> We “simulate complex numbers by means of real numbers,”

What a breakthrough!

----

Related:

https://www.mdpi.com/2673-9984/3/1/9

"our knowledge of quantities is necessarily accompanied by uncertainty. Consequently, physics requires a calculus of number pairs and not only scalars for quantity alone. Basic symmetries of shuffling and sequencing dictate that pairs obey ordinary component-wise addition, but they can have three different multiplication rules. We call those rules A, B and C. “A” shows that pairs behave as complex numbers, which is why quantum theory is complex."

https://arxiv.org/abs/0907.0909

"the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued function of this number pair. By making use of elementary symmetry conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic"

Physicists take the imaginary numbers out of quantum mechanics which resulted in making quantum mechanics even more difficult to work with. Great job! Any mathematician could have predicted that result. TBH, I thought physicists had a better command of mathematics than that.

Also, it's well-known that calling imaginary numbers "imaginary" was sophomoric humor from early mathematicians - they're just as 'real' as the real numbers, not some mathematical invention or fantasy. It’d be nice if we could change the name, but that water has done flowed.

This reminds me of Scott Aaronson's lectures on quantum mechanics that try to explain how probability theory (using negative and complex probabilities) is the core concept: https://www.scottaaronson.com/democritus/lec9.html

As a lay person, I don't see too much of a problem with having "i" included in equations just because it's an invented maths concept. It certainly has very real applications with phases in electronics.