Re: [Phys-l] New gravitational constant

[John Denker <jsd@av8n.com>]

On 01/22/2008 03:21 AM, Savinainen Antti wrote:


> .... the older accepted value was:
>
> (6.67259 +/- 0.001) * 10^(-11) m^3kg^(-1)s^(-2)

Where did that come from?  That looks sorta like the 1986 
CODATA value, except that the uncertainty is misstated.

> have you noticed that the value of the gravitational constant has changed? The
> new value given by CODATA is:
>
> (6.67428 +/- 0.00067) * 10^(-11) m^3kg^(-1)s^(-2)
> <http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=gravitational+constant>

That's old news.  There was a huuuge brouhaha starting in 1996,
when Michaelis, Haars, & Augustin published a measurement of
G that was waaaay outside the previously-accepted error bars.
To deal with this:

] At the end of 1999, an international committee (the CODATA) decided to
] increase the uncertainty of the accepted value for the gravitational
] constant from 128 ppm to 1500 ppm. This remarkable step of increasing
] the uncertainty instead of decreasing was made to reflect the
] discrepancies between recent experiments.

That's a quote from:
  http://www.europhysicsnews.com/full/04/article6/article6.html

Since 1998, the uncertainty has been decreasing, and the nominal
value has settled back to being not too far from where it was 
20+ years ago.

Some CODATA values over the last 20 years are:

      2006       2002       1998       1986
     6.67428    6.67420    6.67300    6.67259      nominal value
     0.00067    0.00100    0.01000    0.00085      uncertainty

> I knew that this constant is very hard to measure accurately but it surprised
> me that the discrepance between the new and old value is so great that they do
> not agree within their uncertainty limits.

Actually there is appreciable overlap between the current
quantity and the 1986 quantity, as you can see if you plot 
the distributions:
  http://www.av8n.com/physics/img48/grav-constant.png

Moral of the story:  Look at the data.  Find a way to plot the
data so you can /see/ what it means.  If you want to know whether
probability distributions overlap, plot the distributions and
look at the overlap.



> On 01/22/2008 06:46 AM, Todd Pedlar wrote:
> > ... if [the shift] were 4 or 5 sigma, then we'd
> > have something to talk about - but shifts of 1 to 2 sigma happen
> > frequently (and do not mean the uncertainty previously given
> > was wrong). 

Agreed.

> > Actually there's an interesting exercise here.  

Yes there is, but maybe not what you thought.

> > If this is
> > the way CODATA reported their previous value
> > (5 places after the decimal with an uncertainty in the
> > third place after the decimal) then they've not learned
> > basic rules of reporting uncertainties that I drum into my
> > students! :)

Maybe it would help to do more thinking and less drumming.
The CODATA team is comprised of the world's leading
metrologists.  It might be worth considering the possibility
that they know what they're doing.

In fact there are exceedingly good reasons for reporting data
such that the uncertainty is dozens of times greater than one
count in the last decimal place.

The "significant figures" rules you learned in high school are
completely unacceptable for serious work, for reasons explained
in detail at:
  http://www.av8n.com/physics/uncertainty.htm