Space Elevators Are Possible

Great! What does the paper say about overcoming some of the problems that seem to make it tough, like the radiation that humans will receive riding up, or avoiding space debris? I'm assuming problems like building a rope strong enough to hold its own weight will be overcome, as well as developing the technology to climb the elevator.

The fragile humans could still hitch a ride on a (reusable) rocket and extraplanetary garbage collection is something that is currently being proposed and could be a good source of materials too.

Radiation is only a minor concern, astronauts in the space station experience similar radiation doses. I assume if it's cheaper to get things into orbit [with the elevator], it's also cheaper to shield the entire contraption. Climbing isn't much of a concern either, they've already run a bunch of tests and NASA has already awarded their prizes out for the challenge. The real issue is mass producing the carbon nanotubes.

It's like saying "Warp drive is possible" then saying all you need to do is build a ship that can manipulate the fabric of spacetime. Well of course that's all you need to do.

Sure, producing carbon nanotubes is easy. I've seen them make the it in a lab. It's making the tubes to spec and making thousands of miles of the stuff that is the hurdle. It's the equivalent of asking computer engineers in the 60s to mass produce 22nm CPUs with billions of transistors. Can it be done? Sure. In about 50 years.

What happens if something hits the cable and it breaks? Does the whole thing drift off into space?

Depends where it hits.

On the tether there is a "zero" point. Below that point things fall toward the Earth, above that point things "fall" away from the Earth.

So it depends on where it broke and how much weight there is above vs below that point. (To keep the tether in the air they put lots of weight above the point, which falls away from the Earth and pulls the tether taught.)

If I were making one of these I'd make several tethers, spaced such that a single object can not break more than one at once. Then tie the tethers together periodically.

This object is about max: https://en.wikipedia.org/wiki/Tunguska_event so I'd make the multiple tethers at least 200m apart. That's pretty far apart, so I'd invest in better detection technology to reduce the size maximum undetected object. (Although that raises the question of what to do if you do find a big one and it's headed right toward you.)