Suppose you were in a free falling box in a strong gravitational field. Is there an experiment that you can do within that box which would measure the accelera

Suppose you were in a free falling box in a strong gravitational field. Is there an experiment that you can do within that box which would measure the acceleration? I think no. Not directly (perhaps you might get clever and do something with tidal forces). And if you can't measure it, why do you assume it's there? By contrast, if you strap a rocket to the box, it's quite easy to measure the acceleration from within the box. To argue that the acceleration exists because the position changes is to assume that the observer's reference frame is somehow the correct one, and Einstein has showed us that that's a problematic assumption.