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 quantu

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.