# Physicists prove Heisenberg's intuition correct

An international team of scientists has provided proof of a key feature of quantum physics – Heisenberg's error-disturbance relation - more than 80 years after it was first suggested.

One of the basic concepts in the world of quantum mechanics is that it is impossible to observe physical objects without affecting them in a significant way; there can be no measurement without disturbance.

In a paper in 1927, Werner Heisenberg, one of the architects of the fundamental theories of modern physics, claimed that this fact could be expressed as an uncertainty relation, describing a reciprocal relation between the accuracy in position and the disturbance in momentum. However, he did not supply any evidence for the theory which was largely based on intuition.

Now Professor Paul Busch of the University of York, UK, Professor Pekka Lahti of the University of Turku, Finland and Professor Reinhard Werner of Leibniz Universität Hannover, Germany have finally provided a precise formulation and proof of the error-disturbance relation in an article published today in the journal *Physical Review Letters*.

Their work has important implications for the developing field of quantum cryptography and computing, as it reaffirms that quantum-encrypted messages can be transmitted securely since an eavesdropper would necessarily disturb the system carrying the message and this could be detected.

Professor Busch, from York's Department of Mathematics, said: "While the slogan 'no measurement without disturbance' has established itself under the name Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results.

"We have shown that despite recent claims to the contrary, Heisenberg-type inequalities can be proven that describe a trade-off between the precision of a position measurement and the necessary resulting disturbance of momentum and vice-versa."

The research involved the scientists considering how simultaneous measurements of a particle's position and momentum are calibrated. They defined the errors in these measurements as the spreads in the distributions of the outcomes in situations where either the position or the momentum of the particle is well defined. They found that these errors for combined position and momentum measurements obey Heisenberg's principle.

Professor Werner said: "Since I was a student I have been wondering what could be meant by an 'uncontrollable' disturbance of momentum in Heisenberg's Gedanken experiment. In our theorem this is now clear: not only does the momentum change, there is also no way to retrieve it from the post measurement state."

Professor Lahti added: "It is impressive to witness how the intuitions of the great masters from the very early stage of the development of the then brand new theory turn out to be true."

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**More information:**The article 'Proof of Heisenberg's error-disturbance relation' by Paul Busch, Pekka Lahti and Reinhard F. Werner is published in

*Physical Review Letters*at DOI: 10.1103/PhysRevLett.111.160405 . Preprint available at http://arxiv.org/abs/1306.1565

**Citation**: Physicists prove Heisenberg's intuition correct (2013, October 17) retrieved 23 August 2019 from https://phys.org/news/2013-10-physicists-heisenberg-intuition.html

## User comments

Osiris1DonGateleyvacuum-mechanicsSo what we still could not be understood is the physical mechanism which explains how its work; here maybe the answer …

http://www.vacuum...19〈=en

VENDItardEUrgeltHere's a good rule of thumb: if you know you are ignorant, keep your opinion to yourself until your ignorance has been rectified.

Of course this is a case of me saying, "Do what I say, not what I do." :P

antialias_physorgYeah...but every electronics tech nowadays gets at least an introductory course in quantum mechanics. So they all know that your "analogy" is bunk.

mohammadshafiq_khan_1John92MoebiusIt seems to me Heisenburg was just stating the obvious. That any invasive measurement, like an x-ray, affects the measured. Just because we don't currently know of any emanations in the quantum realm (sub-quantum?) doesn't mean they don't exist.

TektrixBy the very definition of "quanta", any such "emanation" from the particle is comprised of whole-integer energy quanta. In other words, the particle has to give up quanta to emanate something observable, profoundly affecting the state of the particle.

antialias_physorgIt affects the photons it's catching. That's the point. This means you can never be ultimately sure of what you measure (and hence be ultimately sure of what that tells you about star the photon was emanated from).

This is NOT the same as: "then uncertainty means you cannot get ANY information". Observing a star gets you lots of information. Just not to an infinite number of decimal places.

NoumenonHeisenberg gave a qualitative explanation already known to physics prior to QM, and only as an analogy, when he said 'that the method of observing disturbs what is being measured'. It is more profound than this in qm however, and has to do with non-commuting operators; the commutator of position and momentum is ih-bar, iow, not zero,.... and the Fourier transform of wave-functions. So it is wrong to equate "the observer effect" with the uncertainty principal. This uncertainty relation exists despite an observer,... as for example that virtual particles must be taken into consideration.

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