## An Application of Interval Computations to Gravity

Featured as One of The Major Scientific Results

The March 1996 issue of
Discover,
the popular science magazine,
features, among other stories about the major recent scientific results,
a story about measuring the gravitation constant G (according to
Newton's law, the attraction force of a body with mass M at a distance R
is GM/R^2). Due to the fact that on Earth, the gravitational interaction
between bodies is much weaker than any other interaction, this constant is
the worst known among the fundamental physical constants. What is even worse,
different known measurements of G seem to be inconsistent: there are
several measurement results with accuracy estimates; each gives an
interval of possible values of G, so, ideally, the actual value of G
must be in all of them, but ... these intervals have no common points.
Physicists and applied mathematicians from Wuppertal, Germany,
led by Prof. Dr. H. Meyer (Physics) and Prof. Dr. B. Lang (Math),
analyzed this situation and discovered that this seeming inconsistency
is caused, partially, by neglecting certain physical sources of error,
but mainly, by using approximate error estimation techniques for data
processing algorithms, techniques that often underestimate the
resulting error. Instead, they propose to use computations with
automatic result verification (in particular, interval methods).
The paper by B. Lang and co-authors has appeared in No. 3 (1996) of
Reliable Computing
(for a Postscript version of this paper, click here).
The first author's email is
lang@math.uni-wuppertal.de.
This is the second time in half a year that a result using interval
computations is featured as one of the major scientific breakthroughs:
the previous was the result about the
double bubble featured in November 1995.
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