Thanks for the relativity website.
Would be quite a job to translate the explanations into more transparant form.
The word "time" I think should be replaced by "self-referent reference distance"; as that is what it is. It all needs to be translated into "definition dynamics" to see if there are ny mistakes.
Note this: "two firecrackers go off at the same time".
How do you define simultaneous?
That requires two other firecrackers go off, one before and one after the first two, to say such a thing?
"Same time" means "contained in the same interval".
"Interval" is "proper time".
To claim simultaneity, your two firecrackers must be contained within the interval defined by their interaction with a third.
To talk of "simultaneity"; your two firecrackers must be contained by the same interval.
Any clock measuring the firecrackers forms a meta-clock containing the firecrackers as part of its structure. The firecrackers measure (subtract from) the interval of this meta-clock and it measures (adds to) the interval of the firecrackers.
The allegedly simultaneous firecrackers form a boundary with the meta-clock, which contains the firecrackers.
How do you know the firecrackers are simultaneous? You could imagine any number of tick-tocks between them? Adding unknown data?
The interaction of the firecracker-pair with a measurement firecracker forms a boundary to the allegedly simultaneous explosions (an interval between one firecracker and the clock firecracker contains the second firecracker).
How do you know this boundary firecracker is simultaneous with the pair? It could be any number of tick-tocks between the pair going off and the boundary firecracker explosion. Adding further unknown data?
"Simultaneity" seems to involve "containment by something else".
Doesn't "proper time" involve "containment"?