The Formation and Logic of Quantum Mechanics

Mituo Taketani, Masayuki Nagasaki

João Inácio da Silva Filho

In this work, we make a representation of non-relativistic quantum theory based on foundations of paraconsistent annotated logic (PAL), a propositional and evidential logic with an associated lattice FOUR. We use the PAL version with annotation of two values (PAL2v), named paraquantum logic (PQL), where the evidence signals are normalized values and the intensities of the inconsistencies are represented by degrees of contradiction. Quantum mechanics is represented through mapping on the interlaced bilattices where this logical formalization allows annotation of two values in the format of degrees of evidence of probability. The Bernoulli probability distribution is used to establish probabilistic logical states that identify the superposition of states and quantum entanglement with the equations and determine the state vectors located inside the interlaced Bilattice. In the proposed logical probabilistic paraquantum logic model (pPQL Model), we introduce the operation of logical conflation into interlaced bilattice. We verify that in the pPQL Model, the operation of logical conflation is responsible for providing a suitable model for various phenomena of quantum mechanics, mainly the quantum entanglement. The results obtained from the entanglement equations demonstrate the formalization and completeness of paraquantum logic that allows for interpretations of similar phenomena of quantum mechanics, including EPR paradox and the wave-particle theory.

三男 武谷, 正幸 長崎

Dwijesh Dutta Majumder, Sankar Karan

We present the new mathematical formalisms of Cognitive Quantum Number (CQN), as unified validation logic in human minds and machines. Though our theory is general, on study we concentrate in logic formation in the field of quantum computing specially for information processing in nano-scale devices. Our proposed logic not only allows us to derive the results of quantum state, but also permits their generalization of making available new techniques of logic inference, establishes a direct dynamical link between memory and processing part naturally. We consider quantum logic and cognition of mind in general as Eigen value problems. The role of molecular magnets in the field of quantum computation and mechanism for using it as qubits in the context of quantum phenomenon of spin tunneling in presence of external magnetic fields is formulated. Synthesis and spectral response of nano-particle towards quantum dot formation is also studied. We showed that the spectrum of logic operators and cognition of minds is in exact correspondence of the fundamentals alphabet of logic truth-values. The basic gate for quantum logic operations is also derived.

Mituo Taketani, Masayuki Nagasaki

Graciela Domenech, Federico Holik, Décio Krause

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a labeltensor-product-vector-space-formalism, to use Redhead and Teller’s \nwords, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics.