[contravariant]

>They did this, and observed the ions changing in such a way where there was no driving influence and it's implied that the reason that this behavior was observed is because time symmetry was broken, which is just a fancy way of alleging that the universe is non-deterministic, I think.

Time translational symmetry and determinism have nothing to do with one another. Even a classical pendulum breaks time translational symmetry yet it's fully deterministic. In this cases they do break the symmetry in a more fundamental way, but it still doesn't say anything about determinism.

[dysfunctor]

So what are the implications of an object that breaks that symmetry? Would it be possible to observe an object in different times in the same state, or the same time in different states?

[semiel]

> So what are the implications of an object that breaks that symmetry? Would it be possible to observe an object in different times in the same state, or the same time in different states?

The object would be in a repeating set of states. First state 1, then state 2, then state 1, then back to state 2, etc.

This is not in itself surprising. Think of a pendulum, for instance. The difference here is that the motion is the lowest energy state. Over time, a pendulum swing decays. This does not: it will continue forever, if not disturbed.

The obvious next question is: isn't that perpetual motion? According to the normal dictionary definition of those words yes it is, which is why this is a fascinating discovery. However, it doesn't violate the normal arguments against perpetual motion, because there's no way to extract energy from the system. Anything you did to influence the motion would require adding energy.

[ivoras]

But... don't the process by which this is observed (I mean literally, the machinery used to measure it) introduce energy into (or draw it out) this system?