one quantum specific example:
A quantum example for uniqueness of position
In Quasicrystals atoms are joined together in a long range order. One can visualize this order as Penrose tiling, where a shifted copy will never match exactly with its original. In such an order each intersection, which in quasicrystals marks the position of an atom, is a unique position upon an infinite grid, in that sense each atom have a unique position and in that sense is distinguishable. Atoms that form quasicrystals, (molecules), are quite heavy, and include at least thousands of elementary particles.
In their experiment, M. Torres and Al [11] have found out that the same order can be demonstrated for the electrons themselves:
“The spacing between the wave peaks (of the electron waves) was not constant, as in a periodic wave, but varied quasiperiodically between two values, which were related to the spacing in the pattern on the pan's bottom.”
Experiments revealing the exact circumstances for which a diffraction of quasicrystals disappear, by marking (with radioactive isotope etc.) very few atoms of the grid, might reveal information that will enable further understanding of the role of the unique position of each atom in the quasiperiodic grid. For observable results, doing the diffraction on the molecules as is done now would not be enough, what is needed is to get a refraction off the wave peaks as described in [11] but then how could we mark the electrons?
