#APPLE GRAVITY GUY FREE#

If you put your apple tree in a room, there is no experiment you can do that will tell you whether you are in a room on Earth or in a rocket under power - except opening the door and looking. Here you are doing exactly what I said not to - trying to extend a local model to a global one.

People who say it's more natural or appropriate to consider the apple at rest end up with a lot of explaining to do.ĭoes the video help or hinder your understanding of GR? Is it done to be clever and provocative or enlightening? If flat parts of the Earth rise up to catch things, then why don't we just see chunks of Earth rising up all the time, when we observe things fall? That's what confuses me.Ģ) In the reference frame of the Earth, the apple falls to Earth.ģ) In the reference frame of the apple, the Earth moves.Ĥ) This is true in both Newtonian gravity and GR.ĥ) In the most natural coordinates in which to study the Earth-apple system: Schwarzschild coordinates centred on the Earth (the ball being a test particle whose gravitational effects on local spacetime are negligible): the surface of the Earth is at rest (in these coordinates) and the apple accelerates (in these coordinates).Ħ) In this interpretation: a (real) force is required to keep an object at rest (in Schwartzschild coordinates).

And it does bite if you start talking about the whole Earth. The model works fine as long as you don't push it far enough that the non-flatness of spacetime doesn't come back to bite you. The apple follows a geodesic path, so can be regarded as 'at rest or moving at constant velocity' as Newton's first law would put it, while the floor accelerates for some reason that we don't examine too closely. The reason (at least in this case) is that the floor-is-rising model is essentially a flat spacetime model. I think this is a general observation about general relativity - models that make sense locally can be flat wrong when you try to globalise them. The Earth would have to be expanding at an accelerating rate, and that isn't consistent with observation. However, that picture doesn't really work globally. That makes sense: an accelerometer attached to the apple reads nothing while one attached to the floor reads 1g.

#APPLE GRAVITY GUY FREE#

Locally, you are free to regard the Earth's surface as rising up at 10ms -2 and an apple as not moving.

Apple gravity guy