Quantum Interference, Hidden Symmetries: Theory and Experimental Facts

The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple mathematical idea of linearly combining vectors in a Hilbert space. Specifically, the discussion turns around the connection between symmetries characterizing the wave function and the behavior in time displayed by the quantum flux when the latter is analyzed in terms of streamlines (Bohmian trajectories). This is illustrated with a series of analytical results and numerical simulations, which include Young's two-slit experiment, counter-propagating wave packets, grating diffraction and quantum carpets (e.g., Talbot carpets), and diffraction under confinement conditions. From the analysis presented it follows that quantum paradoxes appear whenever symmetries related to interference are neglected in the interpretation and understanding of the corresponding phenomena.