[Paper Review] Quantum Mechanics from Relational Properties, Part II: Measurement and EPR

Jianhao M. Yang|arXiv (Cornell University)|Mar 12, 2018

Quantum Mechanics and Applications37 references4 citations

TL;DR

This paper reformulates quantum measurement and operation theory by treating relational properties between quantum systems—rather than intrinsic system properties—as fundamental. It derives a mathematically equivalent formulation to standard quantum mechanics, showing that measurement descriptions must be explicitly relative to local observers, resolving the EPR paradox by rejecting the super observer and preserving objectivity through observer synchronization.

ABSTRACT

Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the relational probability amplitude matrix is transformed and how mutual information is exchanged during measurement, we derive the formulation that is mathematically equivalent to the traditional quantum measurement theory. More importantly, the formulation results in significant conceptual consequences. We show that for a given quantum system, it is possible to describe its time evolution without explicitly calling out a reference system. However, description of a quantum measurement must be explicitly relative. Traditional quantum mechanics assumes a super observer who can instantaneously know the measurement results from any location. For a composite system consists space-like separated subsystems, the assumption of super observer must be abandoned and the relational formulation of quantum measurement becomes necessary. This is confirmed in the resolution of EPR paradox. Information exchange is relative to a local observer in quantum mechanics. Different local observers can achieve consistent descriptions of a quantum system if they are synchronized on the information regarding outcomes from any measurement performed on the system. It is suggested that the synchronization of measurement results from different observers is a necessary step when combining quantum mechanics with the relativity theory.

Motivation & Objective

• To develop a relational formulation of quantum measurement and operation theory based on system-to-system relations rather than intrinsic system properties.
• To resolve conceptual tensions in quantum mechanics, particularly the EPR paradox, by abandoning the notion of a super observer with global knowledge.
• To clarify how objectivity in quantum mechanics can be preserved despite observer-dependent descriptions through synchronization of measurement outcomes.
• To establish a foundation for unifying quantum mechanics with relativity by formalizing observer-relative information exchange in spacelike-separated systems.

Proposed method

• Models quantum measurement as a bidirectional probe-response interaction process, using relational probability amplitude matrices to quantify system-to-system correlations.
• Derives the probability of measurement outcomes as the sum of products of relational probability amplitudes across all alternative measurement configurations.
• Reconstructs standard quantum mechanics results (e.g., Born’s rule, Schrödinger equation) from relational properties, showing mathematical equivalence to traditional formulations.
• Analyzes how mutual information is exchanged during measurement, emphasizing that information exchange is relative to a local observer.
• Applies the framework to the EPR paradox, demonstrating that the assumption of a super observer leads to apparent nonlocality, which is resolved by observer-relative descriptions.
• Proposes that consistent descriptions across observers require synchronization on measurement outcomes, enabling objective physical descriptions despite relativity of information.

Experimental results

Research questions

• RQ1 How can quantum measurement theory be reconstructed from relational properties between quantum systems rather than intrinsic system properties?
• RQ2 What are the conceptual consequences of abandoning the super observer in quantum mechanics, particularly in spacelike-separated systems?
• RQ3 How can objectivity in quantum mechanics be preserved when descriptions are inherently observer-dependent?
• RQ4 In what way does the relational formulation resolve the EPR paradox without violating locality or completeness?
• RQ5 What role does observer synchronization play in achieving consistent, objective descriptions of quantum systems across different reference frames?

Key findings

• The relational probability amplitude matrix formalism reproduces standard quantum mechanics results, including Born’s rule and the Schrödinger equation, when there is no entanglement.
• Time evolution of a quantum system can be described implicitly relative to a reference system, but quantum measurement must be explicitly relative to a local observer.
• The assumption of a super observer—capable of instantaneously knowing outcomes from any location—must be abandoned in relativistic settings, especially for space-like separated systems.
• The EPR paradox is resolved not by modifying quantum mechanics, but by rejecting the super observer and redefining physical reality as observer-relative.
• Different local observers can achieve consistent descriptions of a quantum system if they are synchronized on measurement outcomes, preserving objectivity.
• Synchronization of measurement results across observers is identified as a necessary condition for combining quantum mechanics with relativity theory.