"Now, if I attach my reference frame to the elevator, I'll still see the dropped object fall, afterall, doing that is the same as saying I'm in the elevator."<br /><br />Yes, but if you attach your reference frame to an elevator, you will see the object fall with a different acceleration. In fact, depending on the acceleration of the elevator, it might appear that the object is falling and accelerating up. Newton's laws predict acceleration as a function of force, and force as a function of gravity. In a non inertial frame, you will observe accelerations different than those predicted by Newton’s laws<br /><br />For example, if you are in an elevator accelerating up at 20m/s^2, and a brick passes by your window, it will appear to you to be moving at 29.8m/s^2. If the brick has a mass of 10 kg, Newton’s law of gravitation predicts a force of 98 newtons between the earth and the brick, which results in an acceleration of 9.8 newtons. That differs from observation, which is why Newton’s laws don't make the correct predictions in non inertial frames.<br /><br />Newton never discussed fictitious or phantom forces or non inertial reference frames, to my knowledge. To make the correct predictions in non inertial frames, Newton's laws must be modified.<br />