[Paper Review] On Locality, Growth and Transport of Entanglement

Roland Omnès|arXiv (Cornell University)|Dec 3, 2012

Quantum Mechanics and Applications12 references3 citations

TL;DR

This paper proposes that entanglement between macroscopic and microscopic systems originates from a topological property of Feynman paths, which is algebraically expressed via an extended Hilbert space formalism. The resulting 'intricacy'—a local, temporary form of entanglement—can grow and transport coherently, leading to a predecoherence effect that permanently generates incoherence in macroscopic systems, with implications for wave function collapse theories.

ABSTRACT

Entanglement of a macroscopic system with a microscopic one is shown to begin by a topological property of histories in the Feynman formulation of quantum mechanics. This property can also be expressed algebraically on the Schrödinger equation through a convenient extension of the Hilbert space formalism. Entanglement shows then properties of growth and transport, the corresponding local and temporary character of entanglement being called here "intricacy" when it occurs. When applied to the continuous interaction of a macroscopic system with a random environment, intricacy implies a "predecoherence" effect, which can generate and transport permanently incoherence within the system. The possible relevance of these results for a theory of wave function collapse is also indicated.

Motivation & Objective

• To understand the origin of entanglement between macroscopic and microscopic quantum systems.
• To identify a topological mechanism in the Feynman path integral formulation that underlies the initial formation of entanglement.
• To develop an extended Hilbert space formalism that captures the local and transient nature of entanglement.
• To explore how entanglement can grow and transport within a system, leading to persistent incoherence.
• To investigate the relevance of this mechanism for theories of wave function collapse.

Proposed method

• The study uses the Feynman path integral formulation to identify a topological property of histories that gives rise to entanglement.
• A formal extension of the Hilbert space is introduced to algebraically represent the topological entanglement mechanism.
• The model treats the interaction between a macroscopic system and a random environment as continuous, enabling the analysis of entanglement dynamics.
• The concept of 'intricacy' is defined as a local, temporary form of entanglement arising from the topological structure.
• The framework is applied to show how intricacy can lead to a predecoherence effect, generating and transporting incoherence.
• The approach connects quantum foundations with potential collapse models through the emergence of permanent incoherence.

Experimental results

Research questions

• RQ1 How does entanglement originate between macroscopic and microscopic systems according to the Feynman path integral?
• RQ2 What topological or algebraic property in the path integral formalism gives rise to the initial formation of entanglement?
• RQ3 Can the local and temporary nature of entanglement be formalized as a distinct physical quantity, such as 'intricacy'?
• RQ4 How does entanglement grow and transport within a system under continuous interaction with an environment?
• RQ5 Can this mechanism account for a predecoherence effect that leads to permanent incoherence, relevant to wave function collapse?

Key findings

• Entanglement between macroscopic and microscopic systems arises from a topological property of quantum histories in the Feynman path integral.
• This topological origin can be captured algebraically through an extension of the standard Hilbert space formalism.
• The resulting local and temporary entanglement is termed 'intricacy,' which exhibits growth and transport dynamics.
• When applied to a macroscopic system interacting continuously with a random environment, intricacy induces a predecoherence effect.
• This predecoherence effect permanently generates and transports incoherence within the system, even in the absence of external measurement.
• The findings suggest a potential mechanism for wave function collapse rooted in intrinsic entanglement dynamics rather than external decoherence.