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asr comments on Timeless Physics Question - Less Wrong
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You can always "eliminate" complex numbers, in any context, by talking about ordered pairs of reals (or matrices, or whatever) with suitable changes to your formulas. But complex numbers are often a very convenient and powerful notation. Is there reason to think that if you try to do physics with reals only, it'll look any simpler?
Yeah, but going from one complex number to two real numbers doesn't simplify it. Going from one complex number to one real number does.