One of the most powerful ideas in modern physics is that the Universe is governed by symmetry. This is the idea that certain properties of a system do not change when it undergoes a transformation of some kind.
For example, if a system behaves the same way regardless of its orientation or movement in space, it must obey the law of conservation of momentum.
If a system produces the same result regardless of when it takes place, it must obey the law of conservation of energy.
We have the German mathematician, Emmy Noether, to thank for this powerful way of thinking. According to her famous theorem, every symmetry is equivalent to a conservation law. And the laws of physics are essentially the result of symmetry.
Equally powerful is the idea of symmetry breaking. When the universe displays less symmetry than the equations that describe it, physicists say the symmetry has been broken.
A well known example is the low energy solution associated with the precipitation of a solid from a solution—the formation of crystals, which have a spatial periodicity. In this case the spatial symmetry breaks down.
Spatial crystals are well studied and well understood. But they raise an interesting question: does the universe allow the formation of similar periodicities in time?
Today, Frank Wilczek at the Massachussettsi Institute of Technology and Al Shapere at the University of Kentucky, discuss this question and conclude that time symmetry seems just as breakable as spatial symmetry at low energies.
This process should lead to periodicities that they call time crystals. What’s more, time crystals ought to exist, probably under our very noses.
Let’s explore this idea in a bit more detail. First, what does it mean for a system to break time symmetry? Wilczek and Shapere think of it like this. They imagine a system in its lowest energy state that is completely described, independently of time.
Because it is in its lowest energy state, this system ought to be frozen in space. Therefore, if the system moves, it must break time symmetry. This is equivalent tot he idea that the lowest energy state has a minimum value on a curve on space rather than at a single isolated point
That’s actually not so extraordinary. Wilczek points out that a superconductor can carry a current—the mass movement of electrons—even in its lowest energy state.
The rest is essentially mathematics. In the same way that the equations of physics allow the spontaneous formation of spatial crystals, periodicities in space, so they must also allow the formation of periodicities in time or time crystals.
In particular, Wilczrek considers spontaneous symmetry breaking in a closed quantum mechanical system. This is where the mathematics become a little strange. Quantum mechanics forces physicists to think about imaginary values of time or iTime, as Wilczek calls it.
He shows that the same periodicities ought to arise in iTime and that this should manifest itself as periodic behaviour of various kinds of thermodynamic properties.
That has a number of important consequences. First up is the possibility that this process provides a mechanism for measuring time, since the periodic behaviour is like a pendulum. “The spontaneous formation of a time crystal represents the spontaneous emergence of a clock,” says Wilczek.
Another is the possibility that it may be possible to exploit time crystals to perform computations using zero energy. As Wilczek puts it, “it is interesting to speculate that a…quantum mechanical system whose states could be interpreted as a collection of qubits, could be engineered to traverse a programmed landscape of structured states in Hilbert space over time.”
Altogether this is a simple argument. But simplicity is often deceptively powerful. Of course, there will be disputes over some of the issues this raises. One of them is that the motion that breaks time symmetry seems a little puzzling. Wilczek and Shapere acknowledge this: “Speaking broadly speaking, what we’re looking for looks perilously close to perpetual motion.”
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