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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Drago: Le due opzioni. Per una storia popolare della scienza, La Meridiana, Molfetta (BA), 1991
A. Drago: “A characterization of the Newtonian Paradigm”, in G. Debrock, G.B. Scheurer (eds.): Newton’s Philosophical and Scientific Legacy, Kluwer Acad. P., 1988 239–252
to thermodynamics: A. Drago: “The alternative Content of Thermodynamics: The Constructive Mathematics and the Problematic Organization of the Theory” in K. Martinas et alii (eds.): Thermodynamics. Facts, Trends, Debates, World Scientific, Singapore, 1991, 329–344.
A. Drago: “All’origine della meccanica quantistica. Le sue opzioni fondamentali” in G. Cattaneo, A. Rossi (eds.): I fondamenti della meccanica quantistica, Editel, Cosenza, 1991,59– 79.
N.R. Hanson: “Are Wave and Matrix Mechanics Equivalent Theories?”, in H. Feigl, S.Maxwell (eds.): Current Issues in the Philosophy of Science, Halt, New York, 1961, 401–424
L. Mayants: The Enigma of Probability and Physics, Reidel, Boston, 1984.
M.L. Dalla Chiara, G. Toraldo di Francia: La formalizzazione delle teorie fisiche, Boringhieri, Torino, 1992
Dirac, too, asserts that the Heisenberg and Scroedinger pictures are not equivalent; in “Foundation of quantum mechanics”, Nature, 4941 (1964), p. 115–116.
E. Bishop: Foundations of Constructive Mathematics, Mc Graw-Hill, New York, 1967
O. Aberth: Computable Analysis, Mc Graw-Hill, New York, 1980.
A. Pirolo: “Analisi storico-critica delle simmetrie nella fisica teorica”; Tesi di laurea in Fisica, Univ. Napoli, a.a. 1992–93.
L. Carnot: Essai sur les machines en général, Defay, Dijon, 1782.
S. Camot: Réflexions sur la puissance motrice du feu, Bachelier, Paris 1824, (Blanchard 1978). Probably, chemistry too substantiates symmetry by means of the periodic table of elements; however, that does not suggest any formalism. Moreover its PO is based on the problem of the existence of the indivisible of matter; but at present, after the experimental evidence for atoms and molecules, this is no more a problem.
T.F. Jordan: Quantum Mechanics in Simple Matrix Form, John Wiley & Sons, New York, 1985.
T.F. Jordan: op. cit. pag. 3.
T.F. Jordan: op. cit. pag. 187.
I. Lakatos: Mathematics, Science and Epistemology. Philosophical Papers, vol 2, pt. 1.2, Cambridge U.P., 1978.
K. Jagannathan: Review to of T.F.Jordan op. cit., Am J. Phys. 54, (1986), p.1 154.
K. Jagannathan: op. cit. p. l 154, II column.
K. Jagannathan: op. cit. p.1155, II column.
G. Birkhoff, J. von Neumann: “The Logic of Quantum Mechanics”, Ann. Sci, 37 (1936) 23– 43.
T.F. Jordan: op. cit., cap. 23–27.
T.F. Jordan op. cit. cap. 18–22.
F. Richman, R. Mines: Constructive Algebra, Springer, Berlin, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Drago, A., Pirolo, A. (1995). Quantum Mechanics Reformulated by Means of Symmetries. In: Garola, C., Rossi, A. (eds) The Foundations of Quantum Mechanics — Historical Analysis and Open Questions. Fundamental Theories of Physics, vol 71. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0029-8_20
Download citation
DOI: https://doi.org/10.1007/978-94-011-0029-8_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4017-4
Online ISBN: 978-94-011-0029-8
eBook Packages: Springer Book Archive