Definition of Pointer in Measurement

[SheikYerbouti]

Definition of "Pointer"

I am in the process of writing a review-type paper for my intermediate quantum mechanics course. I have chosen to do my paper on the topic of measurement, with a focus on weak measurement. In all of the papers that I am reading, the term "pointer" is thrown around, but I have not seen it clearly defined as all of the papers assume familiarity with the topic. My (vague) understanding of the pointer is that it is coupled with the measured system and, upon measurement, its value will shift by the measured eigenvalue, at least for a projective measurement. However, I am not entirely sure if this is correct and would greatly appreciate elaboration on what the pointer is in the context of measurement.

 

[bhobba]

A 'pointer' is simply some kind of readout that tells you what the outcome of an observation is. The states associated with those outcomes are sometimes called pointer states.

Actually rigorously defining what an observation is in QM is no easy task. It requires decoherence and my suggestion for you is to consult THE textbook on the subject - Decoherence and the Quantum-to-Classical Transition by Schlosshauer
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

I have a copy and recommend it VERY highly.

There you will find definitions of all the usual terms, the various parts to the measurement problem, and what decoherence does and does not do in relation to the issue.

A cut down exposition can be found here:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

But basically it is along these lines. Decoherence converts a superposition to an improper mixed state. The states it is composed of are the possible outcomes of an observation so these days the idea is to say an observation has occurred just after decoherence. This is a totally quantum process and avoids issues of exactly what counts as a measuring apparatus etc.

What you have are so called pointer observables whose eigenstates are stable with respect to the decoherening effect of the environment. These eigenstates are often called pointer eigenstates and is part of solving the preferred basis issue of the measurement problem.

Thanks
Bill

 

[atyy]

In the "orthodox" or "shut-up-and-calculate" Copenhagenish view of quantum mechanics, one divides the universe into macroscopic and quantum realms. The measuring apparatus is on the macroscopic side, and the pointer is simply the thing on the measuring apparatus that tells you the result of the measurement. It is subjective, and requires common sense, since there doesn't seem to be an obvious limit as to what can be treated as part of the quantum realm. Within these interpretations, this is the measurement problem. http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf

There is a process called decoherence, which although it does not solve the measurement problem, does pick out the "pointer basis", ie. the possible eigenstates into which a system may collapse when a measurement is made on it. http://arxiv.org/abs/quant-ph/0306072