Wednesday, February 22, 2017
Thursday, February 16, 2017
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Suppose I throw in a blue color into the water. It becomes blue. It then also throw some salt into it, it becomes salty. The color and taste seem to be additive. But they also seem to be orthogonal -- I can modify one property without affecting orthogonal contribution. Do additivity and orthogonality imply each other?
It looks like additivity acts in one space whereas orthogonality impacts independent axes. Can you unblur this situation especially after I read that QM is based on Hilbert spaces, whose idea is that all values on the same very axis are orthogonal? Probably, we can place all values of color and all taste components on a single axis and thus reduce orthogonality to linearity. Can we?
Aside from that, what is the superposition principle? I read the wikipedia article and I cannot distinguish it from linearity.