ROMA 1 - 1394/04 December 2004 Why does the meter beat the second? P. Agnoli1 and G. D’Agostini2 1 ELECOM s.c.r.l, R&D Department, Rome, Italy (
[email protected]) 2 Universit`a“La Sapienza” and INFN, Rome, Italy (
[email protected], www.roma1.infn.it/˜dagos) Abstract The French Academy units of time and length — the second and the meter — are traditionally considered independent from each other. However, it is a matter of fact that a meter simple pendulum beats virtually the second in each oscillation, a ‘surprising’ coincidence that has no physical reason. We shortly review the steps that led to the choice of the meter as the ten millionth part of the quadrant of the meridian, and rise the suspicion that, indeed, the length of the seconds pendulum was in fact the starting point in establishing the actual length of the meter. 1 Introduction Presently, the unit of length in the International System (SI) [1] is a derived unit, related to the unit of time via the speed of light, assumed to be constant and of exact value c = 299 792 458 m/s.1 The unit of time is related to the period of a well defined electromagnetic wave.2 The proportionality factors that relate conventional meter and second to more fundamental and reproducible quantities were chosen to make these units back compatible to the original units of the Metric System. In that system the second was defined as 1/86400 of the average solar day and the meter was related to the Earth meridian (namely 1/10 000 000 of the distance between the pole and the equator on the Earth’s surface).