Relativity isn't the problem. The problem is that hitting a grain of sand at 0.1 c delivers the energy of several tonnes of TNT.
My guess is that we will colonize the asteroid belt (Palladium! So much palladium!) and send lots of interstellar probes long before we try to send humans outside the solar system. Right now we're like a village that lives by a river and has never reached the mouth talking about sailing across the ocean. There are a lot of intermediate stages.
It's not only about palladium or any other kind of ore. It's that you can launch from there to Earth orbit and spare most of the costs of lifting mass from the surface of our planet. Then you build habitats and ships with that stuff because it's much cheaper. Too bad we don't have neither mining nor factories in space yet. Two not trivial technologies to develop.
The book Delta V [1] explores that scenario, with an asteroid on an orbit close to Earth to minimize the delta v to ship things back home.
> Right now we're like a village that lives by a river and has never reached the mouth talking about sailing across the ocean
And that’s an enormous understatement. Let’s say the villagers have travelled a meager 10 km of the river. Then, the ocean is, ballpark, at most 1,000 times as wide as the distance to the sea.
A thousand times the distance between earth and moon (the farthest humans have travelled) gets you, ballpark, to mars.
A lightyear is ~50,000 times the distance to mars or 50,000,000 times as far as humans have travelled. And yet, in interstellar travel, a lightyear gets you nowhere.
Sure, but the speeds you can realistically reach on the surface of a planet for any lenght of time is also many orders of magnitude less than you can reach in space & you also don't really loose speed by friction. That at least partially compensates for the mindboggling distances in space.
My guess is that we will colonize the asteroid belt (Palladium! So much palladium!) and send lots of interstellar probes long before we try to send humans outside the solar system. Right now we're like a village that lives by a river and has never reached the mouth talking about sailing across the ocean. There are a lot of intermediate stages.