Do Complex Numbers Exist?
Why Hacker News recommends it
HN recommends it as a short, accessible layperson explanation of the real-versus-complex quantum theory debate.
What it is
Sabine Hossenfelder asks whether complex numbers are just a convenient tool or necessary in physics. She discusses a recent paper arguing that quantum mechanics cannot be done with real numbers alone.
Recommended by 3 HN commenters across 3 different months, 2021 to 2023.
What Hacker News said
Strong rec viktorcode · 2022-02 · on “How the modern world arose from imaginary numbers”
I highly recommend video by Sabine Hossenfelder [1] on this topic. She's explaining the topic in layman terms, starting from what does it mean to exist (or be real) in physical sense. Complex numbers, as useful as they are, just an abstraction, a tool which can be replaced with different forms of calculations. That makes the question of "reality" rather complex (pardon the pun). [1] [this video]
Recommends johnp271 · 2021-12 · on “Quantum theory based on real numbers can be experimentally falsified”
There is a nice 10 minute discussion about this paper by physicist Sabine Hossenfelder on her "Science without the gobbelydgook" youtube series (which I recommend). She considers the existential questions regarding necessity of complex numbers a "super-niche nerd fight". You can find the video here [this video] .
Recommends ars · 2023-04 · on “Quantum Physics Falls Apart Without Imaginary Numbers”
This video by Sabine Hossenfelder is probably more informative on this topic: [this video] (it discusses this paper).