Consistency and Linearity in Quantum Theory
Quantum Physics
2009-10-31 v1 Statistical Mechanics
General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two answers must agree. The constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. An immediate consequence is that the Schrodinger equation must be linear: non-linear variants of quantum mechanics violate the requirement of consistency. PACS: 03.65.Bz, 03.65.Ca.
Cite
@article{arxiv.quant-ph/9803086,
title = {Consistency and Linearity in Quantum Theory},
author = {Ariel Caticha},
journal= {arXiv preprint arXiv:quant-ph/9803086},
year = {2009}
}