I don't understand how its a fictitious force and why you need to be in the rotating frame of reference to observe it? In the example of the moon and the earth and its tides. You have the centripetal force causing the tides to increase at the point where the earth is facing the moon and the centrifugal force to form tides where the earth is opposing the moon. Now this can be observed when your at some arbitrary point in space in an inertial reference frame cant it? If im floating in space above the earth at a point where i can observe both points of the earth in mention simultaneously then i would observe both tides would i not? If the centrifugal force was fake, then i would not observe the tide in the opposing side of the earth and if im standing on the earth in the non inertial reference frame i still observe the tide? So i dont understand, i must have something terribly misconstrueded here.