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Results of the welcher Weg experiment of Duerr, Nonn and Rempe are explainedby using ray representations of the Galilei group. The key idea is that thestate of the incoming atom be regarded as belonging to an irreducible unitaryray representation of this group. If this is the case, interaction with aninterferometer with a which-way detector must split this state into the directsum of two states belonging to representations with different internalenergies. (While the zero of internal energy is arbitrary, the differencebetween two internal energies is well-defined and is invariant under unitarytransformations.) The state of the outgoing atom will then be a superpositionof two mutually orthogonal states, so that there will be no interference.Neither complementarity nor entanglement plays a role in this explanation.Furthermore, in atom interferometry it is not enough for a quantum eraser toerase the internal energy difference; to restore interference, two copies of arepresentation have to be collapsed into one. In a direct sum of copies of thesame representation, copies of the same state will still be orthogonal. Theseassertions may be testable, and two new atom interferometry experiments aresuggested. One of them is an `own-goal' experiment which may decisively refutethe explanation offered here, and restore the aura of mystery that this papertries to dispel.

Little-used Mathematical Structures in Quantum Mechanics I. Galilei Invariance and the welcher Weg Problem