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airen comments on Open thread, Oct. 19 - Oct. 25, 2015 - Less Wrong Discussion
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Comments (198)
At least one of us is confused about this post :P
It seems like what you're doing is strictly more complicated than just doubling the number of dimensions in state-space and using those extra dimensions only so you can say the amount of "stuff" goes as amplitude squared. Which is already very unsatisfying.
I'm really confused where frequency is supposed to come in.
It's most likely me being confused.
My picture of it right now is that all the dimensions you need in total, are all the dimensions in state-space + 2 dimensions for the complex amplitude. If this assumption is wrong, then we have found the error in my thinking already!
Note that the two complex amplitude dimensions are of course not like the other dimensions. For every position in the state-space, there is a single point in the amplitude dimensions. Or in my suggestion, a line from origo out to the calculated complex value.
Don't try to think this through with matrices, there's a very real chance that what I'm after cannot be captured by matrices at all. I think you have to do a complete geometric picture of it.