some natural limits
Yes, When it comes to FTL I think we have hit a barrier that will be resolved in the far, far future, if ever. I would say never but when you consider what we have done in the last 1000 years, it is hard to say never.
IMO our interstellar exploration will be a combination of advance propulsion systems attaining increments of light speed and various types of life extention.
The problems of extending our lives to 1000 years+ are minor when compared to the scifi solutions to FTL.
