Complete descriptions

We discuss often about “complete descriptions”… but what does that mean? It mainly means that we get all the information we can get in the given framework. However the “wholeness” of the information depends on the framework. Not all questions are defined in all situations. However, all correctly defined frameworks are complete. They give full information about the system but in the context of a framework that doesn’t allow some questions as “meaningful”. It is very much like the idea of having full information in all cases but the “full information” is not compatible with any kind of questions. The easiest example is of course speed and position. While the full information about the system exists in any representation (the momentum or the position) some questions are meaningless, mainly those that ask about information defined in the other framework. I know, this is a relatively simple observation everyone makes in the first years of quantum mechanics… You will need to change the framework from one to another in order to define the other question correctly and get meaningful answers. Schrodinger’s cat is just a reiteration of the same problem but with the connection being made from “small” to “large conglomerates of particles” … If only physicists would learn mathematical concepts better: closed set, open set, clopen set, completeness, Hausdorff spaces, compact sets, etc.


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