Heisenberg, matrix mechanics, and the uncertainty principle

Bernard Pourprix

In 1927 Werner Heisenberg succeeded in giving a deep physical meaning to the mathematical formalism of the matrix quantum mechanics. He has discovered that parameters associated to conjugate pairs can not be known accurately. It means that the uncertainty principle is embedded in the quantum mechanics formalism itself and has nothing to do with experimental limits. The article shows that the uncertainty principle is the fruit of a long journey with continuous contacts with the outstanding contemporary works of Wolfang Pauli, Paul Dirac and Pascual Jordan. The uncertainty principle appears to be also a particular case of a more general concept: the 'complementary principle' through which various aspects of a single process are complementary and not contradictory: the duality between wave and particle is another example.

Robert Prevedel, Bose-Einstein Condensate

André Michaud

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of Wave Mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum Mechanics, when Schrödinger proved that the Matrix Mechanics independently developed by Werner Heisenberg was equivalent to Wave Mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

Salvatore Capozzıello, Wladimir-Georges Boskoff

P. W. Atkins

Abstract Heisenberg’s uncertainty principle states that: The product of the uncertainties in the simultaneous specifications of two °complementary observables can never be less than a small quantity of the order of h. The precise form of the principle is given in Box U.1. It implies that as one observable is constrained to have a more precise value, so its partner becomes more ill-defined. An experiment designed to measure the two observables simultaneously will be able to determine one precisely only at the expense of losing information about the other (see °duality). The principle was established by Werner Heisenberg in 1927, as a consequence of his formulation of °matrix mechanics.