Encapsulating the strangeness of quantum mechanics is a single mathematical expression. According to every undergraduate physics textbook, the uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle — the more precisely one knows the particle’s position at a given moment, the less precisely one can know the value of its momentum.
But the original version of the principle, put forward by physicist Werner Heisenberg in 1927, couches quantum indeterminism in a different way — as a fundamental limit to how well a detector can measure quantum properties. Heisenberg offered no direct proof for this version of his principle, and expressed his ideas “only informally and intuitively”, says physicist Jos Uffink of the University of Minnesota in Minneapolis.
Now researchers say that they have a formal proof. “Our work shows that you can’t measure something with an accuracy any better than the fundamental quantum uncertainty,” says Paul Busch, a theoretical physicist at the University of York, UK, who with his colleagues posted the proof on 6 June on the arXiv preprint server. Not only does the work place this measurement aspect of the uncertainty principle on solid ground — something that researchers had started to question — but it also suggests that quantum-encrypted messages can be transmitted securely.
In their theoretical work, Busch and his colleagues imagined making simultaneous measurements of a particle’s position and momentum in an arbitrary quantum state. They compared the errors in such measurements to two special cases — in which either the position or the momentum of the particle is well known. They found that the combined errors in measurements of the position or momentum in these two cases obeyed Heisenberg’s principle and was always smaller than for cases in which the two properties were measured simultaneously. This step allowed them to prove Heisenberg’s original conjecture.
Busch and his co-authors’ work “is worth being remembered and maybe even taught through textbooks as the proper version of the Heisenberg error-disturbance relation”, says mathematician Hans Maassen of Radboud University in Nijmegen, the Netherlands. However, the proof has reignited a decade-long debate.