In quantum mechanics, it is impossible to know both exactly where you are and exactly where you are going. This idea, known as Heisenberg’s uncertainty principle, has been a key part of studying the quantum realm for almost a decade – but now physicists are even more certain about their uncertainty.
Before quantum physics was developed, researchers seeking to measure an object more precisely simply reached for better measuring instruments. But in 1927, Werner Heisenberg discovered that, when dealing with quantum-scale objects, there is a fundamental limit on how precisely you can simultaneously measure certain pairs of values, such as position and momentum.
Now, at Kyushu University and at the University of Electro-Communications, both in Japan, have proved that a version of Heisenberg’s uncertainty principle can apply even when measuring just a single variable.
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Since the 1950s, researchers have wondered whether Heisenberg’s description of uncertainty needs to be modified for systems such as two colliding marbles, in which their combined momentum is conserved – meaning it has the same value before and after they crash together. Could this extra constraint on momentum make it possible to “cheat” the uncertainty principle, letting you measure the position of the two balls exceedingly precisely?
For simple systems where measurements return discrete values such as 0 or 1, the answer seemed to be no. But when it comes to systems like the colliding marbles, position and momentum have continuous instead of discrete values, which makes the maths far more complex. Researchers still assumed it wasn’t possible to cheat the Heisenberg uncertainty principle, but until now had been unable to prove it. “For that, a completely new approach was needed, and we constructed it,” says Kuramochi.
To do so, he and Tajima faced the mathematical difficulty of having to carry out calculations and proofs for a very general idea of position – because it can take infinitely many values, it must be represented by an infinite grid of numbers. To get around this, they employed a clever mathematical trick that allowed them to hide this infinite grid within another mathematical object called a function. They could use this function for most of the proof and then switch back to the true representation of position towards the end, after they had completed all calculations that would have otherwise been intractable.
at the University of South-Eastern Norway says that because the new work presents a rigorous mathematical proof, its conclusion “applies completely generally, in all experiments, all measurement interactions, forever”. There is simply no way to sidestep it and get a more accurate measurement of the position of a quantum object, he says.
While the work deepens our understanding of the quantum nature of reality, it is currently unclear whether it can play a role in applications, like in quantum technology, says Loveridge, because the measurement effect is subtle and discerning what experiments it may apply in is difficult. Quantum physics is plagued with questions about how tools used in experiments interact with the objects they are measuring, he says. As such, while physicists may now be more certain about uncertainty, they are still unsure what it means in practice.
Physical Review Letters
