For nearly a century, complex numbers were treated as non-negotiable in quantum mechanics. You can’t just remove them. They were the bedrock. The foundation. The “imaginary” part of reality that makes the equations work.
Complex numbers are not needed for quantum Mechanics
Pedro Barrios Hita says otherwise.
Along with his colleagues, he just published a model that strips away the complex numbers entirely. It works. It matches standard theory. And it changes how we view the fundamental fabric of reality, even if the physics itself stays exactly the same.
The “I” Problem
Complex numbers aren’t like integers. You don’t have 3 apples or 4 dollars. You have a real part and an imaginary part. A multiple of $i$, which is the square root of minus one.
Mathematicians called it imaginary because you can’t measure it. You can’t count it. Yet, engineers use it daily to describe alternating current. Physicists use it for waves. Since the 1920s? Quantum mechanics has been baked into these equations from the start.
Wave functions rely on them. Period.
Then came 2021. A team predicted that real-number quantum mechanics would fail in specific multi-particle experiments. The math suggested complex numbers were mandatory.
The tests happened. The results favored standard quantum mechanics. The real-number version looked broken.
Changing the Rules
The 2021 defeat relied on one thing: the tensor product.
This is the rule taught in every textbook. It combines two particles into one system. It works beautifully for complex numbers. For real numbers, it was a dead end. The correlations disappeared. The math fell apart with three or more particles.
Barrios Hita asked a different question. Why stick to that specific rule?
What if the problem wasn’t the numbers, but how we combine them?
The team found a new rule. One based on locality. An action on one particle shouldn’t affect another unless they interact. In standard quantum mechanics, multiplying a state by $i$ is invisible alone. But in a pair, that $i$ kicks back. It shuffles onto the partner. Physicists call this phase kickback. It’s automatic in the tensor product.
Real numbers can’t kick back. Not naturally.
So they attached a “flag” to each particle. A tracker for what the imaginary unit used to hold. They treated certain flag combinations as identical physically, even if they looked different mathematically.
It’s a bookkeeping trick. A complex number is just two real numbers. Three and four in $3 + 4i$. The $i$ is just a label saying “this one is imaginary.”
His team separated them. Tracked them. Made sure the “kickback” effect still happened using only real values.
A complex number is nothing but two real numbers
A Matter of Convenience
It was a long fight. Making this consistent across multiple particles took time. But once it clicked, the structure was elegant.
This places quantum mechanics in line with other theories. Take electromagnetism. It uses complex numbers all over the place. But are they fundamental? No. They are just useful tools. A shorthand for writing equations without rewriting vectors constantly.
This doesn’t give us faster quantum computers. It doesn’t break physics. It’s limited to systems with finite states for now. Infinite-dimensional systems—the stuff of actual real-world physics problems—still need work. Others are already tackling that next step. Barrios Hita has moved on, studying entanglement as a resource.
But the debate is over.
Complex numbers make the writing easier. They are a linguistic convenience for mathematicians who prefer elegant equations over bulky ones.
Reality doesn’t care if you use $i$ or just keep the flags separate.
The universe runs on real numbers after all.
We just hadn’t bothered to look closely enough until now.
Why did it take us so long to drop the baggage?
Perhaps because we were afraid of the empty space it would leave behind.
