Dear Eckard.
I hope you dont mind an interjection, but I think you may find a very significant error here, re your post,
*Einstein's Poincaré synchronization denies a ubiquitous now.
In "Zur Elektrodynamik bewegter Koerper" he explained how he defined "simultaneity" and "time"*
Because I think I fact Electrodynamics does not provide a valid definition of time or similarity, and provides no proof of time - but only assumes times existence. Specifically...
In the translated version of Einstein's paper (On The Electrodynamics of Moving Bodies),
( https://sites.google.com/site/abriefhistoryoftimelessness/special-relativity/the-electrodynamics-of-moving-bodies )
In section 1 "KINEMATICAL PART, § 1. Definition of Simultaneity", it says...
*If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by "time."*
* If, for instance, I say, "That train arrives here at 7 o'clock," I mean something like this: "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events."*
I think if you look at this very logically and scientifically, it starts by stating *If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time."*, but in fact the example given just, and only compares the *"motion of a material point"*... to *the motion of another material point*.
i.e. the claim is made that we compare motion to a thing called time, but in fact all that is shown is that the location and motion of a large motor, i.e. a train, can be compared to the location and motion of a *"small hand"* attached to a small motor.
(just "calling" a small motor a "watch", is not scientific proof that a thing called time exists and passes).
Also, in saying , "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.", the paper uses the word "simultaneous", and thus, the paper implies (but does not prove in any way at all) that the concept of "different" times is valid.
In fact, the observable truth is that the matter that makes up the train and the "Small hand", always seem to exist, and are always somewhere doing something, whether they are near or far from each other, or are being compared or not. i.e. no proof is given that "different times" or non simultaneity is a valid concept.
If I am wrong about the above please do let me know, but if I am right, consider the consequences.
You might assume the above must be wrong because SR proves "time dilation" and therefore time must exist, But, a proper examination of Electrodynamics ( SR ) (imo) shows it does not prove the existence of time, but only assumes the existence of time.
Thus, what is shown mathematically, and in thought experiments such as the moving light "clock", is imo, not that a thing called time exists, and is dilated with motion, but only that a photon can be set to oscillate between 2 mirrors, and the oscillation is dilated if the box is moving.
i.e, imo, Relativity does not prove the existence of time, or that it can be dilated, or that the concept of non-simultaneity is valid. And thus Minkowski is wrong to conclude that SR shows "only a kind of union" of space and time exist.
Just thought I mention the possibility,(I have a video re what I'm suggesting on the FQXI contest if its of any interest), If I am wrong, and if there is a part of Electrodynamics etc, that actually does not actually just assume "time" exist, but actually shows a valid reason to say "time" exists and passes, i'd appreciate a pointer to which section.
Yours
Matthew Marsden
"Does Time exist? How 'Time travel Paradoxes' can't happen without "the past". "
http://fqxi.org/community/forum/topic/2245