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I stumbled upon this piece of news in the BBC's website http://www.bbc.co.uk/news/science-environment-19489385, discussing this paper http://prl.aps.org/abstract/PRL/v109/i10/e100404, which reports the "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.

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Here is the free arXiv version of the paper. –  Qmechanic Sep 9 '12 at 7:32
Thanks Qmechanic! –  stupidity Sep 9 '12 at 23:18

3 Answers 3

up vote 10 down vote accepted
  1. 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.

  2. 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.

  3. 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.



for some extra discussion and some formulae.

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Thanks Dr Motl for the answers and the link to your blog post. –  stupidity Sep 9 '12 at 23:19

I will argue that the experiment presented in the paper [1,2] actually supports Quantum Mechanics. This may be not quite explicit in the paper, but also there is nothing against the standard view on quantum mechanics in it.

Heisenberg originally stated his principle in terms of measurement-disturbance relationship (MDR). This is how he understood it at that time. The uncertainty principle which was proven theoretically, either in the context of wave mechanics, or from the non-commutativity of the operators, is correct, and it's correctness is acknowledged by the paper. This is called Heisenberg's uncertainty principle (HUP), and is very different from MDR.

The paper refers to previous theoretical works which disprove MDR, and present experimental evidence purported to confirm the violation of the MDR.

Why do I claim that the violation of MDR supports Quantum Mechanics? Because, if MDR would be correct, it would be enough to explain quantum uncertainty. Recall that even Heisenberg originally thought that the uncertainty is due to disturbance caused by measurement. If the states would behave as they are due to the measurement disturbance, then we could consider them classical, and extract Bohr's probability rule as we calculate probabilities in statistical mechanics. But we know this is not true. Quantum states exhibit properties which can't be explained by classical mechanisms. Among these, HUP plays an important role, together with entanglement. The service made by this paper is that it shows that the wrong version of the uncertainty principle can be violated. The authors seem to me to support the HUP:

These two readings of the uncertainty principle are typically taught side-by-side, although only the modern one [HUP] is given rigorous proof.


Our work conclusively shows that, although correct for uncertainties in states [HUP], the form of Heisenberg's precision limit is incorrect if naively applied to measurement [MDR].

Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

arXiv link to the paper

P.S. My answer is in contradiction with the interpretation given in the BBC article Heisenberg uncertainty principle stressed in new test. The BBC article is misleading, because it makes confusion between MDR and HUP.

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"Quantum states exhibit properties which can't be explained by classical mechanisms" - this has never been proven, and is likely incorrect in light of recent experiments with dotwaves and pilot-wave theory. –  B T Jan 23 at 5:45

It may come as a surprise to past and present adherents of Heisenberg's Uncertainty Principle (HUP) but recent mathematical progress means we can also look at uncertainty from a theoretical point of view. Quantum theory depends on HUP and is incomplete as Einstein thought in the 1930's. See book Self-field theory, a new mathematical description of physics, by A.H.J. Fleming, published by Pan-Stanford Press 2012; analytic solutions for the motions of the electron and the proton inside the hydrogen atom have been found obviating the need of the numerical and probabilistic quantum theory. The basis of this new formulation includes the magnetic currents of particles and not just the electric fields as in quantum theory. In this formulation, the photon is composite and hydrogenic-like.

It is well known the inequality relationship of HUP applies to any quantum system in general. The equations for the orbital and cyclotron motions of each electron in self-field theory (SFT) are given as two equality equations. Apart from the 'greater than' relationship compared with the exact relationship, the 3 equations are identical. Whereas there is one inexact relationship in HUP there are two equality relationships in SFT. SFT thus completes the Bohr Theory that did not include any magnetic effect on the electron.

In the light of this mathematics HUP can be seen as a theoretical error; in practice it appears as a numerical error in any computer calculations.

Let me add that HUP will always be a good engineering approximation able to be used across domains from photon to universe in the same way that Newton's law of gravitation is still used today by those involved in gravitational research.

Let me further add that the magnetic moments involved in this new mathematics (SFT) at the terrestrial domain may be able to give us much more quantitative information about the way techtonic plates, earthquakes and tsunamis develop over time.

But there are other benefits like 'clean' chemistry waiting to be investigated.

Tony Fleming

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