Why acceleration due to gravity is not reliably defined? In Sean Carroll's Spacetime Geometry, there is the following line on Page No.50 in 2014th edition:
"The acceleration of a charged particle in an electromagnetic field is uniquely defined with respect to inertial frames.The EEP,on the other hand,implies that gravity is inescapable- there is no such thing as a "gravitationally neutral object" with respect to which we can measure the acceleration due to gravity. It follows that the acceleration due to gravity is not something that can be reliably defined,and therefore is of little use"
But, we do measure acceleration due to gravity of earth and moon.
So why acceleration due to gravity is not reliably defined?
Does this mean we cannot measure the true value of acceleration due to gravity of any massive object?
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Carroll is stating the equivalence principle.

But, we do measure acceleration due to gravity of earth and moon.

I assume you mean here the acceleration of some other object, such as a rock, due to the gravity of the earth (with the moon as an additional example). You can measure the acceleration of a falling rock relative to the earth, and you'll get $9.8\ \text{m}/\text{s}^2$, but that doesn't mean that the gravitational field at the earth's surface is $9.8\ \text{m}/\text{s}^2$. There are also gravitational fields due to the moon, sun, and other bodies. Since gravity is a long-range force, we have no way of ever being sure that we've accounted for all such fields. Some very massive object very far away, which we've never detected optically, could be causing our entire galaxy to accelerate in some random direction at $37\ \text{m}/\text{s}^2$.
In Newtonian gravity, we imagine that we're supposed to know where all the masses are in the universe, so we would add that vector to all the others, and find the true answer. In relativity, it's not possible, even in principle, for us to know where all the masses are in the universe, because most of them are outside our past light cone.
