On 2006-01-13, Mark Calabretta wrote: > I have two time scales, TAI and UT1, that tick at very slightly > different rates. I want to make TAI the basis for civil time keeping > but I need to make adjustments occasionally to keep it in step with > UT1. How do I do it? > > The answer provided by CCIR was to represent TAI in a variable-radix > notation that matches (or appears to match), to within 0.9s, that of > UT1 expressed in the usual calendar/clock format. This is done by > varying the radix of the seconds field in a pseudo-sexagesimal clock > format from 60 to 61 (or in principle 59) on occasions announced 6 > months in advance. > > So if asked for a definition I would say that "UTC (post 1972) is a > representation of TAI such that ... (you know the rest)". > > The point is that UTC is simply a representation of TAI. "Writing UTC > as a real" reveals it to be TAI.
I believe I'm now grasping what you mean: the rate of UTC is the same as the rate of TAI (since 1972), that is, the derivative d( UTC )/d( TAI ) = 1. Hence, when I integrate the "ticks" of UTC I must get TAI, up to an integration constant. This is correct. The integral of d( UTC ) is TAI (up to an integration constant), but this integral is UTC only where UTC is a continuous function of TAI. Astronomers who "write UTC as a real" (eg, in JD or MJD notation) want an approximation of UT1 to point their telescopes, they do _not_ want TAI. They use UTC as a timescale whose values are close to UT1, but whose rate nevertheless is d( UTC ) = d( TAI ) and not d( UT1 ). Such a function cannot be continuous (and it cannot be differentiable everywhere). At the latest discontinuity of UTC, it jumped from a little bit after UT1 to a little bit before UT1. Michael Deckers