OK, wow... I can't pretend to really understand QM or anything, but I do get what the disagreement is here. Daedalus says movement along the X axis implies motion, because it has a function on the y axis that can be measured. Swansont explains the standing wave thing; well done there, but I think it wasn't quite implicit enough.
So the x-axis is time, and we (along with everything else-electrons and standing waves included) are moving (per se) along it at a rate presumed to be constant. Atomic clocks measure a change in state that, as Swansont said, can't be considered motion-- This state-change would be represented by the y-axis, and thus be measurable. The question is, how can something change without movement, and well, the answer is, the way a point in space doesn't move when a sound (or other) wave passes over it. The wave is there, then it's not. In the case of a sound wave, the density has changed, but for subatomic quantum-mechanical thingamajigs, there is no density, there's just existence and non-existence. They phase in and out (ya, QM loses me right about here), without movement in the classical sense. That makes the y axis neither spacial x/y/z, nor time, but rather a 5th dimension to be measured in boolean terms.
Nevertheless, I'd have to argue that anything that exists for any amount of time DOES move in relation to something, as there's always something in motion; and yes, the inability to reach absolute zero does mean that atomic clocks will always have some motion to contend with. But the purpose of this thread is not to question motion, but time.
The only issue with these statements is that you use the word 'motion'. Motion Change is inherent in time. I'd even go so far as to say that without change, time would not exist. It'd certainly have no meaning at all, and it could never be measured. I'd go a step further and say that the 'dimension' of time is little more than an emergent property of change in the three spacial dimensions and the fourth--phasing; time cannot be observed without these, which is why its passage seems relative. These 4 dimensions exist for every point in time we can arbitrarily define. But though we define it, observe it and altogether depend on it, time doesn't exist as a stand-alone dimension. Therefore, time-travel is impossible, because the x-axis which measures it is ultimately imaginary. (time is the y axis)
Ya, so I started off all humble, then my outstanding arrogance came out....better disclaim:
I'm a laymen college dropout with very little scientific training who's done only several hours of online research on the topics of GR, QM, and whatever else sparked my interest while watching the science channel at 4 in the morning. So if I'm wrong about something, CALL ME ON IT! I do hope I at least helped with your disagreements.