Physicists find a loophole in Heisenberg’s uncertainty principle without breaking it

Physicists have measured both the momentum and position of a particle without breaking Heisenberg’s iconic uncertainty principle.

In quantum mechanics, particles don’t have fixed properties the way everyday objects do. Instead, they exist in a haze of possibilities until they’re measured. And when certain properties are measured, others become uncertain. According to Heisenberg's uncertainty, it’s not possible to know both a particle’s exact position and its exact momentum at the same time.

But a new study has shown a clever loophole around this restriction. Physicists in Australia have demonstrated that by focusing on different quantities, known as modular observables, they can simultaneously measure position and momentum.

"You can’t violate Heisenberg’s uncertainty principle," Christophe Valahu, a physicist at the University of Sydney and lead author of the study, told Live Science. "What we do is shift the uncertainty. We throw away some information we don’t need, so we can measure what we do care about with much greater precision."

The trick for Valahu and his team was, instead of measuring momentum and position directly, to measure the modular momentum and modular position — which capture the relative shifts of these quantities within a fixed scale, rather than their absolute values.

"Imagine you have a ruler. If you’re just measuring the position of something, you’d read how many centimeters in, and then how many millimeters past that." Valahu said. "But in a modular measurement, you don’t care which centimeter you’re in. You only care how many millimeters you are from the last mark. You throw away the overall location and just keep track of the small shifts."

Valahu said this kind of measurement is important in quantum sensing scenarios because the goal is often to detect minuscule shifts caused by faint forces or fields. Quantum sensing is used to pick up signals that ordinary instruments often miss. That level of precision could someday make our navigation tools more reliable and our clocks even more accurate.

In the lab, the team turned to a single trapped ion — a lone charged atom held in place by electromagnetic fields. They used tuned lasers to coax the ion into a quantum pattern called a grid state.

In a grid state, the ion’s wave function is spread out into a series of evenly spaced peaks, like the marks on a ruler. The uncertainty is concentrated in the spaces between the marks. The researchers used the peaks as reference points: when a small force nudges the ion, the entire grid pattern shifts slightly. A small sideways shift of the peaks shows up as a change in position, while a tilt in the grid pattern reflects a change in momentum. Because the measurement only cares about the shifts relative to the peaks, both position and momentum changes can be read out at the same time.

That’s where force comes in. In physics, a force is what causes momentum to change over time and position to shift. By watching how the grid pattern moved, the researchers measured the tiny push acting on the ion.

The force of roughly 10 yoctonewtons (10-23 newtons) isn't a world record. "People have beaten this by about two orders of magnitude, but they use huge crystals in very large and costly experiments." Valahu told Live Science. "The reason we’re excited is because we can get really good sensitivities using a single atom in a trap that’s not that complex, and is somewhat scalable."

Even though the force achieved is not the lowest, it proves that scientists can get very extreme sensitivities from very basic setups. The ability to sense tiny changes has wide implications across science and technology. Ultra-precise quantum sensors could improve navigation in places where GPS doesn’t reach, such as underwater, underground, or in space. It could also enhance biological and medical imaging.

"Just as atomic clocks revolutionized navigation and telecommunications, quantum-enhanced sensors with extreme sensitivity could open the door to entirely new industries,” Valahu said in a statement.