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The answers here are very scientific, but I always wondered if having a magnetic shoe sole could fake gravity? Is there a ‘floor’ to stand on in these ships?
Not really, magnets only really pull when they are close enough and would only really fake gravity in helping you maintain one orientation, that could be easier to achieve with velcro shoe soles.
It wouldn't be enough. Sure you could use magnetic boots to keep you "attached," to the outside of a magnetically affected spaceship's outer hull, though I would imagine that with the lack of atmosphere and magnetic field to protect you from space radiation we may be inclined to use materials that aren't necessarily magnetic in nature.
All that was to say, yes it would possibly work as a backup tether, but since nothing is pulling on the rest of your body it wouldn't simulate gravity as much as simulate a tether rope that keeps you from floating away.
Inside the ship it is easier to pretend to be a parkour expert than having magnetic shoes.