We also referred to Newton’s laws of motion there, which were verified by experiment and observation for over 200 years, and are excellent approximations at the scales and speeds of everyday life. However, they break down under certain circumstances such as at very small scales (e.g., microscopic), very high speeds (e.g., near the speed of light), or very strong gravitational fields, and have been refined in the development of Einstein’s theories of relativity and later quantum field theory. Eddington’s eclipse observations in 1919 brought the first important confirmation of Einstein’s theory of gravitation. New experimental phenomena such as the discovery of quasars, microwave background radiation, and black holes, provided a stimulus to general relativity theory.

Other laws are formulated from observations that give rise to so-called empirical laws. For example, a data plot of pairs of certain observations on a graph may suggest that the points are very close to lying on a straight line. This empirical relationship could then be described mathematically by the equation of the fitted line. Another example that is not mathematical arises in the following situation. Suppose we have a bus stop close to our home and we observed the arrival times of buses for say a year.

The picture is not as clear as we would like it to be because of random variations in the system that affect bus travel. However, because of a general regularity observed in bus arrival times, we would suspect that a timetable actually exists designed by someone.