Whenever I read discussions about space travel and trying to approach the speed of light for human travel I have the feeling there's a lot of tunnel vision (excuse the pun). It always seems to assume travelling along a linear path through space.
In my mind, using the admittedly poor analogy of space-time as a membrane that is distorted by gravity, my thinking is we'll find some way to effectively bring two points in space-time adjacent to each other and 'step' between them. Wormholes, Warp, or whatever you want to call it.
Think of a flexible membrane 10 meters long and we are going to travel from one end to the other. We can either travel in a linear fashion over its surface for 10 meters or we can wrap the membrane so both ends are next to each other and travel 0.01m across the gap between them.
Yes, I know there are all sorts of obstacles and arguments against this simplistic visualisation but this is how I've always imagined the physics of any science fiction faster-than-light travel - worm-holes, warp drives, etc.
If you want an actual, real, possible-right-now analogy, think of our current situation where the fastest way to travel from London, UK to Sydney, Australia (1/2 way around the world) is through the atmosphere in an aeroplane travelling ~17000 kilometers and taking at best 19.5 hours.
SpaceX (Musk) Virgin Galactic (Branson), other companies [0], and space agencies [1] have talked about, and are actively working toward, stepping outside the atmosphere into space to reduce the time element to around an hour.
So just like with supposedly faster-than-light travel, by 'stepping outside' the linear/conventional thinking/physics we reduce the time of travel element dramatically. The start and end points don't move but the distance travelled by the transport vehicle itself changes in order to enable the reduction in time.
[0] https://www.telegraph.co.uk/travel/news/new-flights-space-lo...
[1] https://edition.cnn.com/travel/article/hypersonic-flight-air...