[deleted]
Anton,
The idea to use this thought experiment to prove that information-based physics and relativity are incompatible, is quite original. Whether or not you have succeeded in your purpose is another question.
Let's look at one particular detail. The analysis of the thought experiment yields the equation on page 2; you then claim that this equation forms a contradiction with your axioms of information-based physics. The correctness of your proof thus depends on the correctness of the equation, and the correctness of your axioms of information-based physics.
On the right hand side of the equation, we have c²+v²/c²-v². This is a ratio between two real numbers, which is again a real number. So on the right hand side we have a real number. For the equation to be correct, the left hand side must thus also be a real number. That means that the symbols ICharlie and IBob must also be real numbers. From the text it is obvious that these symbols represent information. Thus, in your essay (or at least in the thought experiment), information is a real number. Can you give a motivation for that? E.g. in quantum physics one says that the wave function contains information. But the wave function is a much more complex entity than a real number. So could you elaborate on your choice to represent information by a real number? Or do you mean not information but the amount of information?
Best regards,
Marcoen