Sure you can. One possibility is to put the upper terminal at the L2 Lagrange point. Sure, it’s unstable, but you pretty much need active station keeping anyway, so it’s not a huge deal. Another possibility is to put the lower terminal at one of the poles, which consists of a tower with a rotating pivot. The upper terminal can then orbit at whatever rate you want. This version would also need active power to recover energy losses since it doesn’t get anything from the Moon’s rotation, but solar power should be plentiful at any rate.
In other words, “magic”. :rolleyes:
I would assume that we would have the capability to build such a thing before we have the magic self-healing materials.
The material doesn’t need to be self-healing, just the whole system. Perhaps it would be more palatable to you if it were called “self-repairing”?
We have them already:
Check out Arthur C. Clarke’s The Fountains of Paradise for a good sf novel on building a space elevator: The Fountains of Paradise - Wikipedia
The question is…
Going from 0 mph (1000 mph on planet relative) to 16000 mph (orbital speed), via rope ladder…
Where would you feel the acceleration, if the elevator rises at a moderate rate of 1g all the way to apogee?
Where does the extra energy go?
You cant just poof up to that to that speed and have no consequences. :dubious:
You are not going from 0mph, but at surface rotational speed.
Typically you get to travel at a semi-constant speed up, not accelerating.
Also the trip in the book took IIRC 7 days to geosync.
Gravity goes from 1g on the earth (same as the surface), to zero at geosync to negative beyond geosync. So you would go from 1g to 0g’s over a 7 day period, and that would be gradual (not a instant fall off), at Geosync you need to move your luggage and stuff from the floor to the ceiling as the ceiling becomes the floor.
The part I think you are talking about is the rotational speed, and rotational acceleration. That is what is responsible for the loss of g’s, so you are accelerating at the rate of your current g.
Yes, there are consequences, but maybe not the ones you might expect. The rising elevator car experiences a sideways tug due to Coriolis Force; see this diagram from Wikipedia.
http://upload.wikimedia.org/wikipedia/en/thumb/5/57/Space_elevator_balance_of_forces--circular_Earth--more_accurate_force_vectors.svg.svg/744px-Space_elevator_balance_of_forces--circular_Earth--more_accurate_force_vectors.svg.svg.png
These forces might be sufficiently disruptive that the elevator becomes unusable, or at the very least slow the elevator down to a crawl. The slower the car goes, the lower the resulting Coriolis forces would be.
And while we’re at it, the car can’t rise “at a moderate 1 g”. If it did that, it’d just stay parked at the bottom forever. You’re going to need at least some higher acceleration to get started.
I’m trying to come up with a smart assed remark about Einstein’s idea that in a constantly accelerating reference point, there is no experiment to tell you that you are accelerating, but it’s no go. 
I think I needed to correct/augment my statement on this. It is the initial burst of acceleration, from surface to ‘full climb speed’ is the force that opposes gravity (F=mA), that starts giving forward motion. All the rest of the force just goes to negate gravity and keep the elevator moving upwards at a constant rate.
So it is not the g force that gives the energy, it is the initial g load that is over and above surface gravity that is responsible for the craft rising. As long as power is supplied to the traction motors to oppose gravity the craft will continue on it’s straight line path after acceleration.
As for the orbital velocity change, that would be transferred/supplied from the stalk, which could cause problems as mentioned in the above post.
Aha! I KNEW there would be side-loads! 
Oh, yeah, definitely side-loads; I should have confirmed that earlier. They should be manageable, though, as long as your cable is significantly more massive than your cars, and you have comparable mass going up and down, both of which are reasonable assumptions.
I thought from an earlier post that there were no loads going down.
Yes in the book most loads were up only, then once they got to the ‘top’ used to augment the counterweight. There were a few cars that went both ways however, including maintenance cars.
In the early stages, you’d have a lot more loads going up than down, just because there’s a lot of infrastructure you’ll want in space (such as, for instance, more space elevators or similar devices on other planets). But once you’ve got that infrastructure in place, it makes more sense to keep the loads balanced, even if it means shipping back tons of rock. Heck, a trade of Martian iron ore for Terrestrial seawater would probably be profitable on both ends.
Except that ore (which is more likely to come from asteroids) is far more valuable in space, to build more ships, bases elsewhere in the system, etc.
One thing that might be desirable to import from space would be rare earths mined from asteroids. Our planet has a lot of these, but we can expect that demand for rare earths will go up over time, assuming we have the sort of advanced civilisation in the future that can build space elevators.