JAMP  Vol.6 No.6 , June 2018
Conditional Events and Quantum Logic
Show more
Abstract: This paper begins with an overview of quantum mechanics, and then recounts a relatively recent algebraic extension of the Boolean algebra of probabilistic events to “conditional events” (order pairs of events). The main point is to show that a so-called “superposition” of two (or more) quantum events (usually with mutually inconsistent initial conditions) can be represented in this algebra of conditional events and assigned a consistent conditional probability. There is no need to imagine that a quantum particle can simultaneously straddle two inconsistent possibilities.
Cite this paper: Calabrese, P. (2018) Conditional Events and Quantum Logic. Journal of Applied Mathematics and Physics, 6, 1278-1289. doi: 10.4236/jamp.2018.66107.

[1]   Einstein, A. (1906) Zur Theorie der Lichterzeugung und Lichtabsorption [On the Theory of Light Production and Light Absorption]. Annalen der Physik, 325, 199-206.

[2]   Birkhoff, G. and von Neumann, J. (1936) The Logic of Quantum Mechanics. Annals of Mathematics, 37, 823-834.

[3]   Heisenberg, W. (1930) The Physical Principles of the Quantum Theory. Dover Publications, Dover.

[4]   Feynman, R.P., Leighton, R.B. and Sands, M. (1965) Lectures on Physics, Vol. III: Quantum Mechanics. Addison-Wesley Publishing Co., Barrington.

[5]   Koopman, B.O. (1955) Quantum Theory and the Foundations of Probability. In: MacColl, L.A., Ed., Applied Probability, McGraw-Hill Education, New York, 97-102.


[7]   Bell, J.S. (1964) On the Einstein-Podolsky-Rosen Paradox. Physical Review Journals, 1, 195-200.

[8]   Mermin, N.D. Department of Physics Cornell Arts and Sciences.

[9]   Schrodinger, E.R. (1926) An Undulatory Theory of the Mechanics of Atoms and Molecules. Physical Review, 28, 1049-1070.

[10]   de Broglie, L.V. (1923) Radiations—Ondes et Quanta/Radiation—Waves and Quanta. Comptes Rendus Mathématique, 177, 507-510.

[11]   Bell, J.S. (1966) On the Problem of Hidden Variables in Quantum Mechanics. Reviews of Modern Physics, 38, 447-452.

[12]   Bohm, D.J. (1983) Wholeness and the Implicate Order. Ark Paperbacks, London.

[13]   Goldstein, S. (1996) Bohmian Mechanics and the Quantum Revolution.

[14]   Goldstein, S. (1996) Quantum Philosophy: The Flight from Reason in Science. In: Gross, P., Levitt, N. and Lewis, M.W., Eds., The Flight from Science and Reason.

[15]   Goldstein, S. (2002) Bohmian Mechanics. In: Zalta, E.N., Ed., The Stanford Encyclopedia of Philosophy.

[16]   Einstein, A., Podolsky, B.Y. and Rosen, N. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47, 777-780.

[17]   Russell, B.A.W. and Whitehead, A.N. (1913) Principia Mathematica. Vol. 3, Cambridge University Press, Cambridge.

[18]   Calabrese, P.G. (2017) Logic and Conditional Probability—A Synthesis. College Publications.

[19]   Chang, C.C. and Keisler, H.J. (1973) Model Theory. 2nd Edition, Amsterdam.

[20]   Kolmogorov, A.N. (1933) Foundations of the Theory of Probability. 2nd Edition, Chelsea Publishing Company, New York.