Turns Out Quantum Mechanics Might Not Need Its Imaginary Numbers

Somewhere in high school, a teacher told you imaginary numbers were real, actually, and that physics couldn’t function without them. The square root of negative one, load-bearing. Quantum mechanics leaned on it especially hard. A new paper in Physical Review Letters, from Heinrich Heine University Düsseldorf and the German Aerospace Center, says maybe not.

First, what imaginary numbers are even doing in there. A quantum state carries two pieces of information, an amplitude and a phase, and complex numbers are the tidy two-slot container that holds both at once. Real part, imaginary part. For a century this has been the standard grammar of the theory, and physicists have quietly argued about whether the imaginary bit is genuinely part of nature or just extremely convenient math.

In 2021, a team seemed to settle it. Working from the standard postulates, they concluded complex numbers are indispensable, and experiments backed them up. Case closed, allegedly.

Why physicists thought imaginary numbers were essential

Why reopen it?

Because “indispensable” was resting a lot of weight on those postulates. The Düsseldorf group, led by Prof. Dagmar Bruß and her student Pedro Barrios Hita, took the exact same rulebook and found that one rule, the one describing how you combine two systems into a bigger one, was tighter than it needed to be. Swap it for a different but physically sensible version, and quantum mechanics reformulates itself using only real numbers.

What changes if quantum mechanics uses only real numbers

Here is the part to hold onto before anyone writes a headline about imaginary numbers being fake. Nothing you could ever measure changes. As Bruß puts it, both versions “provide identical predictions for every conceivable experiment.” The double slit still does its thing. Entanglement still works. Same physics, different grammar.

So no, your teacher wasn’t lying, and imaginary numbers didn’t get evicted from reality. What shifted is subtler and kind of lovely. A thing nearly everyone treated as a hard requirement turned out to be one bookkeeping choice among a couple of workable options. The universe, apparently, does not care which pen you use to describe it.