Axioms of Classical Mechanics

Classical mechanics is the investigation of the interactions of material bodies and forces in Euclidean space-time. According to Hamel it is governed by four axioms[1]:

2) Space is isotropic. There exists no preferred direction in space.

3) Every effect must have its cause by which it is uniquely determined. This is also called the causality principle.

4) No particular length, velocity, or mass is singled out.

Homogeneity of space is not natural to us. We think we are at the center of the universe and everything else turns around us. Yet we are just one reference frame. Every person can make the same claim. Homogeneity expresses the fact that all reference frames are equally valid, and therefore there is no preferred location in space. Does the sun revolve around Earth or Earth around the sun? Either statement is valid. It is just a matter of reference.

Homogeneity of time means that there exists no preferred instant of time. In the western world the Julian calendar begins with the birth of Christ, but other civilizations have their own calendars with different starting times. These are just arbitrary man-made beginnings. However, because time is a uniformly increasing measure, it must have had a beginning. That instant, when time was created, is distinct, but we do not know when it occurred. All other times have equal stature.

Space is not only homogeneous, but also isotropic, meaning that all directions in space have equal significance. On Earth we fly by the compass, which indicates magnetic north. But Mars probes navigate in an inertial, sun-centered frame, which is unrelated to terrestrial north. These are man’s preferences. Space itself has no preferred direction.

We all have experienced the causality principle in our lives. I cut my finger (cause), and blood drips (effect). The pilot increases the throttle, the engine in­creases thrust, and the aircraft gains speed or altitude. There are two effects possi­ble, speed and altitude, but each is uniquely determined by the thrust increase. All laws of classical mechanics abide by this causality principle.

The fourth axiom is a source of distress for all of those scientists who have tried for centuries to define the length of a meter. Eventually they agreed to make two marks on a bar of platinum and store it at the Bureau International des Poids et Mesures near Paris at a temperature of 0°C. There you also find the kilogram, well preserved for those who cherish precision. Yet, classical mechanics does not recognize any of these human endeavors.

Modem physics brakes with tradition and violates at least one of these axioms. In relativistic mechanics space is inhomogeneous and nonisotropic (Riemannian space); quantum mechanics does not recognize the causality principle; and the theory of relativity singles out the speed of light.

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