Why Stationary Masses Attract: Explaining GR Intuition

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In summary, in General Relativity, objects are influenced to move along the geodesic shortest distance by the curvature of spacetime. This applies even to initially stationary objects, as they are still moving forward in time and their paths through spacetime are affected by curvature. The idea of stationary objects attracting each other only applies to spatial curvature, not in the time direction.
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bryanso
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TL;DR Summary
How does General Relativity explain two stationary objects in free space attract?
In most intuitive explanation of GR there is always a moving object... the moving object travels along the geodesic shortest distance therefore its path is bent toward a massive object.

But let's start with two masses that are stationary in free space. I don't understand how curved spacetime will start to make them move towards each other in the first space...
 
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This is only a problem if you are only thinking of spatial curvature. There is also curvature in the time direction - indeed, neglecting the spatial curvature is part of the simplification process that yields Newtonian gravity. And there's no way to be stationary in time. So, if you remember that the geodesics are paths in the timelike direction, and it's curvature along that direction that's important.
 
  • #3
bryanso said:
Summary: How does General Relativity explain two stationary objects in free space attract?

In most intuitive explanation of GR there is always a moving object... the moving object travels along the geodesic shortest distance therefore its path is bent toward a massive object.

But let's start with two masses that are stationary in free space. I don't understand how curved spacetime will start to make them move towards each other in the first space...

Your question puzzles me. The simple, intuitive idea is that spacetime is "curved" and objects are influenced to move according the shape of spacetime. The analogy extends to an initially stationary object. Why would a stationary object not respond to a "slope"?

Why do you think objects must initially be in relative motion to attact one another?
 
  • #4
bryanso said:
Summary: How does General Relativity explain two stationary objects in free space attract?

the moving object travels along the geodesic shortest distance therefore its path is bent toward a massive object.
Actually, it is more accurate to say that timelike geodesics are stationary paths of proper time. In particular, the straight worldlines of inertial observers in SR maximise proper time between events.

Regardless, the relevant issue is spacetime curvature, tot spatial curvature. The latter also depends on how you define ”space”, which is up to an arbitrary foliation (slicing in spacelike hypersurfaces labelled by a time coordinate) of spacetime. Worldlines are never ”stationary” in spacetime, if they were we would just call them ”events”.
 
  • #5
bryanso said:
But let's start with two masses that are stationary in free space. I don't understand how curved spacetime will start to make them move towards each other in the first space...
They are stationary in three-dimensional space but not stationary in four-dimensional spacetime; they are both moving forward in time. Their paths through spacetime are initially parallel but because of curvature draw closer and eventually intersect.
 
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Thank you all. This is very clear, even intuitive.
 
  • #7
What? Just like that?

That's not how this is done.

You've got to argue.

Oi. Brutus. This guy doesn't want to argue...
1571339259598.png


:oldbiggrin:
 
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bryanso said:
I don't understand how curved spacetime will start to make them move towards each other in the first space...

 
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> You've got to argue

Good animation. But how come there is no sound! :)

Thanks!
 
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bryanso said:
Good animation. But how come there is no sound! :)
Because there is no sound in spaAaAaAaAace...
 
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FAQ: Why Stationary Masses Attract: Explaining GR Intuition

1. Why do stationary masses attract each other?

According to general relativity, mass causes a curvature in the fabric of space-time. When two masses are present, they create a "dimple" in space-time, causing objects to move towards each other.

2. How does general relativity explain the attraction between stationary masses?

General relativity states that massive objects create a curvature in space-time, and this curvature is what causes the attraction between stationary masses. The more massive the objects, the greater the curvature and the stronger the attraction.

3. Is there a difference in the attraction between stationary masses and moving masses?

According to general relativity, there is no difference in the attraction between stationary masses and moving masses. Both create a curvature in space-time, and this curvature is what causes the attraction.

4. Can the attraction between stationary masses be explained by Newton's law of gravitation?

No, the attraction between stationary masses cannot be fully explained by Newton's law of gravitation. While Newton's law explains the attraction between two masses, it does not account for the curvature of space-time that is responsible for the attraction according to general relativity.

5. How does the concept of space-time curvature relate to the attraction between stationary masses?

The concept of space-time curvature is essential in understanding the attraction between stationary masses. According to general relativity, the curvature of space-time is what causes the attraction between masses, rather than a force acting on them as described by Newton's law of gravitation.

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