It's tricky Pete, rereading it I confuse myself

I want to put it into my own terms, and then I would say that gravity is observer dependent. Then again, I'm always wanting to define it locally. when I say that I agree to that 'gravity must exist everywhere' I'm using what I call a 'global definition', as opposite to a local, it makes it clearer for me defining it such, a local definition of a geodesic versus one where I speak about a whole 'SpaceTime's' gravity.

You write "Einstein did not interpret gravity as a curvature of space-time, rather that space-time curvature is a manifestation of gravity." giving me a feeling that you then may consider it a 'force' defining a SpaceTime. That would then be from what I call a 'global definition', not local.

Alternatively I could read it as a statement that something is needed to create gravity, mass (energy), and so define a SpaceTime. And it is true that the elevator example only can be used ignoring tidal forces, as you otherwise would be able to differ between the 'gravity' you find in a uniformly constantly accelerating rocket, relative on Earth. And so restrict the equivalence principle.

The question then becomes what one consider tidal forces as? Myself I think of it as 'gravity' too and so consider it irrelevant for a wider definition of the equivalence between gravity, and a uniform constant acceleration? Either there is a equivalence, as I think now

and then this exception (tidal forces) is something solvable, or we have a situation in where Earths gravity, as it involve tidal forces, can't be applicable to a uniform constant acceleration of that elevator.

I guess I'm using it in its wider sense, if I now would try to define it.

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If a geodesic is something without 'forces' acting on it, in a free fall finding no gravity acting on you, no friction or resistance retarding your uniform motion, then that should include tidal forces? If I exclude tidal forces from that definition, I come to a definition in where I have to assume that this ultimately will retard my uniform motion, as I think. But I have to admit that I found geodesics to be one of the most difficult assumptions to make, as from my 'global definition' gravity and tidal forces exist everywhere matter is. And if we then include the way binary stars act gravitationally, as well as other tidal forces, then there is a 'friction' to a geodesic too. And all mass have a gravity acting on them, even in a geodesic, the gravity created by its own mass though.

I've been thinking about it actually, now and then, wondering if there is some better definition I can make, the one I'm leaning too is one in where a geodesic will be defined by gravity, including tidal forces, and it won't matter if matter 'spagettifies' under its influence. The directions 'they' take, under and after, such a event should still be geodesics, to make sense for me. So you might be able to see it as 'straight lines', without resistance, although for the poor bast* getting split

, as well as for any other observers, might want to define a 'force' to it.

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But that is what I call a global definition. From a local point of view a ideal geodesic must be free from 'friction', in a constant uniform motion (or uniform gravitational acceleration as it comes down to the same. No 'local gravity'), to fit the idea I have of it.

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If you look at

"Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation.

According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation."

then I feel I have gotten the idea right

That's how I think of 'tidal forces'.