Quantum mechanics reformulated by means of symmetries

Antonino Drago

A. Pirolo

pp. 229-237

in: Claudio Garola, Arcangelo Rossi (eds), The foundations of quantum mechanics, Berlin, Springer, 1995

Abstract

Here we present a formulation of Quantum Mechanics that is founded on the fundamental choices — only potential infinity and problematic organization — that — according to previous results by A. Drago — are characteristic of the alternative theories to the Newtonian one; hence on the symmetries and without differential equations. In this new formulation, the fundamental problem of the theory is recognized in Heisenberg's uncertainty relations. We state the "Uncertainty Principle" by a double negated sentence that is not the same as an affirmative one, that is to say a characteristic sentence of non-classical logic which in this way is introduced from the beginning of the theory. Then, we state the commutation relations by means of the classical symmetries, that essentially follow Jordan's new version of Heisenberg's formulation.