Year: 2012
Type: dissertation
Abstract: This thesis concerns how symmetries impinge on quantum mechanical measurements, \nand preclude certain self adjoint operators from representing observable \nquantities. After developing the requisite mathematical machinery and aspects \nof quantum measurement theory necessary for our analysis, we proceed to critically \nreview the literature surrounding the remarkable theorem of Wigner, \nAraki and Yanase (WAY) that prohibits accurate and repeatable measurements \nof any observable not commuting with an additive conserved quantity, as well \nas discussing the conditions under which approximate measurements with approximate \ndegrees of repeatability can be achieved. We strengthen the original \nstatement of the WAY theorem and generalise it to the case of position measurements \nobeying momentum conservation, leading to a solution of a long-standing \nproblem of Stein and Shimony. A superselection rule appearing as the existence \nof an observable which commutes with all others gives rise to a stronger \nrestriction than the WAY theorem, yielding self adjoint operators which do not \nrepresent observable quantities. We analyse various perspectives on superselection \nrules, aiming to clarify different viewpoints appearing in the literature \nsince the inception of the topic in 1952. We exploit an explicit description \nof relative phase observables which have been lacking in other contributions, \ndelineating conditions under which relative and (prohibited) absolute phases \nbecome statistically close. By providing simple models we are able to mimic a \nnumber of attempts to overcome superselection rules, in order to highlight the \ngeneric features of such attempts. We show that the statistical proximity of absolute \nand relative quantities arises only when there is a highly localised phase \nreference, and that the superselection rule compatible relative phase factors \nbetween certain superpositions takes on the appearence of a forbidden relative \nphase factor in this limit. However, we argue that these relative phase factors \ncan be determined fully within the confines of a superselection rule. \n
Author: Leon Loveridge
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2114804667