Why can we not treat gravity as a force?

A four-vector has certain transformation properties. Those terms involving Christoffel symbols do not. Even in a flat space using spherical coordinates, you would get apparent acceleration for a free particle.

 

Additionally, how would you split the Einstein field equations into a source providing force equation? The Geodesic equation has enough problems as is, interpreting one side as a force, the Einstein field equations would have just infinitely more problems on that front...

 

Reading this thread triggered an interest in fictitious forces and I googled to get more information.Some promising stuff seemed to come up but there was something which confused me.Writing about fictitious forces for "Scientific American" David Pollitzer referred to General relativity and amongst other things stated

"The cornerstone of Einsteins theory,however,is the proposition that gravity is itself a fictitious force(or, rather,that it is indistinguishable from a fictitious force)"

So what is it? Is it considered to be a fictitious force or just indistinguishable from a fictitious force or something else? Thanks if anyone answers.

Try googling What is a "fictitious force"
Caltech 2004 Nobel laureate David politzer writing for "Scientific American"

 

I think that's an unnecessary distinction. If you can't tell a bird apart from a duck, then the bird is a duck, not indistinguishable from a duck.

 

Locally indistinguishable. When you take their derivative you find that fictitious forces do not have Riemann tensors.