Anton
"From this result it is very clear to the me that information based
physics and Einstein's relativity are not compatible"
Leaving aside whether your concept of information, etc, this is not the issue. Einstein's concept of relativity (forget SR which is irrelevant, it is a conceptualised circumstance-he said so) deems there to be a time differential in physical existence. He did not say this as such, but this is the net effect of what he did say, once one discounts his mistakes. That is, he did not understand the reference used in timing, and thereby created an extra 'layer' thereof, which was counterbalanced by his failure to have any observational light.
In other words, he thought he was attributing the time differential to the relativity of observation, which is indeed where the time differential actually occurs. But he was not, because there was no observational light, which is a pre-requisite of sight. Any light Einstein alludes to (ray of, lightening, etc) is not observational light, just a constant against which to calibrate duration and distance, which he happens to exemplify in terms of an example of light. It could have been anything. But he chose examples of light for fairly obvious reasons, ie this is, if it is observational light, and not lightening for example, what enables observation.
What he said he was going to do is irrelevant, it is what he did that matters. That is, his declared second postulate is null and void as normally interpreted, because he did not have any observational light. It is, literally, just a statement of the obvious. Light, as a physically existent entity, always starts at the same speed (because it is the result of an atomic interaction not collision) and like everything else will continue at that speed unless impinged upon. De facto, in its 'pure' state, it will make a good reference constant, especially since, coincidentally, one needs light to observe, although any example of light is not necessarily observational light just because it is light.
The ensuing attempts, including his own, to rationalise observational light speed and rate of change (as manifest in timing) are pointless, because they are chasing an issue which does not exist.
Paul