Galileo's pendulum could have shown that local time is relative Making experiments with pendulums Galileo discovered the following properties: - Pendulums nearly return to their release heights. - All pendulums eventually come to rest with the lighter ones coming to rest faster. - The period is independent of the bob weight. - The period is independent of the amplitude. - The square of the period varies directly with the length. (T=k*sqrt(L)) in a time when the notion of gravity did not exist. Later experiments done before 1687 showed that k is a function of altitude. In other words local time passes with different speeds at different altitudes, being slower and slower as the height increases. If more precise measurements could have been performed then T would have appeared as a vectorial quantity given by the expression: T=k'*r*sqrt(L) where T = pendulum period k' = a constant r = the distance from the center of the earth to the pendulum L = the length of pendulum string A pendulum rotating around the center of an nonexistent Earth would have indicated a local time: T1(r) = k1(r)*sqrt(L) A pendulum rotating around the Earth would have indicated a local time: T2(r) = k1(r)*sqrt(L) + k'*r*sqrt(L) If T2(r) is always measured as being zero then k1(r) = - k'*r In conclusion, something looking like the theory of relativity would have been possible 300 years ago if somebody really wanted to devise such a theory.