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Regarding your last question, it does increase the mass. This explain Einstein 's Equivalence Principle... The mass increase is useful and real in a particles collider like the LHC. And it generates gravity, a relativistic one... Meaning it depends on the observer's referential frame.
A proton is smaller and has more mass than an electron.
I don't find the arrow uncertain, I find it a constant, inside your own frame. The idea of conceptually defining time when comparing frames is, conceptual. The real truth is that your arrow of time never change.And furthermore, we're all carrying our personal SpaceTime with us. Which makes it incredibly difficult to define where a 'frame of reference' starts and ends. If I expect every 'point' to be slightly different gravitationally, and then include relative motion/acceleration I now have two good reasons for that definition. So where do you think your 'frame of reference' is situated? The one I, and you too actually, expect you to have? and how do we join them?I don't need to define a 'time dilation' to any specific 'locality', can you see what I mean? It's a relation, nothing more.==How about accelerations? They are all defined by one thing as I see it, or two actually.They all have 'gravity', and they all expend 'energy'.