Abstract
In this paper a system of axioms is presented todefine the notion of an experimental system. The primaryfeature of these axioms is that they are based solely onthe mathematical notion of a direct product decomposition of a set. Properties ofexperimental systems are then developed. This includesdefining negation, implication, conjunction, anddisjunction on the set \(\mathcal{Q}\) of all binaryexperiments of the system and showing that the resulting structure is aregular orthomodular poset. The theory of observables ofexperimental systems is also developed. Finally, theusual models of experiments from classical as well as quantum physics are shown to satisfythe axioms of an experimental system, and a mechanism tocreate new models of the axioms is given.
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REFERENCES
S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer, Berlin (1981).
A. Dvurečenskij, Gleason's Theorem and Its Applications, Kluwer, Dordrecht, 1993.
J. Harding, Decompositions in quantum logic, Trans. AMS 348 (1996), 1839–1862.
J. Harding, Regularity in quantum logic, Int. J. Theor. Phys. 37 (1998), 1173–1212.
R. V. Kadisson and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. 1, Academic Press, New York (1983).
J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day (1965).
E. Prugovecki, Quantum Mechanics in Hilbert Space, 2nd ed., Academic Press, New York (1981).
P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Veda, Bratislava (1991).
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Harding, J. Axioms of an Experimental System. International Journal of Theoretical Physics 38, 1643–1675 (1999). https://doi.org/10.1023/A:1026607030592
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DOI: https://doi.org/10.1023/A:1026607030592