But we can move the clock through space and it's measured time will change.

 

I know what you mean, but in my opinion you go, methodologically seen, too far. What you can see is that the period of the clock has become longer: compared with a clock in rest in your inertial frame it is slower. So in fact you are comparing two processes. And of course because all processes slow down (compared with your local clock), one can say time has slowed down. But one cannot say that the slower time causes processes to slow down.

one can say time has slowed down. But one cannot say that the slower time causes processes to slow down.

Excellent

I know, but in my opinion it is not enough. Where e.g. an electrical current can have effects, we can use these effects to measure the current. So we measure by means of causal effects of the current. This is definitely not the case with time. The cause of the moving pendulum is gravity and inertia, not time. We cannot remove time, and then the clock stops.

 

Current depends on charge, and you would have a similar difficulty defining charge without some kind of self-reference.

 

But I agree, time is different; we are not at rest with respect to spacetime. There will always be some combination of temporal and spatial motion. While the spatial motion can go to zero, the temporal part can't.

 

I do not think so. In the first place, it is a consistent use of language: space is to time, what length is to duration. Or if you want: space is to length, what time is to duration. We can use lengths and durations to make operational definitions of space and time. But not the other way round.

Even physics has colloquial language use. One of the issues here is that time dilation really should be defined in terms of frequency to be consistent, but it's not. Even in Einstein's day, "time" was used to indicate an interval. t₀=0 in inferred in a lot of instances.