Complex Numbers

No Fooling

As it is April Fools' Day, how about an article that actually fits with the plain (as opposed to metaphorical) theme of the blog?

Imaginary Numbers May Be Essential for Describing Reality  
A new thought experiment indicates that quantum mechanics doesn’t work without strange numbers that turn negative when squared.

Sure, you can skip this if you want; it won't break my heart. But for anyone who's ever laughed at the idea of "imaginary numbers," this one's for you. After all... all numbers are imaginary, in a sense; there's just a subset with the official name of "imaginary."

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

They weren't as disturbed as non-mathematicians, I'm pretty sure of that. Want to disturb a mathematician? Ask one how to divide by zero.

All the numbers on the number line, when squared, yield a positive number; 2² = 4, and (-2)² = 4. Mathematicians started calling those familiar numbers “real” and the apparently impossible breed of numbers “imaginary.”

As I've noted, all numbers are already abstractions. These are just... I guess... more abstract?

Yet physicists may have just shown for the first time that imaginary numbers are, in a sense, real.

Okay, fine; I still say the opposite is true.

“These complex numbers, usually they’re just a convenient tool, but here it turns out that they really have some physical meaning,” said Tamás Vértesi, a physicist at the Institute for Nuclear Research at the Hungarian Academy of Sciences who, years ago, argued the opposite. “The world is such that it really requires these complex” numbers, he said.

Even my own surface exploration of math and physics has led me to the conclusion that if the math exists, eventually some physicist will find an application for it. I may be wrong, but it's happened too many times to count (see what I did there?)

The earlier research led people to conclude that “in quantum theory complex numbers are only convenient, but not necessary,” wrote the authors, who include Marc-Olivier Renou of the Institute of Photonic Sciences in Spain and Nicolas Gisin of the University of Geneva. “Here we prove this conclusion wrong.”

Now, I've always heard that complex numbers also show up in, say, electrical engineering. I wouldn't know. Electricity might as well be magic, as far as I'm concerned. I got somewhat familiar with the math involved because the Mandelbrot set   is just plain fascinating.

Anyway, the article goes on to describe the experiment in question, whereupon it quickly loses me.

What does this all mean? Well, nothing much to everyday life. Maybe it adds another layer of flavor to this blog's title knowing that what is imaginary possesses a kind of reality. Like I said, I just find it interesting, so y'all get to read about it here.