# Question about Gravity and curvature of space time

## Main Question or Discussion Point

Hello all

I just joined this forum so forgive me for jumping right in but I have a question about Gravity and the curvature of space time that I can't get answer with a Google search. My question: though I understand that an object remains in orbit because of the curvature of space time and it is this curvature which is responsible for Gravity, but what causes an object that is stationary to fall toward the center of mass if nothing sets it in motion? Does the curvature of space give it a nudge? If so How? Why does a ball which is motionless in my hand fall if I let go of it without giving a push? I understand that if I set it into motion fast enough that it will fall around the earth following the curvature of space but what makes it move toward center of mass if no force is acted on it?

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e.bar.goum
What happens if you place a ball on a ramp and let go?

It rolls down the ramp. But what sets it in motion?

e.bar.goum
The downwards acceleration of gravity. Perhaps that analogy wasn't as helpful as I was hoping.

In regards to "Why does a ball which is motionless in my hand fall if I let go of it without giving a push" - what you need to wonder is, "why does the ball not always fall to the ground, if gravity is always acting on it?" - The ball remains in your hand, because you are providing an opposing force to gravity - the feeling of weight of the ball. If you remove your hand, you are no longer providing that opposing force, and the net force is downwards, so the ball falls.

What is the force pulling on it? The curvature of space dictates how the ball moves but why it is being pulled toward the center of mass?

e.bar.goum
What is the force pulling on it? The curvature of space dictates how the ball moves but why it is being pulled toward the center of mass?
The force pulling on it is gravity. The force of gravity acts towards the centre of mass, because that's how it acts based on all of our observations. "Why" questions are unfortunate in physics, you rarely get a satisfactory response.

Simon Bridge
Homework Helper
Do you intend to ask about how the curvature of space-time leads to the experience of gravity?

My question: though I understand that an object remains in orbit because of the curvature of space time and it is this curvature which is responsible for Gravity, but what causes an object that is stationary to fall toward the center of mass if nothing sets it in motion?
The same thing that allows the object to remain in orbit also allows an object to fall down. If you understand the one, then you understand the other. I should be able to answer you better if you explain how, by your understanding, the curvature of space-time keeps an object in orbit.

Meantime: what do you mean by "stationary" - OK the object is not moveing: but relative to what?
Everything is in motion with respect to something - when you talk about relativity then you have to specify what things are stationary with respect to.

Does the curvature of space give it a nudge?
No.

Why does a ball which is motionless in my hand fall if I let go of it without giving a push?
Same reason it does not fall if you are in free-fall when you let it go.

What education level do you need the answers to?

Nugatory
Mentor
What is the force pulling on it? The curvature of space dictates how the ball moves but why it is being pulled toward the center of mass?
Take a look at this animation (created by member A.T.):

Welcome to PF Christine,
You are a quite curious one and that quality is appreciated over here. The question you are asking is about the fundamental or I should say that its about the natural property of a mass. The curvature of space-time is just a geometrical representation given by Dr. Einstein about gravity and as it is useful in understanding the concept of gravity on large scale, its generally accepted as a representation model for gravity. For your question, its generally accepted that a curvature of space-time leads to the force of gravity.(At least not until now, anyone has tried to raise question about the fundamentals of GR:L) One has to accept certain postulates to get the desired result from a theory. I hope you got my point.:)

Jonathan Scott
Gold Member
Hello all

I just joined this forum so forgive me for jumping right in but I have a question about Gravity and the curvature of space time that I can't get answer with a Google search. My question: though I understand that an object remains in orbit because of the curvature of space time and it is this curvature which is responsible for Gravity, but what causes an object that is stationary to fall toward the center of mass if nothing sets it in motion? Does the curvature of space give it a nudge? If so How? Why does a ball which is motionless in my hand fall if I let go of it without giving a push? I understand that if I set it into motion fast enough that it will fall around the earth following the curvature of space but what makes it move toward center of mass if no force is acted on it?
You're thinking of ordinary curvature of space, not space-time. Although curvature of space is present in General Relativity and affects very fast-moving objects and light, the main effect of gravity can be described in terms of curvature of space-time with respect to time. That has the effect that if you draw a line representing the path of a particle through space-time (which for a slow-moving particle travels ct in the time direction while it travels distance vt in the spatial direction of travel) then if you look at the direction of that plotted against time you find that it curves towards the gravitational source.

