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 Quote by TurtleMeister It just seems unintuitive to have to set my frame of reference to one or the other objects. Lets take the following example: An object in Earth free-fall will accelerate at the same rate regardless of it's mass. That is true.
As perceived by whom? Let's ignore the Earth's rotation. Suppose we have two observers with infinitely accurate means of assessing acceleration. One is fixed with respect to this non-rotating Earth and the other is fixed with respect to some inertial frame. Both measure the acceleration of an object falling toward their Earth at the same time with their infinitely accurate sensors. The two will measure different accelerations.

Now suppose we use a different test object whose mass is orders of magnitude greater than that of the first test object. Both observers measure the acceleration of this new test object after placing it at exactly the same position with respect to the Earth as the first test object. While the Earth-based observer will measure a different acceleration than measured for the first test object, the inertial observer will see this new object as undergoing exactly the same acceleration as the first test object.

Another way to look at this: Imagine two cars, a blue one and a red one, in a drag race. From the perspective of someone in the grandstands, the blue car's acceleration is amazingly high. From the perspective of the driver of the red car, the blue car's acceleration is fairly small. In fact, the driver of the red car most fervent wish is that the blue car appears to be accelerating backwards.