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This is literally addressed verbatim by the article, and I quote: "One can always devise new mathematical constructs that behave in all the same ways as comple
by Kranar 5y ago
This is literally addressed verbatim by the article, and I quote:
"One can always devise new mathematical constructs that behave in all the same ways as complex numbers even though they’re called something else."
It's honestly as if people are just jumping to comment on the title of the article without actually reading it. The article is fundamentally about how trying to replace complex numbers by some real valued representation of them, for example using a vector of real numbers, or a matrix of real numbers, doesn't work due to the compounding of dimensions. The two examples they give where using pairs of real numbers fails is multiparticle states and a spin 1/2 qubit.
At any rate, there's no point rehashing the article here, since it's all written in a fairly straight forward manner. It's just frustrating reading so many people write the same trivial comment dismissing the article when the article is written precisely to demonstrate why these simplistic dismissals fail.
- kevinventullo 5y agoAs I commented elsewhere, in the multi particle state example you can fix the problem by tensoring with respect to the vector or matrix algebra, so it works just fine. And like of course it does because C itself is isomorphic to these algebras. My point about calling into question what one means by “using complex numbers” is that the article says it is “necessary to establish some ground rules that exclude real-valued quantum theories that restate the standard complex-valued theory by other names” but then handwaves the rules. Presumably you’re only allowed to tensor over R. But more importantly, it provides no motivation for why these ground rules wouldn’t be somewhat arbitrary. I guess I just don’t see the value of removing complex numbers from the formulation.