The modes of physical properties in the logical foundations of physics

Sonja Smets

DOI: http://dx.doi.org/10.12775/LLP.2005.004

Abstract


We present a conceptual analysis of the notions of actual physical property and potential physical property as used by theoretical physicists/mathematicians working in the domain of operational quantum logic. We investigate how these notions are being used today and what role they play in the specified field of research. In order to do so, we will give a brief introduction to this area of research and explain it as a part of the discipline known as “mathematical metascience”. An in depth analysis of Aristotle’s use of the notions of “actuality” and “potentiality” is presented in order to point out exactly how much of the Aristotelian connotations are embedded in the contemporary use of the concepts under investigation. Although we will not focus in depth on all the drawbacks in the early historical development of physics due to the overwhelming influence of Aristotle’s writings, our analysis does touch upon some aspects of the Aristotelian theory of movement that are often overthrown nowadays.

Keywords


actuality; potentiality; physical property; operational quantum logic

Full Text:

PDF

References


Aristotle, The Complete Works of Aristotle. The Revised Oxford Translation, vol. 1, J. Barnes (ed.), Princeton University Press, New Jersey (1995).

Aristotle, The Complete Works of Aristotle. The Revised Oxford Translation, vol. 2, J. Barnes (ed.), Princeton University Press, New Jersey (1995).

Baltag, A., and S. Smets, “The Logic of Quantum Programs”, TUCS General Publication 33, 39–56, Turku Center for Computer Science (2004) arXiv: PITT-PHIL-SCI00001799.

Baltag, A., and S. Smets, “Complete Axiomatizations for Quantum Actions”, in Proceedings of the IQSA2004-conference, to appear in International Journal of Theoretical Physics.

Baltag, A., and S. Smets, “LQP: The Dynamic Logic of Quantum Information”, in Mathematical Structures in Computer Science, Special Issue on Quantum Programming Languages, submitted for publication.

Baltag, A., and S. Smets, “What can Logic learn from Quantum Mechanics?”, preprint to be presented at the workshop on the epistemological lessons of quantum information, ECAP05.

Birkhoff, G., and J. von Neumann, “The Logic of Quantum Mechanics”, Annals of Mathematics 37, 823–843 (1936), reprinted in C.A. Hooker (ed.), The Logico-algebraic Approach to Quantum Mechanics, vol. 1, D. Reidel Publishing Company, Dordrecht, pp. 1–26 (1975).

Coecke, B., D.J. Moore and S. Smets, “From Operationality to Logicality: Philosophical and Formal Preliminaries”, preprint.

B. Coecke, D.J. Moore and S. Smets, “From Operationality to Logicality: Syntax and Semantics”, preprint.

Coecke, B., D. Moore and A. Wilce, “Operational Quantum Logic: An Overview”, in B. Coecke, D. Moore and A. Wilce (eds.), Current Research in Operational Quantum Logic: Algebras, Categories, Languages, Kluwer Academic Publishers, Dordrecht, pp. 1–36 (2000).

Coecke, B., and S. Smets, “The Sasaki Hook is not a [Static] Implicative Connective but Induces a Backward [in Time] Dynamic One that Assigns Causes”, International Journal of Theoretical Physics, to appear (arXiv: quant-ph/0111076).

Einstein, A., B. Podolsky and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”, Physical Review 47, 777–780 (1935), reprinted in J.A. Wheeler and W.H. Zurek (eds.), Quantum Theory and Measurement, Princeton University Press, New Jersey, pp. 138–141 (1983).

Foulis, D.J., “Mathematical Metascience”, Journal of Natural Geometry 13, 1–50 (1986).

Foulis, D.J., “A Half-century of Quantum Logic – What Have We Learned?”, in D. Aerts and J. Pykacz (eds.), Quantum Structures and the Nature of Reality, The Indigo Book of “Einstein Meets Magritte”, VUB University Press/Kluwer Academic Pub., Brussels/Dordrecht (1999).

Foulis, D.J., and C.H. Randall, “A Note on Misunderstandings of Piron’s Axioms for Quantum Mechanics”, Foundations of Physics 14, 65–81 (1984).

Holdsworth, D.G., and C.A. Hooker, “A Critical Survey of Quantum Logic”, Logic in the 20th Century, Scientia Special Issue, Scientia, Milan, 127–246 (1983).

Jauch, J.M., Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts (1968).

Jauch, J.M., and C. Piron, “On the Structure of Quantal Proposition Systems”, Helvetica Physica Acta 42, 842–848 (1969).

Mittelstaedt, P., “Classification of Different Areas of Work Afferent to Quantum Logic”, in E.G. Beltrametti and B.C. van Fraassen (eds.), Current Issues in Quantum Logic, Plenum, New York (1981).

Moore, D.J., “On State Spaces and Property Lattices”, Studies in History and Philosophy of Modern Physics 30, 61–83 (1999).

Piron, C., “Axiomatique quantique (PhD-Thesis)”, Helvetica Physica Acta 37, 439–468 (1964). English Translation by M. Cole: “Quantum Axiomatics” RB4 Technical memo 107/106/104, GPO Engineering Department (London).

Piron, C., Foundations of Quantum Physics, W.A. Benjamin Inc., Massachusetts (1976).

Piron, C., “La Description d’un Systeme Physique et le Présupposé de la Théorie Classique”, Annales de la Foundation Louis de Broglie 3, 131–152 (1978).

Piron, C., “Le realisme en physique quantique: une approche selon Aristote”, in E. Bitsakis (ed.), The Concept of Reality, I. Zacharopoulos, Athens (1983).

Piron, C., Mécanique quantique. Bases et applications, Presses polytechniques et universitaires romandes, Lausanne (Second corrected edition 1998) First Edition (1990).

Smets, S., The Logic of Physical Properties in Static and Dynamic Perspective, PhD-thesis Vrije Universiteit Brussel (2001).

Smets, S., “On Causation and a Counterfactual in Quantum Logic: The Sasaki Hook”, Logique et Analyse 44 (173–175), 307–325 (2001), arXiv: PITT-PHIL-SCI00000619.

Smets, S., “In Defense of Operational Quantum Logic”, Logic and Logical Philosophy 11, 191–212 (2003), arXiv: PITT-PHIL-SCI00000541.

Smets, S., “From Intuitionistic Logic to Dynamic Operational Quantum Logic”, Poznan Studies in Philosophy and the Humanities, to appear.

Verelst, K., and B. Coecke, “Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach”, in G.C. Cornelis, S. Smets, and J.P. Van Bendegem (eds.), Metadebates on Science, The Blue Book of “Einstein Meets Magritte”, VUB University Press/Kluwer Academic Publishers, Brussels/Dordrecht, 163-196 (1999).








Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism