Heh

Sweet idea, assume that you have two objects that move apart. Both defining the other as accelerating away, would that be a real acceleration?

Can one think of a way to disprove it as a acceleration? How about assuming that you have a 'sphere of objects' (planets/suns) surrounding you and you find them all accelerating away from you? Is it them or you? You decide it is them accelerating away and you call up one of them to ask 'what's up with all that acceleration, is it my smell or what'?

Now, if the answer you get is that he, same as you, finds all objects accelerating away from him, where is the acceleration? What degree of freedom, or dimension as they say, are all those objects 'accelerating' in? There is one point more to consider, in all accelerations there should be present a 'gravity/inertia' raising.

If we don't find gravity to raise, can it then be a acceleration?

In what degree of freedom?