In Newtonian physics, object A observes the acceleration of object B precisely when A observes a net force acting on B. How should we understand perceived acceleration under the observed expansion of the universe? Can it be attributed to a force? Does this mean that there is no such thing as an "inertial reference frame?"
Thought experiment: Two spherical objects A and B are at rest in empty space and are charged in such a way that the net force between them (gravitational and electromagnetic) is exactly zero. Thus, there is no observed force or acceleration between them, and thus no movement is possible. Since electromagnetic force and gravitational force are both inversely proportional to the distance squared, no matter the separation between the two, their forces acting upon each other will always net to zero.
After a certain period of time, the space between the two objects is measured to have expanded. How do we explain what happened? At each moment there should be no net force observed between the two, yet there also appears to be a relative acceleration between the two. Should A therefore believe that some force was acting upon B?
I am also interested in the question if these two objects should be considered to exist in the same inertial reference frame. Since there is no "real" net-force between the two, perhaps the answer is "yes". Yet, since there is observed acceleration between the two, perhaps the answer is "no". This thought experiment may demonstrate that the existence of an ideal inertial reference frame, though not theoretically impossible, is an experimentally observed impossibility.