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natural place replaced by natural movement/acceleration

Thanks to Tim, I think I got an iddee biddee grasp of the curvature of time-space.

It seems that Einstein's talk of "curved space" amounts an analogy between inertia and gravitational pull. That is, the Einsteinian recognition of the fact that things naturally accelerate toward each other as long as no (non-gravitational) force intervenes is analogous to the Newtonian recognition of the fact that things naturally move at a constant speed and in a constant direction with respect to each other as long no force intervenes.

And just as a Newtonian would deny that a force is involved in inertia (F=ma means that when 'a' or acceleration equals zero, 'F' or force equals zero), so too an Einsteinian (that would be all of us) denies that a force is involved in gravitation.

To make gravitation "look like" inertia, we might say that space/time is curved.

That is, just as we expect a projectile (not affected by extrinsic forces) to move at a constant speed through a Cartesian grid with a constant slope, so too do we expect it to move when gravitational objects are at work. Except the grid itself is stretched so that the direction at which the projectile moves is curved to us, but "straight" to the projectile.

Think of gravitationally caused movement from the (inertial) perspective of a projectile that has already been thrown and is presently being pulled to the earth. To US, it seems to be falling in a quasi-parabolic/elliptical path to the earth. But as far as IT is concerned, it is moving in a straight line. That is, it does not feel any force acting upon it any more than a person in a car moving in a straight line at a constant speed feels any force acting upon him. Granted, once it hits the ground the ground, it will feel plenty of force. But that is just like a car moving at a constant speed feeling force when it hits a wall.

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