I dont actually get this even in the simplest possible cases. Forget relativistic quantum mumbo-jumbo for a minute, if i have a simple system like a harmonic oscillator built out of a mass and a spring and i do a simple 3D rotation of the Cartesian system axis of course physics stay the same but the equations of motion dont. If the oscillator is horizontal in the "x" direction and i tilt it 45 degrees in the horizontal plane (passive rotation of the axes) then the motion is a mix of motion in the x and y axes, so the equations of motion are clearly different. So wheres the invariance?