How is a "time crystal" different from a plain old [EDIT: quantum] harmonic oscillator?
Energy. A time crystal is at its lowest energy state.
A harmonic oscillator has energy in it - if you took away the energy it would stop moving.
i.e. to stop a time crystal add energy. To stop a harmonic oscillator take away energy.
The other responses have not addressed the possibility that you are referring to a quantum harmonic oscillator. If you are, that is a very good question. I believe the resolution here is that while the phase of a quantum harmonic oscillator in the ground state changes with time, the results of bracketing any hermitian operator (i.e. measuring a physical quantity) does not change throughout time. Therefore in the ground state of the quantum harmonic oscillator, the system is time translation invariant. So a quantum harmonic oscillator does not form a time crystal.
Well, yeah, I thought it was a given that we're in quantum-land here. In classical physics the lowest energy state of a system is necessarily static.
Re:Time crystals might exist after all
by SomeStupidPoint on Sunday September 11, 2016 @01:40PM
(#12474533)
I believe that the idea is the time crystal remains in its ground state the entire time (especially given the work of the author on anyons).
Re:Time crystals might exist after all
by maxwelljoslyn on Sunday September 11, 2016 @03:05PM
(#12475021)
Thank you for dispelling the woo-woo.
Now, there's more to it than that. I'm not proposing this as a full explanation of what it means, just trying to get the B-class sci-fi ideas out of the way to sketch out the complicated bit of what they mean. As a crystal is a periodic atomic structure in space, a time crystal is a periodic atomic structure in time. There's more to both, of course, but that should help get the woo-woo out of the way.