Would it be possible to make a ladder from the moon to the Earth and to be able to climb up it onto the moon?

Question: Would it be possible to make a ladder from the moon to the Earth and to be able to climb up it onto the moon?
- Keywords:
  space
Asked by moseleyj to Andrew, Daniel, Hayley, Natalia, Peta on 15 Nov 2011.
- Daniel Scully answered on 15 Nov 2011:
  
  Not to the moon – the moon orbits the earth so your ladder would get wrapped around.
  
  But actually the idea of building a lift into space is not really so crazy. It’s mentioned a lot in science fiction and the idea is solid science.
  
  You have a very strong cable extending into space, attach a counterweight to the end, and the force of it spinning holds the cable up. You also ensure the end of the lift orbits the Earth at the same rate as it spins – so it’s always above the same place.
  
  Of course you need a very strong material to make the lift out of, and when you go past a certain point the overall force on you is pulling you away from Earth!
  
  If you could build one, it would make travelling to space much safer and require a lot less energy!
- Hayley Smith answered on 15 Nov 2011:
  
  Ah, Daniel beat me too it – see his answer re why not to the moon, but definitely look up “space elevators” the big cable ideas he describes, they’re pretty cool ideas! I remember we had a student presentation competition at university and quite a few people talked about these…! http://en.wikipedia.org/wiki/Space_elevator

Question: Would it be possible to make a ladder from the moon to the Earth and to be able to climb up it onto the moon?