On Ontological Alternatives to Bohmian Mechanics

Area of Science:

• Quantum Mechanics
• Mathematical Physics
• Philosophy of Physics

Background:

• Standard quantum mechanics relies on complex mathematical formalisms.
• Existing interpretations of quantum mechanics offer various ontological perspectives.
• The nature of quantum relations and spatial configurations remains an area of exploration.

Purpose of the Study:

• To interpret the mathematical formalism of quantum mechanics through the lens of relations.
• To propose a novel ontological interpretation of quantum theory.
• To explore the implications of a relational view for entanglement and the measurement problem.

Main Methods:

• Interpreting the wave function (ψ(x)) as a complex-valued relation between an entity and a spatial point.
• Defining entanglement as a relation between two entities or their properties.
• Modeling space as a network of relations, with classical space as a continuum limit.

Main Results:

• Demonstrates that complex-valued relations can describe classical systems.
• Interprets entanglement as defining a "being next to each other" relation, irrespective of classical distance.
• Shows that nearest neighbor configurations are possible within a relational space.

Conclusions:

• This relational interpretation offers a new perspective on quantum mechanics, distinct from existing models like Bohmian mechanics.
• The study highlights the potential for diverse ontological interpretations of quantum theory.
• The relational framework provides a novel approach to understanding quantum phenomena, including entanglement and the measurement problem.