What would be your definition of 'local'? I was merely referring to making measurements at a spacetime point to avoid any arguments over tidal forces and so on.
One where the EP applies.
That makes no sense at all - 'local' in the most extreme definition refers to a single spacetime point, which must see a Minkowski metric. That is why GR guys get so pissed off with people like
Teyssandier who do work implying that you can measure your absolute gravitational potential locally.
For the purposes of this discussion, 'local' means 'human scale', where we assume that we deal with fields weak enough to neglect tidal forces. That's basically any field away from an event horizon or objects moving at relativistic velocity compared to the observer.
Those positions are not incorrect. Their paths would go through the ground so going through the ground is up? There net acceleration is still zero.
Their spatial paths go nowhere - that's the whole point of a geodesic. Their space-time path (the geodesic) goes through the ground, which means that when they come into contact with the ground they experience an acceleration which causes them to leave their geodesic (contact acceleration). The ground is accelerating them upwards. If they are in an inertial reference frame then they're not going anywhere in any meaningful sense, it is the ground that accelerates up to meet them. That doesn't make much sense from the perspective of you standing on the ground, but nature doesn't give a shit what makes more sense to you, that's just the way it is. Get over it.
I can measure the same force whether I am driving my car or a Ferrari. So I drive a Ferrari? A person on the ground is undergoing a constant physical acceleration downwards which causes a normal force to be felt.
No. A person experiences a normal force and hence a normal acceleration as a result of being in contact with a giant mass of rock. There is no 'natural acceleration' since if there was then we would be able to measure it while in free-fall (an inertial frame) with an accelerometer.
In that sense, the skydiver and the person on the ground could agree that the Earth accelerated up to meet them, because that is what the only sensible coordinate system says happened. If you choose to constantly reset the ground to be 'zero' in your co-ordinate system then of course you will get a different result, but that co-ordinate system is a non-inertial one.
The sensible coordinate system you speak of is by definition, accelerating.
Surely a sensible co-ordinate system is one in which 'rest' and hence the zeroes of the axes are defined when no forces are felt on the observer? That frame would be free fall, so if the observer sits at zero until he feels a force on him, then it is the guy on the surface of the Earth that is accelerating, not the free-faller. This makes a lot more sense than setting some arbitrary acceleration (
g) to be 'zero'.
Objects traveling in locally straight paths can still accelerate.
No, they can't. A locally straight path is a geodesic, which follows a straight path through space-time.
Free-fall is inertial motion even thought there is acceleration present.
Free-fall is an inertial frame. You experience no acceleration in an inertial frame. Inertial frames can not accelerate. You are thinking in terms of a non-inertial co-ordinate system - this thinking will lead you to draw incorrect conclusions, as has been demonstrated already.