Contrary to what Red Bull would have you believe, balloons aren't a very effective means of reaching space. A balloon got Felix Baumgartner about 24 miles up, but the cable would have to go out beyond 22,000 miles.
Well you can't just fly 22,000km of cable into space with a rocket, and then drop it down. Using balloons to cover the first few km could save a bunch.
Also, there's a rather large difference between a multi-billion dollar internationally supported scientific operation, and a few million dollar marketing stunt.
If you can make a few hundred meters long carbon nano tube (which we can't right now), what's stopping you from making a balloon with a circumference of a few km, and how much cable could you lift up how high with that?
Since gravity decreases quadratically, the first miles are the ones that count.
Gravity does decrease quadratically, but the origin is the center of the earth, not the cable's anchor. The earth's diameter is over 12000 km, so gravity would not decrease significantly over the 10s of kilometers the balloons supported.
The cable has to be "anchored" beyond the point of geostationary orbit in order for it to pull itself taut and keep itself in orbit, else its own weight would cause it to simply fall back to Earth. Anything less than that would be an extremely tall building, and subject to the same limitations therein.
Also, there's a rather large difference between a multi-billion dollar internationally supported scientific operation, and a few million dollar marketing stunt.
If you can make a few hundred meters long carbon nano tube (which we can't right now), what's stopping you from making a balloon with a circumference of a few km, and how much cable could you lift up how high with that?
Since gravity decreases quadratically, the first miles are the ones that count.