LEGGI FISICHE E LEGGI STATISTICHE. - Within the totality of natural phenomena, which constitute the object of scientific research, two groups may be distinguished. One of them consists of all those phenomena whose succession occurs with invariable regularity, so that it is always possible—starting from observation of the conditions in which the phenomenon occurs at a given instant—to express its past and future evolution by means of mathematical equations: thus one arrives at the formulation of a «physical law», which binds, in a well-defined and constant relationship, the quantities involved in the phenomenon. Laws of this kind have been obtained in the study of classical mechanics, electromagnetism, etc.
There is, 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 reached by abandoning the investigation of the course of individual phenomena and limiting oneself to determining mean values, deduced from the observation of a large number of phenomena of the same type. Contrary to what occurs with physical laws, statistical laws do not allow the evolution of the phenomenon in all its particulars to be inferred with absolute certainty: they permit 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 constitute the object of quantum mechanics. The reasons for the inapplicability of physical laws to this complex of phenomena are not the same in every case. In thermodynamic systems, specifically, the intervention of statistical laws is made necessary by the enormous number of their constituents (the molecules), which makes investigation of the evolution of the molecules one by one practically impossible: no one, however, can exclude a priori the theoretical possibility of knowing the physical laws governing these individual phenomena. In the other phenomena listed above, on the other hand, the application of statistical laws is precluded by the uncertainty principle, which asserts the impossibility of formulating physical laws from which the behavior of individual phenomena could be inferred.
Finally, it is worth noting that statistical laws are not—in practice, as might perhaps initially appear—less rigorous than physical laws: to realize this, it is enough to recall that physics, like all the experimental sciences, never deals with absolute quantities, since every measurement, whatever the degree of precision with which it has been carried out, is always affected by error.