I stumbled upon this piece of news in the BBC's website here, discussing this paper Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements
- What does this mean? The uncertainty principle is wrong!?
- What are weak measurements?
- All in all, what do we learn from this experiment?
I don't have access to the journal, so it would be great if someone who saw and read the paper gave us some answers.
Answer
No, the uncertainty principle isn't wrong. The PRL paper doesn't suggest that the original uncertainty principle relating uncertainties of position and momentum fails. It "only" questions a modified interpretation of the principle that says that the momentum is disturbed at least by $\hbar / 2 \Delta x$ for a given precision of the position measurement $\Delta x$. Even this statement is highly loaded due to some (deliberately?) misleading terminology, as the following paragraphs clarify.
In 1988, Aharonov, Albert, and Vaidman (AVV) designed a clever technique to measure the expectation value of an observable in a state as the average of "weak values" obtained in some contrived time-dependent measurement procedures. The individual measurements disturb the state of the particle less than exact measurements would but it's still enough to obtain the exact expectation value. However, what's problematic is whether the individual terms, the "weak values", should be interpreted as "generalized values" i.e. as properties of the measured system. Stephen Parrott gave the clearest explanations that this ain't the case: the individual weak values are just auxiliary values that say something about the combination (measured system, measuring apparatus, details of the measurement algorithm) so they can't be interpreted as properties of the measured system only and as a consequence, Heisenberg's principles of any form don't have to apply to these quantities.
From this experiment, which generalizes the AAV "weak measurements" to photons in a simple way, we learn that the "weak values" indeed fail to possess some basic properties of actual values. AAV already showed in their very pioneering paper that the weak value of $j_z$ may be 100 even for a spin-1/2 system – this claim was the very title of their paper – which is impossible for the genuine (eigen)values. This experiment shows that if "values" are replaced by the (totally different) phrase "weak values" in a version of Heisenberg's principle, the principle doesn't hold. That shouldn't be surprising for any well-informed person. Of course, there is no evidence that there's anything wrong with quantum mechanics, or Heisenberg's original uncertainty principle which may be rigorously proven. It only tries to question a more informal claim by Heisenberg involving "necessary disturbance" caused by a measurement. But whether it actually succeeds in casting doubts on this statement of Heisenberg depends on whether or not you are willing to classify "weak values" as "sorta values". I think one definitely shouldn't so the paper only brings chaos and deep misconceptions to the readers of the mainstream media who are told that quantum mechanics is in doubt. It's surely not.
See
http://motls.blogspot.com/2012/09/pseudoscience-hiding-behind-weak.html?m=1
for some extra discussion and some formulae.
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