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But I know I'm reaching here. I just like fantasizing about math :).



Is there unitarity, symmetry, or conservation when x^2 ± y^2 = 1?

We square complex amplitudes to make them real.

https://twitter.com/westurner/status/967970148509503488 :

> "Partly because, mathematically, wavefunctions are vectors in a L^2 Hilbert space, which is complex-valued. Squaring the amplitude, rather Ψ∗Ψ=|Ψ|^2 is one way to ensure that you get real-valued probabilities, which is also related to the fact that […]" https://physics.stackexchange.com/questions/280748/why-do-we...




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