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Comment by inkysigma | Hacker News Reader

The article is a bit sparse of technical details but am I misunderstanding what they're doing or are they describing a field that's isomorphic to C but described as a pair of real numbers? If so, I don't see how that meaningfully takes the imaginary numbers out of quantum mechanics any more than renaming imaginary numbers as extended numbers would.

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Yup, swapping the complex numbers with matrices that encode the same transformations:

    a + bi
      ->
    [a -b]
    [b  a]

Here is the paper:

https://arxiv.org/pdf/2504.02808

Even then, all of chemistry DFT is based on the idea that the electron density contains the physical observable information and you and I both know that the overall phase of the wave function isn't physical except through interference. There is plenty of useful qm without C already out there!

"except through the inference" is carrying a lot of weight there. That's pretty physical.

This is referring to the fact that overall phase is not real (no observable difference) but relative phase has. The word “except” is not downplaying its importance, but to emphasize the fact that overall phase isn’t physical.

This might be the crux of the concern though -- "imaginary" numbers are terribly named and even mathematicians can conflate their concept with their name.

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