January 16, 2026 -- Richard Feynman famously said that “nobody understands quantum mechanics.” Quantum theory is so unintuitive, even to experts, that there’s an entire research field called ‘quantum foundations’ dedicated to understanding the theory, often by breaking it down and trying to rebuild it.

One way that quantum foundations researchers at Perimeter Institute interrogate quantum theory is by devising foil theories, a term coined by faculty member Robert Spekkens. Foil theories take quantum theory and make a few small changes to act as a comparative foil or counterexample to the real thing. A tweak or two to the laws of reality allows researchers to better understand quantum’s basic claims and narrow down the exact points where quantum theory breaks down.

“A foil theory shares a lot in common with quantum theory,” explains Yìlè Yīng, a resident PhD student at Perimeter Institute. “It's like a controlled test in an experiment. You only change one or two elements so you can see the consequences of these small tweaks. If they’re too different, it’s hard to learn anything.”

Recently, Yīng and fellow PhD student Daniel Centeno haven’t just been tweaking theories — they’ve been ‘twirling’ them too. And in doing so, they’ve challenged an underlying concept in quantum theory.

How to twirl the world

Yīng, Centeno, Spekkens, and their colleagues published a paper last year where they introduced a new foil theory dubbed ‘twirled worlds.’ It imagines a universe with some unique properties slightly different from our own.

“What if every physical process in this alternative, twirled world had to be symmetrical in some aspect?” the theory asks. For example, what would happen if everything had rotational symmetry, meaning it looks the same when it’s rotated, like a perfectly round sphere?

“The [twirled worlds] foil theory requires that all physical processes, states, measurements, and transformations should be symmetric with respect to the symmetry we pick, like rotational symmetry or phase symmetry,” says Yīng. “Then, we look at the sub theory of quantum theory where this constraint is satisfied to understand certain properties of quantum theory.”

Yīng and Centeno were curious about what would happen to a property known as tomographic locality when studied in a twirled world. Tomographic locality is the idea that you can fully describe a joint system (like two entangled particles) by measuring each part separately. Essentially, you can get a picture of the whole by measuring its parts.

What Yīng and Centeno discovered was that, in a twirled world, tomographic locality is always impossible. And when they expanded out to classical and other non-quantum theories, tomographic locality again wasn’t maintained upon twirling.

“Anytime you impose a symmetry constraint, you end up with a theory that does not satisfy tomographic locality,” explains Yīng. “And it’s everywhere. For any generalized probabilistic theory or operational theory, you will find this failure of tomographic locality when you apply this symmetry.”

What happens when tomographic locality fails

So what do we gain from noticing that tomographic locality fails every time in these conditions? The first consequence is related to the concept of superselection, a rule in quantum that forbids superpositions when quantum states are prepared in certain ways. There has been a multi-decade debate in scientific circles about whether superselection rules are fundamental. Twirled worlds add a new dimension to that debate.

“We learned that the status of whether tomography locality should be satisfied or not is now linked to whether the superselection rules are fundamental or not,” says Centeno. “Essentially, if you take a position about whether these superselection rules are fundamental, you should take a position also about granting tomographic locality or not. These two things are connected and if you have a position about one, you should be coherent.”

The second consequence is that tomographic locality can be further interrogated via the creation of a whole group of related foil theories. With them, researchers plan to probe the boundaries of tomographic locality more precisely and investigate how it can fail.

What about swirling instead of twirling?

Yīng and Centeno call their next set of foil theories ‘swirled worlds.’ The difference between a twirled world and swirled one is that while twirling imposes physical symmetry constraints, swirling imposes nonphysical ones.

“For example, take time reversal symmetry,” explains Centeno. “We cannot reverse time. But imagine you could make your world be time reversal symmetric, meaning that going backwards and forwards in time would be the same.”

In a follow-up paper still in the works, Yīng and Centeno teamed up with another PhD student at Perimeter, Maria Ciudad Alañón, to investigate the consequences of twirling and swirling. One of these consequences arose when they used a theory called Real Quantum Theory, which uses real numbers instead of complex ones.

“By studying the difference between swirling and twirling, we can understand why Real Quantum Theory ends up making the same operational predictions as quantum theory in many cases, but differ in some other cases.” says Alañón.

Using foil theories, physicists are prodding at the very heart of quantum theory. It’s what makes quantum foundations research so exciting: quantum theory can help us understand our very reality.

“If you understand the theory better, then you can understand what exactly is special about quantum theory,” says Yīng. “For me, that’s the most interesting part.”