Can a hammer define a nail?

I have been having a discussion with a friend about understanding of reality in terms of quantum theory. Well the discussion revolved around Physics as a real science; as real representation of reality.

I started to try to understand what I don't know. Without having a deep (or any, for that matter) understanding of quantum mechanics, I started reading some on-line articles, mainly on Wikipedia to understand. It lead me the the Wikipedia article about interpretations of quantum mechanics.

I tried to wrap my head around some concepts. But as you can see there is no agreement even between physicists; how could I understand. Then I tried to look into some of the basic tenets of quantum mechanics; I assumed it to be Schrödinger equation. Again, without understanding any thing at all, what I noticed in the equation was the component iota(ι).

This immediately took my attention to my understanding of complex numbers. Searching for that lead me to a number of resources, including this [1], this [2] and this [3]. Now 1 and 2 here are just trying to create a mental map of some properties of complex numbers, they are using artificial interpretation i.e. multiplication by iota as rotation in two dimensions, without grounding this interpretation, i.e. how does multiplication in general be represented as a rotation. The third [3] one however, explained rather realistically, specially when talking about historic interpretation the author writes "... understand the mathematical process, i.e., that it's all definitions in the end.".

Also trying to understand John Wallis' geometrical interpretation did not resolve my curiosity to my satisfaction.
Getting every one answer leads to several more questions.
Bottom line, for me at least, is that its all about the tools and their usage; as the famous quote suggests, "Shut and calculate" is the best solution so far.


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