Math of General Relativity - Addendum 1
In this rotating Ring World (https://tinyurl.com/yda8kzyq), everything is being pushed up and making everything stick against the inside walls of the cylinder because of the force of gravity. It is not artificial gravity.
Consider a ball laying on one of its streets, relative to an outside observer watching the Ring World turn. At any point in time, you can calculate the path that the ball wants to be in from Einstein's General Theory of Relativity. It wants to keep going in a straight line. Gravity is exerting a force on the ball, gripping in its power, making the ball want to go straight, but the cylinder is making it go in a circle. That is, the street is exerting a force on the ball to make it go in a circle.
A person on the street "sees" this to mean that the ball has WEIGHT. He is correct and so are you, since all explanations must not depend on the observer. Gravity is pushing the ball against the street. Both of you agree.
Again, the principle that you both use is that the path of an object in a gravity field (predicted by Einstein's equation of motion) is held there with gripping force by gravity. More generally, the MOTION of an object, as predicted by Einstein's Geodesic Equation of Motion, is what the objects wants desperately to KEEP doing, gripped by the force of the gravitational interaction.
It sticks to the wall of the Ring World, which is just a street in this case in some part of a Ring World town, from the same physical interaction that a ball sticks to the road on Earth: Gravity.
At this scale, it is easier to see that the trees are not under the influence of "artificial" gravity. It is real.
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The gravitational field around each blade of grass and tree is the same as the field around each blade of grass and tree on the surface of Earth.
Notice that if you drive on a road perpendicular to the cylinder axis, you will increase gravity driving one way and decrease it driving the other. If you drive opposite to the spin and at the radial speed, your gravitational field turns Minkowskian, and you are in a "free fall" or inertial coordinate system. That is, you and the car become "weightless."
That means this: The value of a gravity field can go from a surface-of-a-planet value to a free-fall value by a coordinate transformation among systems that are moving at a constant velocity with respect to each other.
At any instant of time, a car moving at the radial speed is in a Minkowski field, and a system at rest on the cylinder is in a planet-surface field. A ...
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