With displacement, time, and force as basic undefined physical quantities, other physical quantities are defined as combinations of two vector quantities and one scalar quantity. Combinations include multiplication and division of vectors by vectors, scalars by vectors, and scalars by scalars. Defined quantities are vectors, scalars or quaternions, depending on directions of vectors in the definitions. Division of a vector by a vector is equivalent to multiplication of vectors divided by a scalar. The unit of a vector (or scalar) is (...) itself a vector (or scalar) quantity. Thesquare meter (a vector) differs from meter 2 (a scalar), and the cubic meter (a scalar) is different frommeter 3 . The characteristics of displacement, time, and force are considered known from experience. (shrink)

The meaning of the phrase “the direction of time” and the physical problems involved are considered. These problems are discussed and plausibility arguments are given to show that all clocks run in the same direction (almost always), that the most probable development of the Universe during the early stages of the expansion would result in the introduction of some internal organization, and that the expansion of the Universe and the increase in entropy define time directions that have the same sense. (...) The question of what properties of the laws governing the Universe lead to these results is studied. (shrink)