Abstract
Paraconsistent logic (PL) is a non-classical logic that accepts contradiction in its foundations. It can be represented in the form of paraconsistent annotated logic with annotation of two values (PAL2v). When used to model quantum phenomena, PAL2v is called paraquantum logic (PQL). In this work, the concept of PQL is applied to create a logical model presenting the fundamental principles of quantum mechanics that support particle-wave theory. This study uses the well-known Young’s double-slit experiment, wherein quantum phenomena appear when a monochromatic light beam passes through the two slits. We focused on a reference point located between the slits, where we observed the effects of two types of wave interferences in a region defined as a two-wave region (2W region). Considering that the effect in this 2W region is very similar to that studied by Huygens, we adopt a paraquantum logical model in which a particle (or quantum) is represented by two wave functions. The two wave functions result in four State Vectors (Ket, Bra,,) in the PQL Lattice that express the symmetry and the entanglement of Quantum Mechanics. The constructed model adapts well to the quantum phenomena, is strongly consistent, and can be considered as an innovative form of analysis in the field of quantum mechanics. Based on this model, we present in two parts (Part I and Part II) the comparative analysis of values found in SchrÖdinger’s equation and probabilistic models of wave-particle theory using Bonferroni inequality.
Highlights
By the end of the 17th century, several scientists supported the wave theory of light that affirmed the pure wave character of light
Following the Paraquantum Logical Model, in the representation of complex numbers via paraquantum logic (PQL) Lattice, the real part z is related to the certainty degree (DC), and the imaginary part is related to the contradiction degree (Dct)
The intensity of the contradiction degree (Dct) and its Normalized value compared to Quantum energy can be studied in comparison to analysis conducted using Schrödinger’s equation. Such procedures will be discussed in Part II of this work. This first part presents a model based on Paraquantum Logic (PQL) where concentrated oscillation energy particle, an energy Quantum, can be represented by two wave functions
Summary
By the end of the 17th century, several scientists supported the wave theory of light that affirmed the pure wave character of light. While light appeared to behave as a particle flow, there were cases where it exhibited wave characteristics, such as in an interference phenomenon. This contradiction between corpuscular and wave theory was addressed by other scholars, culminating in the development of quantum mechanics from 1900 to 1925 [3]. Classical or Aristotelian logic, which today supports our technology, was created in ancient Greece as a tool to describe a perfect world; its strictly binary laws exclude situations that occur in reality, such as contradictory, incomplete, or uncertain information. Da Costa (1954 onwards) [6]-[8]
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