[Paper Review] Quantum measurements as weighted symmetry breaking processes: the hidden measurement perspective

Diederik Aerts, Massimiliano Sassoli de Bianchi|arXiv (Cornell University)|Jan 20, 2016

Quantum Mechanics and Applications27 references6 citations

TL;DR

This paper establishes a conceptual bridge between Kastner's possibilist transactional interpretation (PTI) and the hidden-measurement interpretation (HMI), showing that the extended Bloch representation (EBR)—a specific implementation of HMI—provides a complete explanation for the Born rule's probabilistic weights in quantum measurements. While PTI explains the transition to a reduced density matrix, it lacks a mechanism for why weights match the Born rule; EBR fills this gap by modeling quantum measurement as a weighted symmetry breaking (WSB) process driven by hidden measurement-interactions, offering both qualitative and quantitative completeness.

ABSTRACT

The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner's possibilist transactional interpretation (PTI) of quantum mechanics - an extension of Cramer's transactional interpretation - and the authors' hidden-measurement interpretation (HMI). Secondly, we observe that although a weighted symmetry breaking (WSB) process was proposed in the PTI, to explain the actualization of incipient transactions, no specific mechanism was actually provided to explain why the weights of such symmetry breaking are precisely those given by the Born rule. In other terms, PTI, similarly to decoherence theory, doesn't explain a quantum measurement in a complete way, but just the transition from a pure state to a fully reduced density matrix state. On the other hand, the recently derived extended Bloch representation (EBR) - a specific implementation the HMI - precisely provides such missing piece of explanation, i.e., a qualitative description of the WSB as a process of actualization of hidden measurement-interactions and, more importantly, a quantitative prediction of the values of the associated weights that is compatible with the Born rule of probabilistic assignment. Therefore, from the PTI viewpoint, the EBR provide the missing link for a complete description of a quantum measurement. However, EBR is in a sense more general than PTI, as it does not rely on the specific notion of transaction, and therefore remains compatible with other physical mechanisms that could be at the origin of the measurement-interactions.

Motivation & Objective

• To clarify the ontological parallels between Kastner’s possibilist transactional interpretation (PTI) and the hidden-measurement interpretation (HMI).
• To identify the missing mechanism in PTI that explains why symmetry breaking weights match the Born rule.
• To demonstrate that the extended Bloch representation (EBR) provides a complete, quantitative explanation of WSB processes in quantum measurement.
• To show that EBR is more general than PTI, as it does not rely on the transactional narrative but remains compatible with other physical mechanisms.

Proposed method

• The authors compare the ontologies of PTI and HMI, focusing on their shared commitment to realism, non-spatiality, and objective state reduction.
• They analyze the transactional narrative in PTI, where retarded offer waves and advanced confirmation waves form incipient transactions in pre-empirical spacetime.
• They introduce the extended Bloch representation (EBR) as a geometric framework that represents quantum states in a generalized Bloch sphere, enabling a description of hidden measurement-interactions.
• The EBR models the actualization of a measurement as a weighted symmetry breaking (WSB) process, where the weights correspond to probabilities predicted by the Born rule.
• The EBR derives the Born rule values not as postulates but as emergent from the structure of hidden measurement-interactions within the generalized Bloch representation.
• The framework remains agnostic about the physical origin of these interactions, treating them as intrinsic to the quantum formalism when represented in the Bloch sphere.

Experimental results

Research questions

• RQ1 How do the ontologies of the possibilist transactional interpretation (PTI) and the hidden-measurement interpretation (HMI) compare in their treatment of quantum measurement?
• RQ2 Why does PTI fail to explain the specific values of the weights in symmetry breaking, despite modeling the transition to a reduced density matrix?
• RQ3 Can the extended Bloch representation (EBR) provide a complete, quantitative explanation of the Born rule weights in quantum measurements?
• RQ4 In what way is the EBR more general than PTI, particularly regarding the physical mechanism underlying measurement interactions?
• RQ5 How does the concept of non-spatiality in PTI and HMI relate to the emergence of spatiality during measurement?

Key findings

• The EBR provides a qualitative and quantitative explanation for the weights in weighted symmetry breaking (WSB) processes, which PTI alone cannot achieve.
• The EBR models the actualization of a quantum measurement as a WSB process driven by hidden measurement-interactions, offering a mechanism for the emergence of probabilities.
• The Born rule probabilities emerge naturally from the structure of the extended Bloch representation, without being postulated.
• The EBR is compatible with multiple physical mechanisms for measurement interactions, making it more general than PTI, which relies on the transactional narrative.
• The framework supports the idea that quantum measurements are not merely discovery processes but also creation processes, where properties are partly actualized by the measurement context.
• The non-spatial nature of quantum entities is preserved in the EBR, with spatiality emerging only upon interaction with a measurement apparatus.