On 2014-11-04 22:26, Steve Allen quoted Bernard Guinot
about the unit for the difference TAI - UT1:
Guinot explained this using the term "graduation second"
in section 2.2 of 1995 Metrologia 31 431
http://iopscience.iop.org/0026-1394/31/6/002
He points out that the way the IAU has written the definitions of the
time scales uses a subtly ambiguous notation. He writes
The numerical value of UT1(IERS)-TAI does not
of course, express a duration. In this context, the "s"
only conveys the information that the readings of the
two time scales are expressed in graduation seconds.
Guinot comes back to this question, and revises his position,
in [Guinot 2011, section 7.a, p 4139], where he exposes the
underlying fundamental question: how can the set of spacelike
and timelike coordinates be given consistent dimensions
(invariant under the Minkowski group). He writes:
(a) Unit of relativistic coordinates
Some authors consider the relativistic coordinates as dimensionless,
others give a special name to their unit, such as the ‘TCB second’ or
a global name such as ‘graduation unit’. I was myself
in favour of the latter name. However, after long discussions with
eminent metrologists, Quinn and de Boer, I agreed that it was
simpler to name ‘second’ the graduation unit. Thus, more generally,
all quantities having the dimension of time have the second (without
any qualifier) as their unit, even if they have different natures,
such as time interval and reading of a time scale. If the logic of
this point of view seems rather obscure, then it is possible to
consider it as a convention which has the merit of being in
agreement with the quantity calculus. It also agrees with the
metrological rule that the unit does not define a quantity.
While I can only agree with Guinot's position, I am not sure whether
space coordinates and relativistic change of coordinates can be modeled
neatly in that way. Amazing that simple questions about time scales
can lead to such really fundamental conceptual issues!
Reference:
[Guinot 2011] Bernard Guinot: "Time scales in the context of general
relativity". in: Philosophical Transactions of the Royal Society A.
vol 369 p 4131..4142. 2011-09-19. online at:
[rsta.royalsocietypublishing.org/content/369/1953/4131.full.pdf]
Michael Deckers.
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