Probabilistic vs optical interpretation of quantum mechanics

Although electrons and photons produce the same interference patterns in the two-slit experiments, the description of these patters is markedly different. This difference was analyzed by Bohm. Later on Sanz and Miret-Artes and others were able to squeeze the differences to zero. Fortunately, they left some room for developments presented in this Letter. We noticed that in the absence of sources the electromagnetic field can be represented by the complex scalar field. It is demonstrated that the same fields are being used in the non relativistic Schr\"odinger equation. The connection between the electromagnetic and Schr\"odinger fields allows to study the topology of zero sets (Chladni patterns) of Schr\"odinger eigenfunctions. The existence of these patterns is contingent upon the existence of eigenvalues of multiplicity higher than one. This is permissible only in Schr\"odinger's version of quantum mechanics. Presence of multiplicities is making quantum mechanical and topological entanglements equivalent.