Question

I think the reason of asking the question solely lies in the confusion that different answers cause as they are somehow different answers on the same questions, or not maybe the same.

First Explanation I found is, I read this where author explains active transformation. Basically, to explain this in ball/earth example it would be as: I'm on the ground and I am at the origin of my own coordinate system, ball is dropped from some height y relative to me and I observe its motion. Bob is already on some height above ground(standing on a roof of the house and he is at origin of his own coordinate system), he drops a ball from the same height relative to him and observes it in his coordinate system.

Then, I read this and there, what is done is I stand again on the ground, ball is dropped from some height y and observe its motion. Then ball is moved up and dropped from a higher height(coordinate system stays fixed).

Then I read this where author mentions that in active transformation, all points are moved(not just one point, but all). In terms of earth ball, I stay on the ground, ball is dropped from some height and then by active transformation, what we do: all points of space is shifted(earth and everything else is shifted upwards), but I stay at the same place with my coordinate system fixed. Now, every point just became y+a instead of y.

I got lost what is correct and what not. Would you be able to shed some light and let's use the earth/ball example as in -

do we move all points of space which would cause earth and everything else be shifted upwards while I stay fixed with my coordinate system or
just move ONLY the ball's dropping location or
Bob comes into play and he drops it from a higher location, but now observes it in his own coordinate system ?

Answer 1

During an active transformation, all points in space, including the Earth and everything else, are moved while the coordinate system remains fixed.

Step-by-step explanation:

In the context of the example you provided about a ball being dropped from a height, the correct explanation is that during an active transformation, all points in space are moved, including the Earth and everything else. However, your coordinate system remains fixed.

So if you are standing on the ground and drop a ball, an active transformation would shift all points in space upwards, including the Earth, while your coordinate system remains fixed. This means that every point in space, including the ball, would have a new position relative to your coordinate system.