The Probabilistic Argument for a Nonclassical Logic of Quantum Mechanics

Patrick Suppes

S?awomir Bugajski

Patrick Suppes

The aim of this paper is to state the single most powerful argument for use of a non-classical logic in quantum mechanics. In outline the argument is the following. The working logic of a science is the logic of the events and propositions to which probabilities are assigned. A probability should be assigned to every element of the algebra of events. In the case of quantum mechanics probabilities may be assigned to events but not, without restriction, to the conjunction of two events. The conclusion is that the working logic of quantum mechanics is not classical. The nature of the logic that is appropriate for quantum mechanics is examined.

Weidong Tang

Hardy-like proofs for some quantum mechanical properties, such as Hardy-like nonlocality and Hardy-like contextuality, provide us two probabilistic no-go theorems by logical contradictions. Inspired by this, one may conjure that there are some other nonclassical properties which can also be revealed by Hardy-like arguments. In this work, we present an unconventional kind of quantum pigeonhole effects using Hardy-like arguments and show how to systematically construct them. Besides, we introduce a kind of ``projected-stabilizer state, say projected-coloring graph states, associated with a special type of coloring graphs called projected-coloring graph states. We build a one-to-one connection between a given projected-coloring graph (state) and a Hardy-like quantum pigeonhole In this sense a Hardy-like quantum pigeonhole paradox may also be referred to as a ``quantum coloring paradox.

Stanley Gudder

Gino Tarozzi, Alwyn van der Merwe

The Italian Debate on Quantum Paradoxes.- 1. The Epistemological Roots of Quantum Paradoxes.- Waves, Particles and Complementarity.- Chance: Chaos or Logic?.- Some Critical Considerations on the Present Epistemological and Scientific Debate on Quantum Mechanics.- 2. Einstein Locauty, Separable Reality, and Quantum Correlations.- Physical Consequences of Reality Criteria for Quantum Phenomena.- Possible Link Between EPR Paradox and Waves.- A Criticism of Some Recently Proposed Models that Violate the Bell Inequality.- A Phenomenological Analysis of the EPR Argument.- 3. Causal and Deterministic Interpretations of Quantum Formausm.- Causal versus Orthodox Interpretation of Quantum Mechanics.- Perspectives of Physical Determinism.- Determinism, Separability, and Quantum Mechanics.- 4. Quantum Theory and Gravitation.- Can Singularities and Multidimensional Spaces Influence the Evolution of Quantum Mechanical Systems?.- Subquantum Mechanics and Graviton Blas.- 5. Logic and Probability in Quantum Mechanics.- Foundations of Quantum Mechanics. A Quantum Probabilistic Approach.- On the Adequacy of a Nonclassical Logic for Quantum Theory.- Remarks on the Hypothesis of Hidden Variables.- 6. Historical Developments of the Einstein-Bohr Controversy.- Historical Considerations on the Conceptual Experiment by Einstein, Podolsky and Rosen.- Continuity and Discontinuity: The Einstein-Bohr Conflict of Ideas and the Bohr-Fock Discussion.- How Italian Philosophy Reacted to the Advent of Quantum Mechanics in the Thirties.- Italian Studies in the Foundations of Quantum Physics. A Bibliography (1965-1985).