The search for free energy
Again and again we see a machine developed, with a few people reporting that is produces over unity results. Often patents are granted - so other people should be able to reproduce the results - but they never can. In the following decades there are always problems - financial, technical, personal - which prevent a commercial power supply from being built. Of course the real reason that it can't be built is that it's impossible. But people still go on believing.
Vacuum energy seems to be a popular source for free energy devices, but since their designs have little to do with quantum field theory one might just as well say that the energy appears by magic.