I am sure that the next big step in FTL or time travel will be a completely revamped understanding of the equation for "time". Since time doesn't exist but we insist on it, it keeps "ruining" the equations for true progress.
Think of it like this - We look at a star blazing at 20 million light years away. The light taking 20 million years to get to us should mean we are looking backward in time. But we aren't really. As we stand there, looking at the light, the planets surrounding that star, possibly filled with intelligent life looking back, are doing it in real-time.
We are looking backward in time, but on the other end is a real-time event occurring and only our perception of time and distance distorts the truth.
Leave the math on the table, go outside and look at any given star. It's old light, but across that space is a real-time event. How do we bridge the gap and remove that pesky 'ol time equation?