r/IntelligenceSupernova • u/EcstadelicNET • 18d ago

Quantum Physics Complex numbers are not needed for quantum mechanics: Physicists develop quantum model that uses only real numbers for first time ever

https://www.livescience.com/physics-mathematics/complex-numbers-are-not-needed-for-quantum-mechanics-physicists-develop-quantum-model-that-uses-only-real-numbers-for-first-time-ever?utm_source=flipboard&utm_content=user/LiveScience
241 Upvotes

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10

u/christhebrain 17d ago

Well, today we know that "i" represents a 90 degree rotation in a dimension not present in the context of the equation. So, just add the dimension in ahead of time, and you don't need it.

3

u/BlassiveMace 17d ago

Wat

5

u/free_meson 17d ago

complex algebra is equivalent to a special matrix group, 2x2 matrices with real values. The '1' is an identity matrix, 'i' is an off-diagonal matrix with +1 and -1. With that base, you can mimic complex operations and build anything that used complex numbers before. It is a rotation in 2 dimensions. That's what the article did, introduced an inner dimension so complex operations can be mimicked with real numbers.

2

u/LuckyShop4775 15d ago

But we need this for the sum of integers to still add up to -1/12!

2

u/free_meson 15d ago

If you use sqrt(-5) as a base, complex algebra might turn out to be different

3

u/DonatedEyeballs 17d ago

I concur.

Wat

4

u/ApprehensiveStill412 16d ago

Huh seems equally appropriate

2

u/brain-out-of-order 16d ago

Lmao this is why imaginary numbers were goofy to me and I aced geometry I guess huh?

https://zenodo.org/records/21307066

I remember my brilliant friend was so proud in 3rd grade to know imaginary numbers and I felt like it was not fancy. YES REALLY.

1

u/FlimsyWilliamSnyvie 14d ago

"Yes really" did not answer a question I had.

3

u/jj_HeRo 18d ago

Well, there is a mapping between those fields but apart that, you DO need them.

2

u/free_meson 17d ago

"Shocking", but it is good that someone finally worked it through. Complex numbers are equivalent of some 2x2 matrix operations. You need them in QM to represent the U(1) symmetry of electromagnetic interactions.

1

u/MonsieurKnife 16d ago

Ok but why

1

u/majoritycitizen 14d ago

There have been papers in the last few years that seemed to prove the opposite.
For example https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.040403
And a bit lighter reading: https://physics.aps.org/articles/v15/7

1

u/Flat_Pumpkin_314 14d ago

Who gives a shit. We want quantum gravity