[Paper Review] An Introduction to the Neutrosophic Probability Applied in Quantum Physics

Florentín Smarandache|ArXiv.org|Oct 10, 2000

Advanced Mathematical Theories20 references18 citations

TL;DR

This paper introduces neutrosophic probability as an extension of classical and imprecise probability to model quantum phenomena with indeterminacy, such as Heisenberg's Uncertainty Principle, Schrödinger's Cat, and bosonic statistics. It proposes a three-valued framework (truth, indeterminacy, falsity) to capture the inherent uncertainty in quantum systems more comprehensively than traditional probability.

ABSTRACT

In this paper one generalizes the classical probability and imprecise probability to the notion of "neutrosophic probability" in order to be able to model Heisenberg's Uncertainty Principle of a particle's behavior, Schr"dinger's Cat Theory, and the state of bosons which do not obey Pauli's Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from "neutrosophy".

Motivation & Objective

• To address the limitations of classical and imprecise probability in modeling quantum systems with inherent indeterminacy.
• To extend probability theory to incorporate indeterminacy as a fundamental component, inspired by neutrosophic logic.
• To provide a mathematical framework capable of describing superposition and non-exclusion statistics in quantum mechanics.
• To formalize the behavior of particles under the Uncertainty Principle and the state of macroscopic quantum superpositions like Schrödinger's Cat.
• To offer a probabilistic model applicable to bosons, which do not obey Pauli's Exclusion Principle, using a three-valued probability system.

Proposed method

• Proposes neutrosophic probability as a generalization of classical probability, assigning three components: truth, indeterminacy, and falsity.
• Introduces a probability model where each event has a truth-membership, indeterminacy-membership, and falsity-membership in the interval [0, 1].
• Applies the neutrosophic probability framework to quantum systems by allowing for non-zero indeterminacy in measurement outcomes.
• Uses the neutrosophic framework to model superposition states, such as Schrödinger's Cat being both alive and dead simultaneously with a degree of indeterminacy.
• Extends the model to describe bosonic states where multiple particles can occupy the same quantum state, using indeterminacy to represent the lack of exclusion.
• Relies on the foundational principles of neutrosophic logic and neutrosophic set theory to formalize the three-valued probability structure.

Experimental results

Research questions

• RQ1 How can classical probability theory be extended to model quantum systems with inherent indeterminacy?
• RQ2 In what way does neutrosophic probability better represent the superposition principle in quantum mechanics compared to classical or imprecise probability?
• RQ3 How can the indeterminacy component in neutrosophic probability describe the behavior of particles under Heisenberg's Uncertainty Principle?
• RQ4 Can neutrosophic probability model the macroscopic quantum superposition of Schrödinger's Cat more naturally than traditional frameworks?
• RQ5 How does the neutrosophic approach handle the non-exclusion statistics of bosons, which violate Pauli's Exclusion Principle?

Key findings

• Neutrosophic probability provides a three-valued probability model (truth, indeterminacy, falsity) that extends classical and imprecise probability.
• The framework allows for the representation of quantum superpositions, such as Schrödinger's Cat, by assigning non-zero values to indeterminacy.
• The model captures the uncertainty in particle position and momentum as per Heisenberg's Uncertainty Principle through the indeterminacy component.
• Bosonic states, which allow multiple particles in the same state, are naturally modeled by high indeterminacy values in the neutrosophic framework.
• The paper establishes a theoretical foundation for neutrosophic probability in quantum physics, though no numerical simulations or empirical validations are provided.
• The approach is presented as a conceptual and mathematical generalization, with potential for future application in quantum information and indeterminate systems.