As Homer tells us, Odysseus made an epic journey, against the odds, from Troy to his home in Ithaca. He visited many lands, but mostly dwelt with the nymph Calypso on her island. We can imagine that his wife, Penelope, would have asked him about that particular time. Odysseus might have replied, “It was nothing. In fact, it was less than nothing. Negative five years I dwelt with Calypso. How else could I have arrived home after only ten years? If you don’t believe me, ask her.”

Quantum particles, it turns out, are just as wily as Odysseus, as we have shown in an experiment published in Physical Review Letters. Not only can their arrival time suggest that they dwelt with other particles for a negative amount of time, but if one asks those other particles, they will corroborate the story.

In thermodynamics, an “adiabatic process” is a system change that transfers no heat in or out of the system. Any and all energy change in that system are therefore accomplished by doing work on the system, work being action that moves matter over a distance. (An example is a bicycle tire pump or lifting a box from the floor.)

The “adiabatic theorem” says that if you change a system slowly enough, it will remain in the same energy state. For example, if you walk slowly enough holding a full cup of coffee, the coffee will not spill—the coffee system has time to relax back to its steady state—but if you make a quick and sudden change while holding the coffee cup, some coffee will spill over the cup’s edge.

There is a similar theorem in quantum mechanics—a quantum system that is changed (perturbed) slowly enough will remain in its existing quantum state (often its ground state), while a sudden change, such as a photon impinging upon an atom, changes its energy state.