I don't understand why an apple falls from a tree

I don't understand how General Relativity describes an apple falling from a tree. I have read things that made it more confusing (e.g. the earth actually moves towards the apple which made no sense to me) and I can't think of the Apple falling in non-Newtonian terms. If there is not a downward force pulling it towards the earth then why does it fall that way as it follows the curve of spacetime caused by the earth's mass? I guess part of the problem is that I don't really understand spacetime curving beyond the popular image of it as a fabric being indented by a planet which then causes other objects to follow the curve it caused, I.e. gravity. That only makes conceptual sense to me, I have no real understanding beyond that.

I'd appreciate any help to try and make it click in my mind. Here are some things I learnt that helped me understand a little:

-From the apple's perspective it is travelling in a straight line. Similarly, the earth 'believes' it is travelling in a straight line but we observe it orbiting the sun due to spacetime bending.

-When the Apple is on the branch it is travelling in time but not space. When it falls it travels in both.

Reply 1

lerjj

Original post by Shook

Not that I know any general relativity either per se, but the following might help:

In special relativity, there is a notion of "proper time", which can be thought of as the arclength of a path that a particle travels along. This is assuming that you treat the particle's trajector as a curve in 4-D spacetime. General relativity (and maybe special?) says that particles travel along paths which have maximal proper time.

The thing to notice about GR is that the "arc length" of your trajectory is dependant upon the co-ordinate system in that if the space is warped, the arclengths will all change, and so the longest arc will change shape - this is the gist of how GR lets you calculate trajectories AFAIK. So presumably in the apple case, the apple falles straght down because that's an extremal path through space-time.

I don't know much/any GR beyond pop science though, so that may all be completely wrong. I think it makes more sense that the whole "the apple is always in free-fall" nonsense though :smile: