Uncertainty reigns over Heisenberg's measurement analogy
Nov 1, 2013 18 comments
A row has broken out among physicists over an analogy used by Werner Heisenberg in 1927 to make sense of his famous uncertainty principle. The analogy was largely forgotten as quantum theory became more sophisticated but has enjoyed a revival over the past decade. While several recent experiments suggest that the analogy is flawed, a team of physicists in the UK, Finland and Germany is now arguing that these experiments are not faithful to Heisenberg's original formulation.
Heisenberg's uncertainty principle states that we cannot measure certain pairs of variables for a quantum object – position and momentum, say – both with arbitrary accuracy. The better we know one, the fuzzier the other becomes. The uncertainty principle says that the product of the uncertainties in position and momentum can be no smaller than a simple fraction of Planck's constant h.
When Heisenberg proposed the principle in 1927, he offered a simple physical picture to help it make intuitive sense. He imagined a microscope that tries to image a particle like an electron. When light bounces off the particle, we can "see" and locate it, but at the expense of imparting energy and changing its momentum. If less light is used, the less the momentum is perturbed but then the less clearly it can be "seen". He presented this idea in terms of a trade-off between the "error" of a position measurement (Δx), owing to instrumental limitations, and the resulting "disturbance" in the momentum (Δp).
Not necessarily wrong
Subsequent work by others showed that the uncertainty principle does not rely on this disturbance argument – it applies to a whole ensemble of identically prepared particles, even if every particle is measured only once to obtain either its position or its momentum. As a result, Heisenberg abandoned the argument based on his thought experiment. But this did not mean it was wrong.
Then in 1988 Masanao Ozawa at Nagoya University in Japan argued that Heisenberg's original relationship between error and disturbance does not represent a fundamental limit of uncertainty. In 2003 he proposed an alternative relationship in which, although the two quantities remain related, their product can be arbitrarily small.
Ozama then teamed up with Yuji Hasegawa at the University of Vienna and others in 2012 to see if his revised formulation of the uncertainty principle held up experimentally. Looking at the position and momentum of spin-polarized neutrons, they found that, as Ozawa predicted, error and disturbance still involve a trade-off but with a product that can be smaller than Heisenberg's limit. (See "Neutrons revive Heisenberg's first take on uncertainty".)
At much the same time, Aephraim Steinberg and colleagues at the University of Toronto conducted an optical test of Ozawa's relationship, which also seemed to confirm his prediction. Ozawa has since collaborated with researchers at Tohoku University in another optical study, with the same result.
Now, Paul Busch at the University of York and colleagues have published calculations that defend Heisenberg's position. Busch, Pekka Lahti of the University of Turku and Reinhard Werner of Leibniz University claim that Ozawa's argument does not apply to the situation Heisenberg described. "Ozawa's inequality allows arbitrarily small error products for a joint approximate measurement of position and momentum, while ours doesn't," says Busch. "Ours says if the error is kept small, the disturbance must be large."
Johannes Kofler of the Max Planck Institute of Quantum Optics in Garching, Germany explains: "The two approaches differ in their definition of Δx and Δp, and there is indeed the freedom to make these different choices." Kofler, who was not involved in this latest work, adds: "Busch et al. claim to have the proper definitions, and they prove that their uncertainty relation always holds, with no chance for experimental violation."
Truer to Heisenberg?
The nub of the disagreement is which definition is best. Ozawa's is based on the variance in two measurements made sequentially on a particular quantum state. Whereas that of Busch and colleagues considers the fundamental performance limits of a particular measuring device, and thus is independent of the initial quantum state. "We think that must have been Heisenberg's intention," says Busch.
But Ozawa feels Busch and colleagues are focusing on instrumental limitations that have little relevance to the way devices are actually used. "My theory suggests if you use your measuring apparatus as suggested by the maker, you can make better measurement than Heisenberg's relation," he says. "They now prove that if you use it very badly – if, say, you use a microscope instead of a telescope to see the Moon – you cannot violate Heisenberg's relation. Thus, their formulation is not interesting."
Steinberg and colleagues have already responded to Busch et al. in a preprint that tries to clarify the differences between their definition and Ozawa's. What Busch and colleagues quantify, they say, "is not how much the state that one measures is disturbed, but rather how much 'disturbing power' the measuring apparatus has".
"Heisenberg's original formula holds if you ask about 'disturbing power' but the less restrictive inequalities of Ozawa hold if you ask about the disturbance to particular states," says Steinberg. "I personally think these are two different but both interesting questions." But he feels Ozawa's formulation is closer to the spirit of Heisenberg's.
In any case, all sides agree that the uncertainty principle is not, as some popular accounts imply, about the mechanical effects of measurement – the "kick" to the system. "It is not the mechanical kick but the quantum nature of the interaction and of the measuring probes, such as a photon, that are responsible for the uncontrollable quantum disturbance," says Busch.
In part the argument comes down to what Heisenberg had in mind. "I cannot exactly say how much Heisenberg understood about the uncertainty principle," Ozawa says. "But I can say we know much more than Heisenberg," he adds.
Busch and colleagues describe their results in Physical Review Letters.
Aephraim Steinberg and colleagues write about their experiment in this feature article about weak measurement: "In praise of weakness".
About the author
Philip Ball is a science writer based in the UK