch, and many different epochs for such counts;
> changing
>      a notation does not change the time scale anymore than an
>      elevation is changed by switching its notation from foot to
> meter.
>
>      When it is said that UTC is just TAI with the points on the
>      time line relabeled, this just means that the function from TAI
>      values to UTC values ("labels") is injective (ie, different
> values
>      of TAI are mapped to different labels). This is correct for a
>      suitable choice of leap second notations -- but it does not
>      tell us much about how UTC depends on TAI. In the the same
>      way, one could say that x³ is just a relabeling of x, but this
>      does not tell us how x³ depends on x, it doesn't allow
>      comparison of x³ with x, taking the derivative etc.

I take your point: to do anything useful we need more than labels--we
need to know how those labels relate to time.  To some extent, we are
misled by the similarity in structure between UTC labels and TAI labels
into thinking that they are related more fundamentally than they
actually are.

Suppose we define the difference between TAI and UTC as follows: write
down the current value of UTC, and measure how many seconds before TAI
has that same value.  That works fine except during a leap second, when
we will wait in vain for a TAI time that ends in 23:59:60.  I think it
would be reasonable to say that TAI - UTC has no meaning during a leap
second.

> > >       Another notation for leaps in UTC was recommended by the
> > > IAU in
> > > 1970:
> > >           9.4. The time of an event given in the old scale,
> > > before the
> > >           leap second, will be given as a date in the previous
> > > month,
> > >           exceeding 24h if necessary. The time of an event given
> > > in
> > > the
> > >           scale after the step will be given as a date in the new
> > > month,
> > >           with a negative time, if necessary.
> > >       Resolution adopted by the 14th General Assembly of the IAU
> > > in
> > > 1970,
> > >       online at
> > > [
> > > https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FEF0CB0CE755B4F67813AEC1E3596DEF/S0251107X0002023Xa.pdf/commission_31_time.pdf
> > > ]
> > So the alternative notation for 2016-12-31T23:59:60Z would be 2016-
> > 12-
> > 31T24:00:00Z.
>      No, the IAU mean 2017-01-01 - 01 s, a negative value
>      for time of day.
>

If I am reading section 9.4 correctly, they are defining two time
scales: the old scale (before the leap second) and the scale after the
step.  In the old scale the leap second at the end of 2016 would start
at 2016-12-31T24:00:00 and end at 2016-12-31:24:00:01.  In the scale
after the step the leap second would start at 2017-01-01:00:00:-1 and
end at 2017-01-01T00:00:00.

Before the leap second starts it is best to use only the old scale, and
after the leap second ends the best scale to use is the scale after the
step.  During the leap second both scales are useful.
John Sauter (John_Sauter at systemeyescomputerstore.com)

--
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