Physics is defined by its symmetries, from thermodynamics laws like the conservation of mass and energy, to the principle that the universe is basically the same all over. Symmetry can also suggest some truly bizarre ideas. One of those ideas is time crystals.
The definition of a crystal is simple enough - it's any solid whose constituent parts are arranged in an orderly, repeating pattern extending out in all three spatial dimensions. Although crystals themselves are defined by their symmetrical arrangement, they actually represent a form of what's known as spontaneous symmetry breaking in closed systems.
The idea here is that if you have a bunch of free atoms whizzing around, the overall system can display symmetry. But if those atoms suddenly come together to form a crystal, the overall symmetry of the system has been reduced onto one particular subgroup, namely the crystal. The overall spatial symmetry has been been broken, but the periodicity that defines the crystal's structure means it hasn't been entirely lost.
While that may be a bit theoretical, it's all fairly straightforward. The intriguing question is one that is often asked of physical phenomena - if this process exists in the three spatial dimensions, could it also occur in the dimension of time as well? That's the question currently being investigated by MIT physicist Frank Wilczek, who won the 2004 Nobel Prize along with David Gross and H. David Politzer for their work on the strong nuclear force.
Wilczeck, along with collaborator Al Shapere from the University of Kentucky, has just published two papers examining how the mathematics that govern crystal formations in space could also work in time. They argue that time translation symmetry - the notion that a system will maintain the same features over a given interval of time - can be broken in low energy states and then reduced to a smaller part of the system, which they call time crystals.
The key here is that the system being described is in its lowest energy state, which means that there should be no movement in it at all. But if something inside the system starts moving, then the time translation symmetry has been broken. What Wilczeck and Shapere argue is that these moving objects could simply get stuck in an eternal loop. The periodic movement of the object through time is just like the periodic arrangement of a crystal's internal structure through space, and the end result is the same - symmetry is broken, but it isn't lost.
We don't yet know if time crystals exist, and Wilczeck and Shapere aren't claiming otherwise - they're simply saying that it's mathematically possible for the crystals to exist. There are some real world reasons to think such crystals might exist, specifically in the realm of superconductors. These can carry currents even in their lowest energy state, which is a form of movement, and those electrons passing through superconductors could theoretically keep moving forever.
If time crystals really are out there, we could be looking at some potentially fascinating applications for them. The periodic nature of time crystals means they would perhaps be the most basic, fundamental form of timekeeping in the universe - as Wilczeck writs in one of his papers, "Spontaneous formation of a time crystal represents the spontaneous emergence of a clock." These time crystals might also have a home in quantum computing, where they could be arranged as qubits and used to undertake calculations at zero energy.
The one thing time crystals won't give us, however, is perpetual motion. Well, that's not exactly the case. A time crystal would be able to move periodically forever - which is the literal definition of perpetual motion - but it wouldn't actually allow us to get any energy from the system, which is generally what people really mean when they refer to perpetual motion. Time crystals would only exist in the lowest energy state, so it would be impossible to gather any usable energy from this eternal loop in time.