(The word "curvature" in this ordinary sense of plotting a curved path against a coordinate grid is not the same as the intrinsic "curvature" caused locally by mass in General Relativity, which is more like the curvature of the surface of a ball, and is effectively measured by the way in which the total angle around a closed path differs from the normal flat space value).

Do you intend to ask about how the curvature of space-time leads to the experience of gravity?

I think so yes. But from what I gather no one really knows
Do you intend to ask about how the curvature of space-time leads to the experience of gravity?

The same thing that allows the object to remain in orbit also allows an object to fall down. If you understand the one, then you understand the other. I should be able to answer you better if you explain how, by your understanding, the curvature of space-time keeps an object in orbit.

Meantime: what do you mean by "stationary" - OK the object is not moveing: but relative to what?
Everything is in motion with respect to something - when you talk about relativity then you have to specify what things are stationary with respect to.

No.

Same reason it does not fall if you are in free-fall when you let it go.

What education level do you need the answers to?
I'll reply at lunch when I have more time. I'm at work right now but thank you for the reply.

Last edited by a moderator:
Do you intend to ask about how the curvature of space-time leads to the experience of gravity?

The same thing that allows the object to remain in orbit also allows an object to fall down. If you understand the one, then you understand the other. I should be able to answer you better if you explain how, by your understanding, the curvature of space-time keeps an object in orbit.

Meantime: what do you mean by "stationary" - OK the object is not moveing: but relative to what?
Everything is in motion with respect to something - when you talk about relativity then you have to specify what things are stationary with respect to.

No.

Same reason it does not fall if you are in free-fall when you let it go.

What education level do you need the answers to?
Stationary with respect to the curved space of the object it orbiting.

Welcome to PF Christine,
You are a quite curious one and that quality is appreciated over here. The question you are asking is about the fundamental or I should say that its about the natural property of a mass. The curvature of space-time is just a geometrical representation given by Dr. Einstein about gravity and as it is useful in understanding the concept of gravity on large scale, its generally accepted as a representation model for gravity. For your question, its generally accepted that a curvature of space-time leads to the force of gravity.(At least not until now, anyone has tried to raise question about the fundamentals of GR:L) One has to accept certain postulates to get the desired result from a theory. I hope you got my point.:)
So space is not really physically curved by a mass?

Simon Bridge
Homework Helper
Stationary with respect to the curved space of the object it orbiting.
No such thing ... something moves with respect to another object in space.
Now you are switching to space alone? Please make up your mind.

Do you intend to ask about how the curvature of space-time leads to the experience of gravity?
I think so yes. But from what I gather no one really knows
How can anyone "really know" anything? What does that even mean?
I have a feeling you are trying to explore philosophical issues.

General relativity is a mathematical framework that can be used to describe the geometry of events in space-time.
The effect of energy in this framework is to give the space-time manifold an intrinsic curvature depending on the energy density distribution.
We have evolved to model events as a progression of 3D space events in a distinct time dimension ... when you make the projection from space-time for a particular observer in 3D space watching events unfold over time you get a mysterious force pulling high-density pockets of energy together. This is understood as a pseudoforce similar to the centrifugal force in a rotating room or the way objects get pulled to one wall when a room is accelerating.

The "reality" of this intrinsic curvature is a philosophical issue - which we wont go into here - in science the reality of a mathematical model depends upon it's empirical foundation: how good is it at predicting the results of experiments, and how hard have people tried to find an experiment that it does not predict? In that sense the intrinsic curvature is as real as any other well-supported model.

Hello all

I just joined this forum so forgive me for jumping right in but I have a question about Gravity and the curvature of space time that I can't get answer with a Google search. My question: though I understand that an object remains in orbit because of the curvature of space time and it is this curvature which is responsible for Gravity, but what causes an object that is stationary to fall toward the center of mass if nothing sets it in motion? Does the curvature of space give it a nudge? If so How? Why does a ball which is motionless in my hand fall if I let go of it without giving a push? I understand that if I set it into motion fast enough that it will fall around the earth following the curvature of space but what makes it move toward center of mass if no force is acted on it?
It may be useful to note that in contrast with the way you formulated it, GR according to Einstein is practical about "space" and "time", interpreting those concepts as tools to describe observations [1]. GR thus provides an improved and verifiable description of effects of gravitational fields, free from metaphysical claims. A very nice and clear graphical illustration was provided in post #8.

Also, for sure gravitation is not like "rubber bands" pulling on objects; there is no force involved in that sense. Nevertheless, GR is a field theory [2]. Perhaps a good way of looking at it, is that all objects have a natural tendency to move towards mass as described by GR.

