how do you replace elevator hoist ropes?
You dont you get somone qualified to do so.
Are you asking for a technology that could take their place or how to fix them? A megnetic field or complex sorts could be easily used instead of hiost ropes. Many modes of transportation are possible due to magnets. an emergency rope could be in place just in case. I agree though, if you're trying to fix them, you need an expert.
Make sure the elevator is at the bottom of it's travel, and blocked against falling further. If the hoist rope is not broken, disconnect one end from the elevator. They make a tool I always called Japanese handcuffs that fit over the rope. It is a tool made of fine woven cable that when pushed on endways the inside diameter Increases, and when pulled on it gets smaller. If the end is not smooth, cut it smooth. Attach enough rope to the end of this rope with the Japanese handcuffs and engage the motor. When the new end arrives at the elevator, tie it off to whatever it is tied to taking out all the slack you can. Cut off the excess and tie off the other end and you are done.