# [ntp:questions] Leap second to be introduced in June

Brian Inglis Brian.Inglis at SystematicSw.ab.ca
Fri Jan 23 06:32:24 UTC 2015

```On 2015-01-22 11:04, William Unruh wrote:
> On 2015-01-22, David Malone <dwmalone at walton.maths.tcd.ie> wrote:
>> William Unruh <unruh at invalid.ca> writes:
>>
>>> Note UTC differs from TAI by an interger number of seconds, AND that
>>> integer changes with the leap second. Ie, it cannot be continuous if TAI
>>> is continuous.
>>
>> That assumes that UTC can be represented as a real number with the
>> standard topology, which doesn't seem to be what TF.460 says. It
>> describes each second as labelled, which means that you have to
>> stitch together all possible unit intervals for each second with
>> some topology, and then you can ask if the path taken by UTC through
>> this space is continuous.

> General relativity assures us that time exists and is measured by a
> metric. Take that metric and define a proper time say at the center of
> the earth. Now one can ask whether TAI or UTC is a function of that
> time.
> Consider some labeling of the time. Jun 30 23:59:00 and Jul 1 00:01 let
> us say. Now when we look at TAI, that second one is one second one is
> 120 seconds ( as measured by that metric) later than the first. For
> UTC it is 121 seconds later than the first. As one hunts in toward
> midnight, say Jun 30 23:59:58 vs Jul 1 00:00:02 say, that interval is
> still 1 second different in the two scales. And for Jun 30
> 23:59:59.999999999 and Jul 1 00:00:00.000000001
> while TAI says that difference is .000000002 sec, UTC says it is
> 1.000000002 sec different.
> That for all purposes is a discontinuous function of the time as defined
> by General relativity. Now, it is true that UTC does give a name to that
> second that lies between the two times, but giving it a name does not
> make the function continous.
> UTC is a function which is linear and continuous for all times which are
> not the leap second, but is discontinous at the leap second. The limit
> of the function as delta t goes to zero of the two scales is not the
> same. Limit as delta t goes to zero  t_relativity (UTC Jun 30 23:59:59.999...
> -Delta t) is not equal to Limit as delta t goes to zero t_relativity
> (UTC Jul 1 00:00:00:.00000.... +Delta t) while it is for TAI. The fact
> that UTC gives a name ( 23:59:60) to that extra second does not alter
> the above fact.
> The fact that UTC publishes a list of when those discontinuities occur
> is also irrelevant. That one says a function is discontinuous at some
> value of x and how much it is discontinous, does not alter the fact that
> it is discontinous.

TAI, TT, UTC, UT, UT0, UT1, UT2 are empirical time scales based on
measurements not functions, with some scales having fairly simple
relations, and UTC stepping by leap seconds.
The relative values on these scales are only available accurately
when they are published about a month after the time, with estimates
available later each day from some labs, based only on those individual
labs' standards, which may need corrected later in the month.
So none of these simplified arithmetical approaches are anything more
than working approximations to the nearest jiffy, and they are not really
useful unless you are working in astronomy or physics related fields.
POSIX allows you to do useful calculations on civil times based on mean
solar seconds, but there are no useful sources for synchronizing or
calibrating POSIX time, as all time sources use scales based on SI seconds.
--
Take care. Thanks, Brian Inglis
```