The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. This paper proposes an in-depth analysis of superpositions. It claims that superpositions must be considered when one cannot distinguish between possible paths, i.e., histories, leading to the current state of the system. In such a case the resulting state is some compound of the states that result from each of the possible paths. It claims that states can be compounded, i.e., superposed in such a way only if they are not orthogonal. Since different classical states are orthogonal, the claim implies no non-trivial superpositions can be observed in classical systems. It studies the parameters that define such compounds and finds two: a proportion defining the mix of the different states entering the compound and a phase difference describing the interference between the different paths. Both quantities are geometrical in nature: relating one-dimensional subspaces in complex Hilbert spaces. It proposes a formal definition of superpositions in geometrical terms. It studies the properties of superpositions.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number
dp447.
Did you know? You can include your works in the database easily by uploading them on the Munich Personal RePEc Archive (MPRA) if you do not have access to an institutional RePEc archive.