[ajross]

This is a clever analogy, but it's actually a little specious.

The reason the "g-meter" (e.g. a weight on a scale) doesn't move in the gravity case is that the weight is affected by the same field. The weight is a weight and feels gravity just like you and everything else in your environment does.

But by construction, you're imagining that the scale you have holds a different electrical charge than the object to which it's attached. Which is "normal" according to our everyday experience, but just an artifact of the way charges work on large objects (they distribute themselves on the "outside" of a conductive environment and everything inside tends to have a neutral distribution).

But that's just arbitrary. You could equally demand (in your gedankenexperiment, though doing this in practice would be very difficult) that your electrical charge be distributed just like the mass is, in which case the force measured would be zero too.

[User23]

As an aside there are real gravimeters that aren’t scales and they are sensitive enough to detect a person walking around the room they are in and snow accumulating on that building’s roof. Yes that’s right they detect the gravitational force exerted by the snow’s mass.

[pdonis]

> Yes that’s right they detect the gravitational force exerted by the snow’s mass.

No, they don't. Gravimeters of the type you describe measure the coordinate acceleration of a freely falling test object in the accelerated frame of the gravimeter. In other words, it's the gravimeter (the part that isn't the freely falling test object) that has a force acting on it, which makes it accelerate upward (proper acceleration--an accelerometer attached to the gravimeter reads nonzero), and a freely falling test mass therefore appears to accelerate downward (coordinate acceleration in the frame of the gravimeter), just as if the gravimeter were inside an accelerating rocket out in deep space far from all gravitating bodies.

In other words, gravimeters of this type rely on the equivalence principle, which is the same principle that GR uses to justify the statement that gravity is not a force.

[ben_w]

Rather more pertinently to the question "why is gravity different?", we can measure the time dilation caused by a gravitational potential change of less than 1cm near the surface of the Earth: https://physicsworld.com/a/gravitational-time-dilation-measu...