# [om] Units example usage ?

Andreas Strotmann Strotmann at rrz.uni-koeln.de
Tue Apr 29 11:43:59 CEST 2003

```Bill Naylor wrote:

> On Tue, 29 Apr 2003, Bill Naylor wrote:
>
>
>>Date: Tue, 29 Apr 2003 09:16:59 +1200 (NZST)
>>From: Bill Naylor <Bill.Naylor at mcs.vuw.ac.nz>
>>To: om at openmath.org
>>Subject: Re: [om] Units example usage ?
>>
>>On Mon, 28 Apr 2003 sal at dcs.st-and.ac.uk wrote:
>>
>>
>>>Date: Mon, 28 Apr 2003 09:07:23 +0100
>>>From: sal at dcs.st-and.ac.uk
>>>To: om at openmath.org
>>>Subject: Re: [om] Units example usage ?
>>>
>>>Irrelevant but:
>>>
>>>Glancing at the CD I see that you say the Speed of Light is approximately nnn
>>>m/s. Isn't it exactly that by the definition of the second?
>>>
>>>	Steve
>>
>>You may be correct, I'm not a physicist, I assumed (wrongly) all these
>>(physical) things where approximate, anyway the definition of approximate
>>is sufficiently 'woolly' that eq may be taken as a special case of approx
>>(no?)
>>
>
>
> The NIST reference on Constants, Units and Uncertainity defines a second
> as:
>
> "The second is the duration of 9 192 631 770 periods of the radiation
> corresponding to the transition between the two hyperfine levels of the
> ground state of the cesium 133 atom."
>
> however I see that the definition of the meter (according to NIST) is:
>
> "The meter is the length of the path travelled by light in vacuum during a
> time interval of 1/299 792 458 of a second."
>
> so you still get exact equality,
>

... by the *current* definition.  The *original* definition of the meter was
1/10,000,000th of the distance between the equator and the pole of the
Earth(*),
which was not exact to so many digits, of course.  The definitions of
meters and seconds change constantly as the NISTs of the world come up
with ever more exact ways of measuring the units.

Similarly, the above only defines exactly the light *second*.  A *year*,
however, would still be a measured quantity, namely the time it takes
the Earth to go once around the Sun, and thus the value of a light
*year*, the example given in the FMP, would still be approximate (unless
someone defines an exact value for the year in a light year somewhere).

-- Andreas

(*) this was in analogy to the nautical mile with its 90 nautical
degrees replaced by 100 decimal "degrees" and 60 nautical minutes
replaced by 100 "decimal" minutes.  Needless to say, this was an
invention of the French revolution.  The meter made it into general
popularity, but decimal degrees/hours didn't.
--
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