Compatible quantum theory.

Area of Science:

• Quantum Mechanics
• Foundations of Physics
• Mathematical Physics

Background:

• Quantum mechanics (QM) formulations are categorized as realistic or operationalist.
• Classical mechanics serves as a realistic theory, but generalizing it to QM faces logical inconsistencies.
• Existing realistic QM formulations often require external entities, deviating from a purely system-based description.

Purpose of the Study:

• To present a realistic formulation of quantum mechanics called Compatible Quantum Theory (CQT).
• To address the limitations of previous realistic QM approaches by integrating microscopic and macroscopic components.
• To derive fundamental QM principles like Born probabilities and consistency conditions within a new framework.

Main Methods:

• Developing a 'microscopic' part (MIQM) based on Hilbert space ontology and noncontextual probabilities, utilizing Gleason's theorem and Nistico's dynamics.
• Introducing a 'macroscopic' part (MAQM) to select a physical framework and resolve microscopic indeterminacy.
• Analyzing framework selection through phenomenological or fundamental macroscopic mechanisms, including decoherence.

Main Results:

• MIQM successfully derives Born probability formulas and consistency (decoherence) conditions for quantum frameworks.
• The microscopic theory yields multiple contextual truths ('c-truths'), indicating physical indeterminacy and incompleteness.
• MAQM provides a mechanism for framework selection, completing the theory by breaking microscopic framework symmetry.

Conclusions:

• Compatible Quantum Theory (CQT) offers a coherent and realistic formulation of quantum mechanics.
• The theory necessitates a macroscopic component to resolve microscopic indeterminacy and select a physical framework.
• CQT provides a novel perspective for understanding various quantum mechanics interpretations and the role of decoherence.