Damn small edit timelimits!
[quote user="EddiePedant"]But, if we wanted to calculate in this 2g frame a lot, we might just use this "anti-gravity" pseudo-force to make our calculations a bit easier. Would "anti-gravity" be any more real then?[/quote]
Depends on your definition of "real". Who says that an inertial frame is more "real" than a non-inertial one anyway?
All frames are equally valid. You cannot preferentially choose one frame over another. Yes, you can easily generalize a set of laws for the set of inertial frames, but that doesn't doesn't make non-inertial ones into pseudo-frames and it doesn't make forces in those frames into "pseudo-forces" either.
What if that box dropping at 2g had no windows? What if you had no other frame of reference to compare it to? How would you know your frame was not "real"?