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 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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