Objects traveling at different speeds experience time at different rates. OK, I can accept that as a brute fact, and not worry about it.
But suppose I wave my hand up and down. Then the particles in my hand should be experiencing time a teeny, teeny bit slower than the ones in my shoulder, which are not moving as fast (relative to my center of mass). So after I am done waving, or maybe only while I am waving, my arm is in a different time than my shoulder. So my shoulder exists in my hand’s future, so to speak.
Is that right? Does it ever catch up? Or is it simply the case that every single atom/sub-atomic particle/quark is in a different time from every other? Are some in each other’s future and some in each other’s past, like my wife and the old girlfriend of mine she met at my high school reunion?
It’s not just that some are ahead and others are behind. Each particle has its own definition of “ahead” and “behind”. It’s possible for A to observe that it’s ahead of B, and B to observe it’s ahead of A and for both of them to be correct.
I don’t know if it makes sense to talk about one thing being in another thing’s future.
If you think about it, we really don’t have an absolute measure of time. We can only measure time in terms of movement, chemical changes, radioactivity, etc. Relativistic effects change all of those and they do them in a sneaky way so that everything still works even when we can’t wrap our heads around it. Mass increases, distances shrink, chemical and subatomic reactions slow down.
So even if you could wave your arm at 90% of c, all you’d notice is that your fingers processed half of the chemical reactions as the cells in your chest, divided half as slowly, etc.
Time might not be tearing you apart but gravity certainly is. What if gravity is just time, maybe they are one and the same? So called Gravitons might actually be “interdimensional” time particles.