If anybody goes back down, they reverse the movement they caused climbing up.

but hes in zero gravity , he can let go of the ladder after he reaches the end and then apply a tiny force that will send him to the other end.

so he will exert more force climbing than he will returning.

and the tiny force he applies to get to the other end
will cancel out when he reaches the other end.

we could eventually design a human powered spaceship
that has artificial gravity and reactionless propulsion.

as in people at both ends creating artificial gravity by jogging around a circular track.

and people jogging towards one end in the artificial gravity
then climbing up to zero gravity and then propelling themselves
back to the other end , then climb back down and jog to the other end again.

we would really have some healthy astronauts.

3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.