I have been going over a bit of a thought experiment in my head lately. And wondering if someone more informed on the matter can share their thoughts
Let's start with the premise that rocket/ propulsion technology is continuing to develop at some sort of rate. Not exponentially, but it would be logical to assume that in 100 years rockets will be faster than they are today (minus any doomsday scenario).
Let's say just for the sake of the thought experiment, we have the technology to cryo freeze passengers until they arrive. (This isn't really relative to this "Paradox", but it makes the thought experiment more relatable)
Let's say that starting today, we start sending a rocket to or closest star- Proxima Centauri every 50 years.
Over the span of say 10,000 years we would have sent 200 rockets. But would this not mean that due to ongoing technological advances that the 200th rocket would arrive first and the 1st rocket would arrive last?
So until we reach a speed threshold (e.g speed of light), it would be pointless sending multiple rockets to one star, since no matter what, people in the future will arrive there before you.
Does this logic make sense? Has anyone thought of this before?
What fast a rate of speed development is required for this to happen?
How slow a rate of speed development is required for it NOT to happen?