The motion of a conductive wire in a uniform magnetic field causes electric field in the wire (thanks to the magnetic force that pushes free charges). From relativistic point of view, it should not matter whether the wire is moving and the field is stationary, or the field is moving and the wire is stationary. But how can you distinguish moving and stationary uniform field in equations?
Another example. Let us have two disc magnets and a conductive disc between them. The magnetic field passing through the disc is axially symmetric. If the disc spins, the electric field builds up within the disc (pointing radially). What happens if you spin the magnets? It should have the same effect, but the field is in fact still the same although the magnets are spinning, so how could it affect the disc?