Authors: Steve faulkner
Abstract Textbook theory says that the Canonical Commutation Relation derives from the homogeneity of space. This paper shows that the Canonical Commutation Relation does not derive from homogeneity of space or the homogeneity symmetry itself, but derives from a duality viewpoint of homogeneity, seen both from the viewpoint of position space, and from the viewpoint of momentum space, combined. Additionally, a specific particular fixed scale factor, relating position space with momentum space is necessary. It is this additional scaling information which enables complementarity between the system variables and makes the system unitary. Without this particular scaling, the Canonical Commutation Relation is left non-unitary and broken. Indeed, unitarity is separate information, unconnected and logically independent of the quantum system's underlying symmetry. This single counter-example contradicts the current consensus that foundational symmetries, underlying quantum systems, are ontologically, intrinsically and unavoidably unitary. And thus removes ‘unitary ontology’, as reason, for axiomatically imposing unitarity (or self-adjointness) — by Postulate — on quantum mechanical systems.
foundations of quantum theory, quantum mechanics, wave mechanics, Canonical Commutation Relation, symmetry, homogeneity of space, unitary.
Comments: 5 Pages.
Unique-IP document downloads: 34 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.