Special Relativity. Lifetime.

[Alex K]

Clocks need to be synchronized, presumably, because we can observe discrepancies in their synchronization if they emerge. That is all we have access to, not time. I don't know how atomic clocks work, but I doubt they are tapping into anything called time either, they are independent of it. All clocks present some form of observable motion or change to our minds, so we can abstract the notion of time from it.

The formula doesn't change because of this, but perhaps the conclusions drawn from it do. Again, disclaimer, I don't fully know what physicists mean by terms such as time dilation. But it seems incorrect to conclude time has changed in any way based on the physical changes of a clock. It is like assuming time stops whenever I stop a clocks hand from moving. Or perhaps like having a ruler made of rubber, and assuming the world is constricting whenever I stretch the ruler out.

You can always take the position that time as Das Ding an sich is never accessible directly, and I cannot argue with that. What I can say is that all physical processes are affected by dilation the same way, and it therefore is in any meaningful sense a dilation of time. It would be a mistake to just view it as a "malfunctioning" of a clock bc all processes, even the most fundamental ones we know such as particle decay, are affected by it the same. Same goes for curvature of spacetime which is directly observable as gravitational redahift. It is a slowing of time itself in any sense if all temporal processes we know adhere to it.