Experimental Physicist here. I don&#x27;t know how unlikely it is that I&#x27;m reading this on a Friday night. No, I have a life, really.<p>We know quite a bit about electromagnetism.  There probably is lots of undiscovered fundamental physics. However, we wouldn&#x27;t necessarily need to discover new physics in order to do cool stuff like float something on the Earth&#x27;s magnetic field.  The breadth of phenomena which electromagnetism covers is huge, and many people spend a whole career working with just that one force.  It might just be that we haven&#x27;t thought of the right way to use it yet.<p>The difficulty with floating something on the Earth&#x27;s magnetic field is actually less about the strength of the field, than it is about its gradient. Because the Earth is so big, for the field to change by a few percent takes many miles of distance This is assuming we are talking about the average field as a whole, and not any anomalies which distort it, because if you are using a distortion of the field, whatever is distorting the field, like a magnet, is really what you will be pushing against.<p>Because force = energy divided by distance, and the strength of the earth&#x27;s magnetic field is essentially a energy density, if even a weak field changed over a small distance, an appreciable force could be generated on an object which interacted with that high gradient field.<p>But since the Earth&#x27;s field changes very slowly over distance, most of the ways of interacting with the field (like using an electromagnet such as in an electric motor) won&#x27;t give us very much force. Instead, we would have to use some other means which depended less upon the field gradient.  Some of these other effects would be e.g. the Hall effect, or an E x B drift.