# How do I prove quantum physics

## Quantum physics: uncertainty proven

The strange thing about quantum mechanics can be summed up in a single formula: the uncertainty relation. According to the textbooks, it says that it is in principle impossible to know the exact position and momentum of a subatomic particle - the more precisely you know the position of the particle at a given point in time, the less you know about the value of the momentum.

The original formulation of the principle, which the physicist Werner Heisenberg established in 1927, describes the indeterminacy in a different way - than the fundamental limit with which a measuring device can measure quantum states. Heisenberg provided no direct evidence for this formulation of the principle and expressed his ideas "only informally and intuitively," says the physicist Jos Uffink of the University of Minnesota in Minneapolis.

#### This article is contained in Spectrum - Die Woche, KW 28, 2013

Now researchers believe they have finally found a formal proof. "Our work proves that nothing can be measured with higher accuracy than the fundamental uncertainty allows," says Paul Busch, theoretical physicist at the University of York, who and his colleagues published the proof in advance on June 6th on arXiv [1 ]. In doing so, they not only place the role of the measurement process in quantum mechanical indeterminacy on a solid basis - a role that physicists have already begun to doubt - but also provide an indication that messages encrypted using quantum cryptography can be transmitted securely.

### Theoretical measurement

In their theoretical work, Busch and colleagues looked at measurements in which the position and momentum of a particle in any quantum state are determined at the same time. They then compared the accuracy of these measurements with two special cases in which either the position or the momentum of the particle is known exactly. It turned out that in the two special cases the combined accuracy in the position and momentum measurement on the one hand obeys Heisenberg's relation and on the other hand is always higher than in measurements in which both quantities were determined at the same time. This move allowed them to prove Heisenberg's original guess.

The work of Busch and his co-authors "should be remembered", says mathematician Hans Maassen from Radboud University in Nijmegen. "It is quite possible that it will soon be presented in textbooks as the actually correct formulation of Heisenberg's uncertainty principle." But other colleagues are less confident, as the evidence has rekindled a ten-year-old debate.

### Heated debate

In 2003, the physicist Masanao Ozawa, who is now doing research at Nagoya University in Japan, proposed that the interpretation of Heisenberg's uncertainty principle, which attributes the uncertainty of the system to the measurement process, could be violated. Ozawa's theory was published in 2004 [2] and confirmed last year when a team led by Aephraim Steinberg and Lee Rozema from the University of Toronto presented the results of an experiment in which they determined the polarization of a single photon along two perpendicular directions [3] .

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