About the Exact Role of Disturbance in Heisenberg's Uncertainty Relation

Abstract

It is generally accepted that the disturbance interpretation cannot explain Heisenberg's uncertainty relation ∆x ∆p ≈ h. In this paper a clear distinction will be made between the notion of state preparation and measurement, and the disturbance that is referred to in Heisenberg's disturbance interpretation is usually the disturbance that is caused by the measurement. The main goal of this paper is to examine and discuss to what extent disturbance during the state preparation plays a role in the interpretation of Heisenberg's uncertainty relation. This examination will be done in the context of the single-slit experiment. To conclude this paper a novel single-slit experiment will be proposed and discussed with which a clearer insight could be gained in the exact role of disturbance when a quantum system passes a single-slit. RésuméIl est généralement accepté que l'interprétation de perturbation ne puisse pas expliquer la relation d'incertitude de Heisenberg ∆x ∆p ≈ h. Dans cet article une distinction claire sera faite entre la notion de la préparation de l'état et la mesure, et la perturbation à laquelle il est fait référence dans l'interprétation de perturbation de Heisenberg qui est généralement la perturbation causée par la mesure. L'objectif principal de cet article est d'étudier et d'examiner dans quelle mesure la perturbation pendant la préparation de l'état joue un rôle dans l'interprétation de la relation d'incertitude de Heisenberg. Cet examen sera fait dans le cadre de l'expérience de fente-unique. Pour conclure cet article, une expérience de fente-unique nouvelle sera proposée et examinée grâce à laquelle un aperçu plus clair pourrait être obtenu du rôle précis de la perturbation quand un système quantique passe une fente-unique.

On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality

“…It was even claimed that HUR acts like a Copenhagen doctrine propagated in quantum mechanical texts without consistent proof [7], as far as failing to clearly include the quantum fluctuation information for the quantum objects in focus, especially relating with the wave-particle feature [8,9]. As such, no definitive argument was delivered so far in linking HUR with the wave-particle duality in measurements ( i.e.…”

“…it was eventually criticized as being no more than the experimental realization of the operatorial (non)commutation relation [ x , p ] = iħ that implicitly contains the incompatibility between the coordinate and momentum spaces [ 4 – 6 ]. It was even claimed that HUR acts like a Copenhagen doctrine propagated in quantum mechanical texts without consistent proof [ 7 ], as far as failing to clearly include the quantum fluctuation information for the quantum objects in focus, especially relating with the wave-particle feature [ 8 , 9 ]. As such, no definitive argument was delivered so far in linking HUR with the wave-particle duality in measurements ( i.e.…”