How would one examine the boundary between motion and non-motion? An object is at rest in relation to another object. A force acts upon it and causes it to move. It seems there must be a point of boundary (in time) on either side of which the conditions are different: static on one side, moving on the other. But any attempt to examine the boundary runs smack into uncertainty, which is very likely a far grosser condition than the boundary itself. Does the question imply quantum time? One can talk of continuous acceleration, but no matter how finely you divide the time interval, there is still a point of change, which seems to suggest quantum time, which in turn quantizes motion. Just curious. Any insights?

if you were to push a broken down car, the back would start moving, say at time 0s, but at that time and for a short time after, the front will still be stationary. Due to the slow propagation of then energy you put in, although I don't know if that is sub-light speed, for sure, so time=0s might be relative, but as it's a 3dimensional object, I suppose that the energy might not be able to take the fastest route to the front of the car.

so bodies don't change velocities like ridged bodies....

if that's any help.

I probably wrote that too quickly and perhaps not clearly enough. I had in mind something more nearly on quantum scales. Think point particle, but regardless of the scale of the object, it is either moving, or not moving, and that dichotomy of possibilities indicates a change boundary. What, precisely, happens at that boundary, and when. It's hard to imagine that the change between static and moving states occurs continuously, because if you continue to divide the time interval, there must ultimately be a final yes or no condition of movement. That says quantum time more and more strongly to me, but I've never been a strong proponent of quantum time. The question arose in an examination of the ideas posed in the ATM post "Time, Motion, and Gravity", which with the help of member 01101001 I have finally succeeded in getting posted.

I can't really help, but actually I'm not entirely positive that this is a question that can be answered. To me, it sounds a bit like something related to Zeno's paradoxes. In other words, "how can anything change at all?"

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As above, so below

I'm afraid it's left me in a similar quandary, though Zeno's paradoxes can be answered, and are not paradoxes at all.

anyway, it's not a matter of things moving or not moving, all you have are changes in relative velocity.

The relativity was stated in the original question, but yes, you are correct, though it does not change the nature or validity of the question.

Sorry, I quoted my own title incorrectly above: the ATM post should read Motion, Duration, and Gravity. It's late. Past my bedtime.