Understanding the Pointer States

Abstract: In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in the Everett's relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett's thesis. In this article, we review the measurement process according to von Neumann, Everett's relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek's primordial paper that consolidated the concept of pointer state, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems -- one representing the main system, the other the measurement apparatus -- and a thermal bath -- representing the environment -- we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.