Earlier quoted context omitted.
You are mixing two things up - figuring out the time an event happened and trusting a timestamp that someone attached to an event. Within a single inertial reference frame there is a canonical way to order events, namely by the time coordinate in that reference frame which is the same everywhere. And for all practical purposes of building a distributed system on Earth, Earth is an internal reference frame. Ensuring t…
You didn’t explain how a distributed byzantine system can synchronize a global time that’s continuous. I am saying that you won’t be able to — local time is continuous and you should use that for comparisons. It’s nowhere near as straightforward as you think to make global time work. You will find that “making sure nobody can or will cheat” will require exactly the kind of effort that will make the concept of a globa…
I never addressed what else is necessary to make this work in the presence of Byzantine faults. But I am also pretty sure that just sending information about events from A and B to C and asking C about the ordering is not sufficient, after all C may be faulty and give a wrong answer, change its mind after every query, or just not respond at all. Admittedly you did not provide many details, so I may very well totally misunderstand what you had in mind.
But, just to repeat, I am not really addressing the requirements of a Byzantine fault tolerant system, I am just saying that the special or general theory of relativity is not relevant for distributed systems on Earth.