One Thing Is Certain: Heisenberg's Uncertainty Principle Is Not Dead

Experimenters violate Heisenberg's original version of the famous maxim, but confirm a newer, clearer formulation

George Musser

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What Einstein's E=mc2 is to relativity theory, Heisenberg's uncertainty principle is to quantum mechanics—not just a profound insight, but also an iconic formula that even non-physicists recognize. The principle holds that we cannot know the present state of the world in full detail, let alone predict the future with absolute precision. It marks a clear break from the classical deterministic view of the universe.

Yet the uncertainty principle comes in two superficially similar formulations that even many practicing physicists tend to confuse. Werner Heisenberg's own version is that in observing the world, we inevitably disturb it. And that is wrong, as a research team at the Vienna University of Technology has now vividly demonstrated.

Led by Yuji Hasegawa, the team prepared a stream of neutrons and measured two spin components simultaneously for each, in direct violation of Heisenberg's version of the principle. Yet, the alternative variation continued to hold. The team reported its results in Nature Physics on January 15. (Scientific American is part of Nature Publishing Group.)

Heisenberg inferred his formulation in 1927 via his famous thought experiment in which he imagined measuring the position of an electron using a gamma-ray microscope. The formula he derived was ε(q)η(p) ≥ h/4π. This inequality says that when you measure the position of an electron with an error ε(q), you cannot help but alter the momentum of the electron by the amount of η(p). An experimenter cannot know both the position and the momentum precisely; he or she must make a tradeoff. "For that reason everything observed is a selection from a plenitude of possibilities and a limitation on what is possible in the future," Heisenberg wrote.

The same year, Earle Kennard, a less-known physicist, derived a different formulation, which was later generalized by Howard Robertson: σ(q)σ(p) ≥ h/4π. This inequality says that you cannot suppress quantum fluctuations of both position σ(q) and momentum σ(p) lower than a certain limit simultaneously. The fluctuation exists regardless whether it is measured or not, and the inequality does not say anything about what happens when a measurement is performed.

Kennard's formulation is therefore totally different from Heisenberg's. But many physicists, probably including Heisenberg himself, have been under the misapprehension that both formulations describe virtually the same phenomenon. The one that physicists use in everyday research and call Heisenberg's uncertainty principle is in fact Kennard's formulation. It is universally applicable and securely grounded in quantum theory. If it were violated experimentally, the whole of quantum mechanics would break down. Heisenberg's formulation, however, was proposed as conjecture, so quantum mechanics is not shaken by its violation.

In 2003 Masanao Ozawa of Nagoya University developed a new formulation of the error–disturbance uncertainty that Heisenberg aimed to express, but this time on much firmer footing. Derived mathematically from quantum measurement theory, the new formulation describes error and disturbance as well as fluctuations: ε(q)η(p) + σ(q)η(p) + σ(p)ε(q) ≥ h/4π. Hasegawa's team is the first to have demonstrated the violation of Heisenberg's inequality and the validity of Ozawa's inequality. It did so by directly measuring errors and disturbances in the observation of spin components. Even when either the source of error or disturbance is held to nearly zero, the other remains finite.

"I think it is significant, especially for experimental physics, that measurement errors and disturbances are clearly distinguished from quantum fluctuations in Ozawa's formulation," said Shogo Tanimura of Nagoya, who is independent from Ozawa's group. "Physicists thought that the only way to reduce errors is to suppress fluctuations. But Ozawa's inequality suggests that there is another way to reduce errors by allowing an object system to have larger fluctuations, although it may sound contradictory."

Ozawa's formulation confirms an emerging trend in probing the foundations of physics: to hew closely to what experimenters directly see in the lab—a so-called operational approach. "The error–disturbance uncertainty relation is much more important than that of fluctuations," says Akio Hosoya, a theoretical physicist at Tokyo Institute of Technology, "because in physics the final say comes from experimental verification." Heisenberg would be pleased that the limitation we can know about the world, which he aimed to expressed, was this time clearly revealed with the new rigorous, experimentally verified formulation. The new uncertainty relation between measurement error and disturbance is no more just conjecture, but physical law.

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