It's quite easy to prove them different Mike so you're perfectly correct. They are not the same in form of time dilation, as observed from some thought up point in SpaceTime. And in fact, as all points are equivalent there can be no exact definition of the arrow, except, if using a strictly local definition in which case 'the arrow' always will be the same for you, no matter where you go, or how fast relative something else.

What makes 'time dilations' are two things. Gravity/mass/accelerations and relative uniform motion. Motion is split into relative uniform motion, and then accelerations which locally becomes ones 'gravity'. They both warp and twist the room time geometry, differently depending on the observer being 'inside' the motion acceleration mass versus 'outside' observing it, with the added effect that a acceleration also locally becomes a gravity.

When you look at SpaceTime you have two choices, either you see it as one whole undifferentiated thingie or you decide that locality rule. If you use the first you get 'streams of time' in the 'ocean' of SpaceTime joined conceptually by Lorentz transformations. If you use the later you get one arrow, same for all observers. The only thing differing it being where you are, observing the rest of your SpaceTime/universe, as defined from your clock and ruler.

The first way of defining it also will find that all positions are observer defined, gravity will also be observer defined, even the constant 'c' can from some points of view become observer defined as in different accelerations. From the view of locality all definitions must go out from the room time geometry you exist in, and they will all be as true locally. In that view 'c' becomes a constant defining/explaining why we see both time dilations as well as Lorenz contractions. Lorentz transformations naturally follows from that constant being the same everywhere, and 'anytime'.

And in the end it all becomes a question of geometry, mass/energy, 'motion' and radiations constant. In that universe 'locality' describes, radiation is what binds it seamlessly for all observers, although 'distorted' relative each other.

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And if mass is equivalent to energy, then that has to be the ultimate description of 'something', joining it all into one definition.

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Eh, need to correct myself.

Inertia is a resistance to motion but it is as well a resistance to 'change'. That means that in a (relative) uniform motion (in space) inertia will act on anything changing the equilibrium presented by that 'motion' as defined by the observer.

Inertia is weird