[pdonis]

> Put this way, isn't it almost begging the question? In GR the definition of acceleration is movement in contrast with the movement of gravity.

No, it isn't. You have it backwards. The definition of acceleration in GR is proper acceleration, i.e., what an accelerometer reads. The "movement" property is then a consequence of this plus picking an appropriate frame of reference.

> If instead we had a universe where instead of all matter having a gravitational effect, it was that all matter had a magnetic effect the we'd see no acceleration due to the magnetic effect

Yes, you would, because unlike gravity, magnetism does not obey the equivalence principle, so differently charged objects in the same magnetic field with the same initial conditions can have different motions. With gravity, all objects in the same field with the same initial conditions have the same motion, regardless of their mass. That is why it is possible to model gravity using spacetime curvature, and that property is unique to gravity.

[lostmsu]

I'm sure you are familiar with Kalusa-Klein theory (knowing that it is incomplete and/or doesn't describe our universe), don't you think that motion in that theory is less bound to gravity alone like the parent comment suggests because the notion of proper time is different?

I tend to gravitate toward the same line of thinking because of the existence of black hole charge limit.