PHYSICAL LAWS AND STATISTICAL LAWS. - In the complex of natural phenomena that form the object of scientific research, two groups can be distinguished. One of them is constituted by all those phenomena whose succession occurs with inescapable regularity, such that one can always - starting from the observation of the conditions under which, at a given instant, the phenomenon occurs - express its past and future evolution by means of mathematical equations: one thus arrives at the formulation of a "physical law," which binds, in a well-defined and constant relationship, the quantities that enter into the phenomenon. Laws of this type have been obtained in the study of classical mechanics, electromagnetism, etc.
There exists, however, a vast complex of phenomena, constituting the second of the categories mentioned above, for which the formulation of physical laws proves impossible. Their interpretation is obtained through empirical rules, the so-called statistical laws, which are arrived at by renouncing the investigation of the development of individual phenomena and limiting oneself to the determination of average values, deduced from the observation of a great number of phenomena of the same type. Contrary to what occurs for physical laws, from statistical laws one does not infer with absolute certainty the evolution of the phenomenon in all its particulars: they allow only the prediction of its average course with a very high probability.
Statistical laws govern thermal processes, the disintegration of radioactive substances, and the phenomena that form the object of quantum mechanics. The causes of the inapplicability of physical laws to this complex of phenomena are not the same for all. Precisely in thermodynamic systems the intervention of statistical laws is made necessary by the enormous number of their constituents (the molecules), which renders practically unfeasible the investigation of the evolution of molecules one by one: no one, however, can exclude a priori the theoretical possibility of knowledge of the physical laws that govern these individual phenomena. On the other hand, in the other phenomena listed above the application of statistical laws is excluded by the uncertainty principle, which asserts the impossibility of the formulation of physical laws from which the behavior of individual phenomena could be inferred.
It is well to note finally that statistical laws are not - as might perhaps appear at first glance - in practice less rigorous than physical laws: it suffices, to realize this, to recall how physics, like all experimental sciences, never has to do with absolute quantities, inasmuch as every measurement, whatever the degree of precision with which it has been conducted, is always affected by error.