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De Broglie‘s Quantum Football

Can we understand matter waves using macroscopic analogues? Consider the thought experiment where a football player kicks balls through slits in a wall. If one of these slits is closed, we expect to find the balls with a narrow distribution of possible locations in the goal. If we open the right slit instead of the left one this should result in the same distribution – just slightly shifted to the right.

soccer1The illustration indicates that this is not all that is observed – if we were able to scale up Planck’s constant to h=1 Js. Already with a single slit open, the distribution would then be broadened – as it must be, because of Heisenberg’s uncertainty relation.

The surprising phenomenon in the double slit experiment is the absence of balls in certain locations that were still hit by particles, when a single slit was open. How can every individual ball „know“ about the status (open/closed) of both slits in the wall, if it flies only through one of them? How could it gain information about locations, that may be several hundred times further apart than the ball measures across?


This seems not to fit with our daily experience.

Is the Ball on the left or is it on the right hand side? These states seem to be mutually exclusive. And yet, the corresponding wavefunction passes both slits. If we associate it “ontologically” with the ball itself, we run into contradictions with our concepts of reality. If we regard it as an information wave, how is this information then connected to the observed reality in the detector? These questions still trigger scientific debates.

Such experiments have never been done with real balls and they won’t be in a long time, for many reasons. However, in 1999 such experiments have been realized at the University of Vienna with the world’s smallest football, the fullerene C60 (Arndt et al., Nature 401, 680, (1999)). This carbon molecule is a perfect replica of a football: 60 corners (C – atoms) arranged in 20 hexagons and 12 pentagons. The online Simulation follows a modern version of this idea, where fluorescent molecules allow to visualize the arrival of each individual particle (Juffmann et al. Nature Nanotechnology (2012) 7, 297).