Eugeniu,
I was increasingly aghast as I read your attack on the heart of established physics. But what really made me shake my head was towards the end when you left reality behind and wrote that these different spaces are 'invisible' and;
"Different from visible spaces, which have a physical existence within the space of the universe, orthogonal spaces, while physically embedded in the universe, are at the same time external to it."
So just when the ruling paradigm was entirely prostrate and at your mercy you finished it off with the best weapon you had at your disposal, an imaginary orthogonal pillow!!
So back to imaginary space-time and spooky wonderland physics we go then. But I tease you Eugeniu, I really was aghast, but at how brilliant your conception and analysis was ('brilliant' measured in the FQXi metric of how close to my own). But I could forgive you the "external physical embedded internal orthoginal" explanation when I read your last paragraph, and reality existing way beyond the sky. Now that is precisely where I'd like to show you it is, and 'detectable', and more real than you could dream of as the weapon to finish the job.
I've found there are indeed; "two independent physical spaces for relative motion to occur, and not, as Einstein thought, merely two abstract mathematical coordinate systems." The big next step is that these REAL spaces (frames) are "mutually exclusive". Nested at all scales, only existing around matter ('nothing' cannot move) so reference frames are independent REAL physical spaces in their own right, with boundaries where a well known (but not yet well interpreted) physical mechanism implements the effects of transformation.
Too good to be true? Of course it is. Far too good. Completely unbelievable. But true it in none the less. You may note that Fig 3 of my essay bears a passing resemblance to the inclining plane of your nicely interpolated Minkowski one. Here it makes a simpler point, that 'light vectors' is the wrong concept, and 'paths' are not normal to causal wavefronts. But do read the essay (and my last few here) before I overload you with more. Vesselin also promised to read it.
best wishes
Peter