Why do objects follow a geodesic?

[Zayan]

TL;DR Summary

If general relativity explains that gravity is the consequence of the spacetime curvature making objects follow a geodesic, why do objects follow the curved path in the first place.

Gravity is considered as a bending of spacetime due to massive objects. And hence other objects around the curvature follow a geodesic path. My question is, why do they follow the path? Can't they be stationary? What's the cause behind objects even moving in the first place? I sometimes hear the analogy that it's like how a ball rolls down a slope. But isn't that the very thing we are explaining? Why it happens in the first place? Sounds a bit circular reasoning to me. Can anyone explain or add something I'm missing here.

 

[martinbn]

May be the language confuses you. The do not follow a path in the usual sense. Their worldlines are geodesics in space-time.

 

[Ibix]

The geodesic is the path with zero acceleration, so it corresponds locally to a requirement of conservation of energy and momentum. "Free particles follow geodesics" is the curved spacetime generalisation of Newton's first law, basically.

Yes, analogies with things rolling down a slope are circular, and are not particularly accurate either. You won't find them in textbooks on GR.

 

[ersmith]

Remember that the paths objects take are geodesics in *spacetime*, not just space. So the answer to "can't they be stationary" is that objects aren't stationary in time. In some sense they're constantly "moving forward in time"; although probably a better way to think of it is to consider the path as a whole, namely the world line of the object through space *and* time.

 

[Dale]

Can't they be stationary?

As others have said, we are talking about spacetime. So no, you cannot be stationary. You cannot stop traveling through time.

why do they follow the path?

This is Newton’s first law, expressed in terms of spacetime. Newton’s first law says that if an object is not experiencing any forces, then its worldline is a straight line. Straight lines are geodesics.

I sometimes hear the analogy that it's like how a ball rolls down a slope. But isn't that the very thing we are explaining? Why it happens in the first place? Sounds a bit circular reasoning to me.

Yes. That is a bad analogy. Note that it is not the reasoning of GR, just a bad analogy.

Can anyone explain or add something I'm missing here.

Try my explanation here: https://www.physicsforums.com/insights/understanding-general-relativity-view-gravity-earth/

 

[A.T.]

Can't they be stationary?

Stationary in space means you only advance along the time dimension, like the apple initially does in the below animation.

 

[Orodruin]

As others have said, we are talking about spacetime. So no, you cannot be stationary. You cannot stop traveling through time.

Just to add to the confusion, an object can follow a world line that is called “stationary” also in spacetime, but it is not what the OP believes it is and it requires the spacetime itself to be a stationary spacetime. Stationary worldlines are also not generally geodesics so they would typically require proper acceleration to be provided in some manner.

(On A-level; the stationary worldlines would be the integral curves of the timelike Killing vector field in a stationary spacetime)

 

[haushofer]

What exactly do you expect that physics can answer, regarding "why"-questions?

Why does Newton's first law hold in classical mechanics? That's how God made it all up. Blame God for it.