to see why consider it such as both time dilation and length contractions are true statements. That's what I think they are at least

The world becoming observer dependent. Now create a system, let's call all objects in it moving 'observers' of each other, inside some common space. Motion exist and is easy to prove logically, so they are indeed moving. Each one of them will define this 'common space' differently. and all of them will be correct. there exist no (common) gold standard experimentally. Now try to put up a unitary field that take all this into consideration, giving us one practical description of that space, I will be pleased if you succeed. You cannot use Lorentz transformations for it, because they are simply logic, knitting together my description of a reality with yours. The space in where a Lorentz transformation exist is purely mathematical, but the universe you meet exist, and will always be locally true for you.

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you might say that a Lorentz transformation, in itself, is neither here nor there. It's a link between two observers, giving a necessary logic and causality to a universe. because that is what physics are, a logic, or several depending on how you look at it. Same with everything else, all sciences assume logic to exist.

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you could look at it this way. what do you need to construct a 'common space'?

Causality should be there, if you want it to be understandable.

Causality is a primary logic you need. Break it and the common space we define, our 'universe' becomes something else. What causality need to exist is a arrow. That arrow need a direction. Each one of us have a locally true, four dimensional reality, with a locally true arrow pointing us from our birth to our death. Then we have causality that knits together my local reality with yours, into that 'common space' or universe, as described through a Lorentz transformation.

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The 'gold standard' that do exist, and create our physics are all local definitions, as 'c' and other constants. We use those for all sciences, and when we assume the universe to have the same physics, laws etc we go out from such local definitions, expecting them to be true wherever we go to measure them. So locally no ambiguities exist, there we can agree on that my time is yours too

If it wasn't we wouldn't have 'repeatable experiments' and a computer would consist of 'black magic', as would the universe, or 'white' for those preferring that.

So relativity could be seen as a 'wrong statement', in a sense, as everything isn't relative, not when locally defined. But observing that common space it becomes relative, observer dependent.