In about 2001 or so, reports began to surface about a new kind of thruster for a spacecraft. This thruster was said to produce a slight push in a way that violated the law of Conservation of Momentum. Despite this difficulty, there were experiments which seemed to support the possibility that the thruster worked.
The general idea was that microwaves would be produced and sent into a cavity where they would be reflected from the walls. One name given to this technology was resonant cavity thruster. Somehow the microwaves resonating within the cavity would produce a small thrust.
The objection that this violates a law of physics is not without basis. It would be similar to sitting in the driver’s seat of a car and pushing on the dashboard, expecting this to move the car forward.
Despite this objection, several scientists built and tested devices based on the principles offered by the inventors. Among them, NASA participated. NASA initially reported a slight effect; however, more careful measurements showed that the effect was caused by thermal effects.
The consensus is that the EM drive doesn’t actually produce any thrust at all.
It may seem puzzling why any scientists would try this drive, when the supposed effect was known to violate the laws of physics. However, these “laws” of physics are principles we have devised to explain what we see. It is not impossible that our understanding of the world is mistaken, and some of our “laws” are not so solid as we thought. It may not violate physics, but only what we thought we knew about physics. It helps to keep an open mind.