‘Time Crystals’ Could Upend Physicists’ Theory of Time

Wouldn't tidal forces influence Earth's orbit much more than gravitational radiation? Although I suspect both are far too small to measure on a human time scale.

Maybe I can help give insight into this topic to those without a physics background. Our current best theory that describes reality at the small scale is quantum mechanics. In quantum mechanics, each "system" -- a collection of particles that you are interested in -- corresponds to one wavefunction (literally, a mathematical function). Glossing over some details, this is a function of spatial coordinates (a vector r) and time (t). For example, if your system is hydrogen, your wavefunction is a function of two coordinates -- the electron's position and the proton's position -- and time. You can perform some linear algebra on this function to predict what state the system will be in at any future time. And you can also predict what your measurements (position, momentum, spin, etc.) of this system will be. The Schrodinger equation is what governs the evolution of the wavefunction. I'll refer you to Wikipedia if you want to know the details of that equation.

In chemistry you have what are called stationary states. These are solutions to the time-independent Schrodinger equation Hψ(r) = Eψ(r) [H is an operator; E is a scalar]. Now, when you plug ψ(r) into the time-dependent Schrodinger equation, you get Ψ(r, t) = exp(-iEt/hbar)ψ(r), where i is the imaginary unit, E is the energy, t is time, and hbar is the reduced Planck's constant. So you can see there is clearly a time dependence.

However, when you measure some property of a system, you aren't measuring the wavefunction but rather the results of some linear operator acting on the wavefunction (each operator corresponds to a probability distribution of what measurement you will get). So despite the fact that the wavefunction has a time dependence, your measurement probability distribution functions do not!

Now the other thing you need to know is that so far these stationary states all correspond to ground states. What is a ground state? It is the lowest energy level that a system can obtain. You might think that the different orbitals an atom can have in chemistry are all stationary states, but they're not. They can spontaneously decay to a lower-energy state. You need quantum field theory to prove that, and I don't even know how to do that, so I won't.

The deal with these time crystals is that Dr. Wilczek has proposed a lowest-energy system that corresponds to cyclical time-varying measurement probability distribution functions. So despite being a stationary state, your measurements depend on when in the cycle you take them! This has not ever been done experimentally, so it looks as though the Zhang and Li group are going to attempt to do so.

The ion lattice is in its ground state, it can't release any more energy to get into a lower state, but it moves. They couldn't get a lattice into the ground state until recently due to excess heat from contaminants in the "trap".

Exactly.

The actual interesting thing about this crystal is that the atoms will spontaneously start spinning as you remove energy from the system. Ie, in the ground state (the lowest energy state) the atoms are in motion. This is in contrast to all the physical systems we are familiar with where the ground state is motionless.

The reason it is called a 'time crystal' is that the ground state 'breaks symmetry' in time in the same way that a regular crystal 'breaks symmetry' in space - in the sense that if you translate the system in space, you do not usually get back its original state, unlike a gas. And, this symmetry breaking occurs as you cool the system. Crystals self-organize in a periodic grid as you cool them from the liquid state, just as this time crystal will set itself in periodic motion as you cool it.

One consequence of the symmetry breaking is that the atoms will have to move either clockwise, or counterclockwise, and will "randomly" choose one of the two.

(1) How can the ground state not be an energy eigenstate? By definition, the lowest-energy state has a well-defined energy (that is, the lowest energy) and therefore ought to be in an energy eigenstate?

(2) You said: "Our current best theory that describes reality at the small scale is quantum mechanics." I don't disagree, but I'd like to emphasize that "at the small scale" might not have been necessary. I think it's a shame when people think that quantum mechanics only applies to small things.

(3) The way that I understand time crystals is that they are analogous to real crystals. And just as the translational symmetry of a crystal creates a corresponding quasi-momentum for the momentum, so does the time-translational symmetry introduce a quasi-energy similar to energy. Is that correct? Perhaps it helps answer my first question.