I suppose I'll answer anyway, even if the question has nothing to do with quantum physics.
According to currently accepted theories, there cannot ever be faster-than-light travel. The only way for future technology to achieve FTL travel is if current theories are wrong.
When will we realize that the current theory is wrong and replace it with a better one? Who can say? Science tends to work in leaps and bounds -- contradictory evidence collects like snow on a mountain until someone shouts and starts an avalanche. There is probably no way to predict, in even vague terms, when we might reach another turning point in physical understanding.
One would think that, as science progresses, it stabilizes onto a set of valid theories. When these accepted theories no longer change for a very long time, one might even be willing to declare them "done." Modern physics has been evolving very quickly in the last 200 years or so. But how long is 200 years in terms of scientific evolution? How can anyone say with even tenuous conviction that 200 years is or is not enough time for mankind to learn all the rules? How about 2000?
I guess the bottom line is that it's pointless to concern yourself with the duration of a process you've never seen before.
- Warren