RE: [office-formula] Straw poll - slug (and lightyear)

["Dennis E. Hamilton" <dennis.hamilton@acm.org>]

David, thanks for the source on the SI units. This is fascinating.  

I like the number 299792458, though I would never call it "exact" for the
speed of light.  

I think it is better to say that the meter is defined to be the distance
light travels in a vacuum in exactly 1/299792458 second.  It is then
tautologous to observe that the speed of light in m/s is exactly the
reciprocal of that.  That seems to be what the description in section
2.1.1.1 is saying when it says "it follows that ... is exactly ... ."

The time-unit, 1 second, is similarly based on observation of a physical
phenomenon.  1 second is defined to be the duration in which there are
9192631770 periods of the radiation corresponding to a Caesium 133 atom at
rest [hmm] at a temperature of 0K [oh oh] going through a particular
periodic transition.  It is then tautologous to observe that the frequency
of such radiation, v(hfs Cs), is exactly 9192631770 Hz.  (section 2.1.1.3)

Now, one still has to be careful about what one says is exact by
extrapolations using these numbers.  For example, the smallest exact
measurement of time that we have, under this standard, is 1/9192631770
second, because of limitations on the physics of the standard.  That's
slightly more than 10^-10 seconds, or 100 picoseconds.  (We deal with
shorter time intervals and how that is done is an interesting topic all of
its own.)  I was curious about this because in even that brief moment,
1/9192631770 second, light will travel about 32.6 cm in a vacuum.

I think the moral of the story is that it is not reliable (and certainly not
very meaningful) to compute the light year to centimeters.  In fact, I would
not expect to see much better than 9 decimal digits, no matter how exact the
conversion factors are. We should probably be happy if an OpenFormula
evaluator comes up with something at least as accurate as 9.46073 X 10^15 m.

- Dennis

PS: This suggests that the number Patrick found is incorrect as far as SI is
concerned.  The light year is apparently closer to 9.46073 X 10^17 cm
(9.46053 X 10^17).  I don't believe my TI BA-35 calculator could have gotten
it that wrong with its 10-digits of precision.


-----Original Message-----
From: David A. Wheeler [mailto:dwheeler@dwheeler.com] 
Sent: Friday, April 09, 2010 08:44
To: patrick@durusau.net
Cc: office-formula@lists.oasis-open.org
Subject: Re: [office-formula] Straw poll - slug (and lightyear)

[ ... ]
The speed of light in a vacuum is defined to be exactly 299 792 458 metres
per second
(the meter is defined in terms of the speed of light in vacuum).
Source: International Bureau of Weights and Measures (2006), The
International System of Units (SI) (8th ed.), p. 112, ISBN 92-822-2213-6,
http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
A year, for light-year purposes, is exactly 365.25 days, as we've already
discussed.

[ ... ]