  A century after its conception, quantum mechanics still hold surprises that
contradict many "common sense" notions. The contradiction is especially sharp
in case one consider trajectories of truly quantum objects such as single
photons. From a classical point of view, trajectories are well defined for
particles, but not for waves. The wave-particle duality forces a breakdown of
this dichotomy and quantum mechanics resolves this in a remarkable way:
Trajectories can be well defined, but they are utterly different from classical
trajectories. Here, we give an operational definition to the trajectory of a
single photon by introducing a novel technique to mark its path using its
spectral composition. The method demonstrates that the frequency degree of
freedom can be used as a bona fide quantum measurement device (meter). The
analysis of a number of setups, using our operational definition, leads to
anomalous trajectories which are non-continuous and in some cases do not even
connect the source of the photon to where it is detected. We carried out an
experimental demonstration of these anomalous trajectories using a nested
interferometer. We show that the Two-state vector formalism provides a simple
explanation for the results.
