Relational Quantum Mechanics and the PBR Theorem: A Peaceful Coexistence

Area of Science:

• Quantum Mechanics
• Foundations of Physics
• Interpretational Frameworks

Background:

• Relational Quantum Mechanics (RQM) posits wave functions as informational, not absolute states.
• The PBR theorem suggests wave functions cannot solely represent knowledge of an underlying ontic state.
• An apparent conflict exists between RQM's epistemic view and the PBR theorem's conclusions.

Purpose of the Study:

• To demonstrate that Relational Quantum Mechanics (RQM) is compatible with the PBR theorem.
• To resolve the perceived inconsistency between RQM's interpretation of wave functions and the PBR theorem.
• To explore the limitations of the PBR theorem in the context of relational quantum mechanics.

Main Methods:

• Detailed analysis of the foundational assumptions of the PBR theorem, specifically Harrigan and Spekkens' ontological model categorization.
• Comparison of the implicit assumptions regarding the nature of ontic states in the PBR theorem with the core principles of RQM.
• Investigation into the possibility of deriving a 'relational' PBR-type theorem.

Main Results:

• The implicit assumptions within the PBR theorem's ontological models are incompatible with the fundamental tenets of RQM.
• The PBR theorem's conclusions do not invalidate RQM's epistemic interpretation of the wave function.
• A 'relational' PBR-type theorem cannot be derived, highlighting specific limitations of the original theorem.

Conclusions:

• The apparent conflict between RQM and the PBR theorem is dissolved by revealing incompatible foundational assumptions.
• RQM's epistemic view of the wave function remains viable and is not contradicted by the PBR theorem.
• The study identifies previously undiscussed limitations of the PBR theorem concerning relational quantum mechanics.