Regretfully I did not find a direct answer to your question as I understand it in the peer reviewed literature (I have searched for the same). Perhaps there is a publication that I'm not aware of. I did find a reasonable looking answer by "Googling" on the Internet but it's not allowed to ask here for highly valued comments by specialists!
As a substitute, what I personally found helpful is the explanation of why light bends towards mass according to Einstein, here, from p.821 (this is also known as "gravitational lensing"): https://en.wikisource.org/wiki/The_...Perihelion-motion_of_the_paths_of_the_Planets.

[1] Einstein, "Relativity, the special and general theory", Minkowski's four-dimensional space - http://www.bartleby.com/173/17.html
[2] Einstein, "Relativity, the special and general theory", The Gravitational field - http://www.bartleby.com/173/19.html

Dale
Mentor
So space is not really physically curved by a mass?
I think that the key thing that you are missing is that GR considers gravity to be the curvature of spacetime, not just space. A "stationary" object is still "moving" through time. So nothing in gravity needs to set it in motion, it is already moving. All that needs to happen is for the curvature to cause some of the "motion" through time to curve into motion through space.

A.T.
The force pulling on it is gravity.
I don't think this is helpful. The OP asks about the GR model, where gravity is modeled via space-time geometry, not via a pulling force.

No such thing ... something moves with respect to another object in space.
Now you are switching to space alone? Please make up your mind.

How can anyone "really know" anything? What does that even mean?
I have a feeling you are trying to explore philosophical issues.

General relativity is a mathematical framework that can be used to describe the geometry of events in space-time.
The effect of energy in this framework is to give the space-time manifold an intrinsic curvature depending on the energy density distribution.
We have evolved to model events as a progression of 3D space events in a distinct time dimension ... when you make the projection from space-time for a particular observer in 3D space watching events unfold over time you get a mysterious force pulling high-density pockets of energy together. This is understood as a pseudoforce similar to the centrifugal force in a rotating room or the way objects get pulled to one wall when a room is accelerating.

The "reality" of this intrinsic curvature is a philosophical issue - which we wont go into here - in science the reality of a mathematical model depends upon it's empirical foundation: how good is it at predicting the results of experiments, and how hard have people tried to find an experiment that it does not predict? In that sense the intrinsic curvature is as real as any other well-supported model.
Sorry I guess I have gotten myself in trouble here. I'm an engineering student not a physicists.

A.T.
Take a look at this animation (created by member A.T.):

Also this very similar one, with more explanation, and the case of vertical upwards throw:

So space is not really physically curved by a mass?
Space-time is curved, and the time dimension crucial for gravitational attraction. Space (without time) is also curved, but that is not mainly relevant for gravitational attraction. The pictures here might be helpfull:

http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html

I think that the key thing that you are missing is that GR considers gravity to be the curvature of spacetime, not just space. A "stationary" object is still "moving" through time. So nothing in gravity needs to set it in motion, it is already moving. All that needs to happen is for the curvature to cause some of the "motion" through time to curve into motion through space.
Ok now I think I get it. Because space and time are the same any object in space is already in motion through time?

Simon Bridge
Homework Helper
Sorry I guess I have gotten myself in trouble here. I'm an engineering student not a physicists.
... Well, from an engineering perspective, space-time is really curved in the same way that the centripetal force is the real force in rotational motion. We can do our maths either way but one way has less voodoo. Newton's gravitation has this spooky "action at a distance" thing (how does an object know about the mass some way away that it is supposed to fall towards?)

You seem to be getting there though.

... Well, from an engineering perspective, space-time is really curved in the same way that the centripetal force is the real force in rotational motion. We can do our maths either way but one way has less voodoo. Newton's gravitation has this spooky "action at a distance" thing (how does an object know about the mass some way away that it is supposed to fall towards?)

You seem to be getting there though.

Ok now I think I get it. Because space and time are the same any object in space is already in motion through time?
Is that correct?

Dale
Mentor
Ok now I think I get it. Because space and time are the same any object in space is already in motion through time?
Yes, essentially. There are a few mathematical subtleties about how time is different from space, but they are part of the same mathematical structure (called a pseudo Riemannian manifold), so in essence that is the correct idea.

Yes, essentially. There are a few mathematical subtleties about how time is different from space, but they are part of the same mathematical structure (called a pseudo Riemannian manifold), so in essence that is the correct idea.
Thank you!