Prolegomena to a Structuralist Reconstruction of Quantum Mechanics

Authors

  • Joseph D. Sneed Division of Liberal Arts and International Studies, Colorado School of Mines

DOI:

https://doi.org/10.48160/18532330me1.51

Keywords:

structuralism, quantum, mechanics, probability

Abstract

A structuralist “reconstruction sketch” of an idealized theory is provided. This theory, QM, has some essential features of quantum mechanics. QM is a theory about abstract “result-observation events”, formal characterizations of interactions among physical systems and their results. QM is a stochastic theory and in the stochastic apparatus some features of “real life” quantum mechanics are recognizable. The result-observation events themselves exhibit neither essentially quantum mechanical features nor essentially physical features. At the level of the basic theory element QM is more like a specialization of probability theory than a physical theory. It is only at the level of specialization of the basic theory element that essentially physical and quantum mechanical features may be introduced. The account provides a “reconstruction sketch” rather than a reconstruction largely in that no account is given of physically interesting specializations. It also falls short of a full reconstruction in that the mathematical apparatus is restricted to finite structures.

References

Ballentine, L.E. (1986), “Probability Theory in Quantum Mechanics”, American Journal ofPhysics 54(10): 883-889.

Ballentine, L.E. (1998), Quantum Mechanics: A Modern Development, Singapore: World Scientific Publishing Co.

Balzer, W., Moulines, C.U. and J.D. Sneed (1987), An Architectonic for Science. The Structuralist Program, Dordrecht: Reidel.

Birkhoff, G. (1967), Lattice Theory, Providence: American Mathematical Society.

Caves, C.M, Fuchs, C.A. and R. Schack (2002), “Quantum Probabilities as Bayesian Probabilities”, Physical Review A 65(022305), arXiv:quant-ph/0106133v2.

Fano, U. and L. Fano (1959), Basic Physics of Atoms and Molecules, New York: Wiley.

Feynman, R.P ., Leighton, R.B. and M. Sands (1965), The Feynman Lectures on Physics vol. III: Quantum Mechanics, Reading, MA: Addison-Wesley.

Halmos, P.R. (1958), Finite-Dimensional Vector Spaces, Princeton, NJ: V an Nostrand.

Herbut, F. (1992), “Quantum Interference Viewed in the Framework of Probability Theory”, American Journal of Physics 60(2): 146-149.

Held, C. (2008). “The Kochen-Specker Theorem”, in Zalta, E.N. (ed.), The Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/archives/win2008/entries/kochen-specker/.

Jammer, M. (1966), The Conceptual Development of Quantum Mechanics, New York: McGraw-Hill. Lombardi, O. and M. Castagnino (2998) “ A modal Hamiltonian interpretation of quantum mechanics”, Studies in History and Philosophy of Modern Physics 39: 380-443.

Jaynes, E.T. (2003), Probability Theory: the Language of Science, New York: Cambridge UniversityPress.

Moyal, J.E. (1949), “Quantum Mechanics as a Statistical Theory”, Proceedings of the Cambridge Philosophical Society 45: 97-124.

Messiah, A. (1961), Quantum Mechanics, Vols. I, II, Amsterdam: North-Holland.

Nielson, M.A. and I.L. Chuang (2000), Quantum Computation and Quantum Information, Cambridge: Cambridge University Press.

Schmidt, H.-J. (2003), “Structuralism in Physics”, in Zal ta, E.N. (ed.), The Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/archives/spr2003/entries/physics-structuralism/.

Sneed, J.D. (1964), The Projection Postulate and Quantum Mechanical Measurement, unpublished Ph.D. dissertation, Stanford University.

Sneed, J.D. (1970), “Quantum Mechanics and Classical Probability Theory”, Synthese 21: 34-64.

Sneed, J.D. (1971), The Logical Structure of Mathematical Physics, Dordrecht: Reidel, 2ndrevised ed. 1979.

Stegmüller, W. (1979), The Structuralist View of Theories, New York: Springer.

von Neumann, J. (1955), Mathematical Foundations of Quantum Mechanics,translated from the German edition by R.T. Beyer, Princeton: Princeton University Press.

Wigner, E.P. (1932), “On the Quantum Correction for Thermodynamic Equilibrium”, Physical Review 40: 749-759.

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Published

2011-04-01

How to Cite

Sneed, J. D. (2011). Prolegomena to a Structuralist Reconstruction of Quantum Mechanics. Metatheoria – Journal of Philosophy and History of Science, 1(2), 93–130. https://doi.org/10.48160/18532330me1.51