Physical Indeterminism

PHYSICAL INDETERMINISM. - Physical i. depends on the uncertainty principle, the foundation of atomic mechanics, due to W. Heisenberg.

In classical mechanics determinism holds, already summarized by P. S. Laplace in a passage that has remained famous (Théorie analytique des probabilités, 3rd ed., Paris 1820, p. VII); it affirms that when the coordinates (position) and the momentum (velocity) of every point of a system at a given instant are assigned, the state of the system at that instant is completely determined; every further condition is either incompatible with the preceding ones or already contained in them. Consequently, given the state of a system at a certain instant, the value of the positions, of the velocities and of their functions, relative to the system at that instant, is fixed, and so is the result of every measurement of these quantities carried out at that instant. If moreover the forces acting on the points are known, given the state of the system at a certain instant, the state of that system at every other past or future instant is likewise precisely determined, and therefore the result of any measurement at any instant is foreseeable with precision as great as one pleases (v. DETERMINISM).

In 1927, W. Heisenberg, in a famous paper, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik (in Zeitschrift für Physik, 43 [1927], pp. 172-83g.) established the uncertainty principle: it is conceptually impossible to determine the position and the momentum of a particle at a given instant with a precision greater than that indicated by the relations

Δₓ Δₚ ≥ frac{h}{4π}, Δ_y Δₚ ≥ frac{h}{4π}, Δ_z Δₚ ≥ frac{h}{4π}; where Δₓ Δ_y Δ_z are the indeterminacies of the coordinates, Δₚ, Δₚ, Δₚ those of the respective momenta, h is M. Planck's constant.

The uncertainty principle is a consequence of the permutation relations in matrix calculus and was demonstrated by E. Schrödinger also with the principles of wave mechanics; physically it depends on the ineliminable perturbation that observation produces in the phenomenon. It is therefore not due to experimental errors, but expresses a physical law, as M. Planck's constant indicates.

Since the state of a system is defined by a set of conditions such that every other is either contained in them or incompatible with them, the uncertainty principle changes the concept of the state of a system of classical mechanics, in that it does not permit the exact measurement of the positions and at the same time of the momenta of the points. In quantum mechanics the state of a system is defined by a complex of all those measurements that are mutually compatible, according to the uncertainty principle. The system maintains its state as long as it remains isolated and, this condition persisting, the laws of quantum mechanics allow its development at every future instant to be predicted exactly. If however we make measurements on it, the isolation generally ends and the state changes: therefore, once the state of a system has been determined in quantum mechanics, the result of a further observation cannot generally be calculated; it is possible only to calculate the possible results of every observation with their respective probabilities. In general these possible results constitute a continuous or discrete infinity. This is precisely physical i. These concepts apply to elementary phenomena, whereas for macroscopic phenomena, where particles in an extremely great number are involved, their measurements are an average and determinism therefore holds.

Many interpret the uncertainty principle as the negation of an objective physical determinism, that is, of a univocal, predetermined causality, in the elementary particles where pure chance would reign, albeit with tendencies toward the different possibilities (cf. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Berlin 1932; A. Eddington, Sur le problème du déterminisme, Paris 1934, p. 11; E. Persico, Analisi del determinismo fisico, in Fondamenti logici della scienza, Turin 1947; L. De Broglie, Fisica e microfisica, trans. by G. Crescenzi, Turin 1950, p. 205-89g.); but this entails grave philosophical difficulties. Indeed, while the indeterminate is potency and the determinate is act, «agere... est per se proprium actus, inquantum est actus» (Sum. Theol., 1a, q. 115, a. 1) and «propria forma uniuscuiusque, faciens ipsum esse in actu, est principium operationis ipsius» (ibid., 2a-2ae, q. 179, a. 1, ad 1). Therefore every reality acts insofar as it is determined by a form. This can be: either a psychic representation which, if of a spiritual order in an intelligent subject, can be the principle of a free action, that is, self-determined and indeterministic; or a real form. In a non-knowing being, for example in the atomic world, action proceeds from a real, determined, necessary form; it will therefore be a necessary deterministic action. This excludes objective i. in the atomic world.

The uncertainty principle indicates only the impossibility of measuring a phenomenon without disturbing its process. The atomic world is indeed deterministic, although we cannot ascertain this because of the imprecision of our observations, an imprecision that is given by the uncertainty principle.

Roberto Masi