Quantum Interference in Time

I discuss the interpretation of a recent experiment showing quantum interference in time. It is pointed out that the standard nonrelativistic quantum theory does not have the property of coherence in time, and hence cannot account for the results found. Therefore, this experiment has fundamental importance beyond the technical advances it represents. Some theoretical structures which consider the time as an observable, and thus could, in principle, have the required coherence in time, are discussed briefly, and the application of Floquet theory and the manifestly covariant quantum theory of Stueckelberg are treated in some detail. In particular, the latter is shown to account for the results in a simple and consistent way.