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Question: When a sky-diver jumps out of a plane (ignoring air resistance) the skydiver is at rest with regards to forces acting on him. So I have some questions:

  1. What does it mean in terms of relativity that the earth rises to meet the sky-diver? if the sky-diver is accelerating downwards, that isn't a force (in Einsteinian mechanics). If acceleration is absolute between reference frames, does that mean that since the sky-diver is accelerating it does NOT appear that the earth is rising up to meet them?

  2. If the gravity is not a force then why does the falling speed of the diver seem to accelerate? is this just a pseudo-force? or is it something else?

If it is a pseudo force, is it because of inertia? if so, how does that work (how does inertia cause acceleration in terms of speed?)

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    $\begingroup$ You spoke of "force" but @Dale's answer mostly says "acceleration." That's because, in General Relativity (GR), gravitation is not a force. In GR an object upon which no forces act (e.g., you, after you step out of the airplane) always follows a path called a geodesic. That is, the closest thing you can have to a "straight line" in curved space. You fall toward the ground because in GR, geodesics bend toward massive bodies. $\endgroup$
    – Solomon Slow
    Commented Jan 11 at 1:59

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What does it mean in terms of relativity that the earth rises to meet the sky-diver? if the sky-diver is accelerating downwards, that isn't a force (in Einsteinian mechanics). If acceleration is absolute between reference frames, does that mean that since the sky-diver is accelerating it does NOT appear that the earth is rising up to meet them?

There are two distinct concepts of acceleration. One is called proper acceleration and the other is called coordinate acceleration.

Coordinate acceleration is the second derivative of the coordinate position. This type of acceleration is relative to the chosen coordinate system.

Proper acceleration is the acceleration measured by an accelerometer. This type of acceleration is invariant (what you called “absolute”) meaning that all reference frames agree on it.

These two concepts of acceleration are connected as follows. In an inertial frame an accelerometer that is momentarily at rest will have the same proper acceleration and coordinate acceleration.

An accelerometer on the ground measures an invariant acceleration of $1\ g$ upwards, and an accelerometer attached to a free falling sky diver measures an invariant acceleration of $0$.

In the ground’s frame the ground has $0$ coordinate acceleration and the sky diver has a coordinate acceleration of $-1 \ g$. Neither of these match the proper acceleration, so the ground’s frame is non inertial.

In the sky diver’s frame the ground has an acceleration of $1 \ g$ and the sky diver has an acceleration of $0$. These both match the proper acceleration, so the skydiver frame is inertial.

If the gravity is not a force then why does the falling speed of the diver seem to accelerate? is this just a pseudo-force? or is it something else?

Indeed, it is an inertial force due to using the non-inertial reference frame of the ground.

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    $\begingroup$ why is the skydiver's coordinate acc -1g? Why not +1g? $\endgroup$
    – Marco Chacon
    Commented Jan 10 at 21:06
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    $\begingroup$ Because in the ground’s frame the skydiver is accelerating downward, not upward. I am assuming the usual practice as having upward be positive and downward be negative. $\endgroup$
    – Dale
    Commented Jan 10 at 21:18

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