Question about Gravity and curvature of space time

[Christine88]

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?

 

[e.bar.goum]

What happens if you place a ball on a ramp and let go?

 

[Christine88]

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.

 

[Christine88]

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]

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]

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.):

 

[aditya ver.2.0]

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]

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).

 

[Christine88]

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

https://www.physicsforums.com/threads/question-about-gravity-and-curvature-of-space-time.778417/goto/post?id=4893782#post-4893782
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.

 

[Christine88]

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.

 

[Christine88]

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]

Stationary with respect to the curved space of the object it orbiting.

No such thing ... something moves with respect to another object in space.
Anyway - I thought you were asking about a space-time description?
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.

Unless you can ask clear questions you are unlikely to get helpful answers.

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 won't 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.

 

[harrylin]

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]

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.

 

[Christine88]

No such thing ... something moves with respect to another object in space.
Anyway - I thought you were asking about a space-time description?
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.

Unless you can ask clear questions you are unlikely to get helpful answers.

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 won't 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

 

[Christine88]

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]

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.

 

[Christine88]

... 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]

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.

 

[Christine88]

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!

 

[WannabeNewton]

See here (go to last paragraph if you want to skip the details): https://www.physicsforums.com/threa...visualization-of-gravity.726837/#post-4597436

 

[m4r35n357]

DaleSpam's is the direct answer to your question; everything is always in motion through spacetime. Mathematically this is encapsulated by a vector called the four-velocity. You should be able to find many resources on this at various levels, but to reiterate, everything is always in motion through spacetime, so it doesn't need any initial nudge to start falling.
Say you are holding an apple. You are diverting the apple from following its natural path through spacetime, by exerting a force on it which you feel as its weight. When you let it fall the apple reverts to its natural path. The name of this natural path is the geodesic. Hope this helps.

 

[Christine88]

DaleSpam's is the direct answer to your question; everything is always in motion through spacetime. Mathematically this is encapsulated by a vector called the four-velocity. You should be able to find many resources on this at various levels, but to reiterate, everything is always in motion through spacetime, so it doesn't need any initial nudge to start falling.
Say you are holding an apple. You are diverting the apple from following its natural path through spacetime, by exerting a force on it which you feel as its weight. When you let it fall the apple reverts to its natural path. The name of this natural path is the geodesic. Hope this helps.

Why do objects accelerate when falling as opposed to a constant velocity?

 

[A.T.]

Why do objects accelerate when falling as opposed to a constant velocity?

Photons falling vertically at light speed, do stay at a constant velocity, and do not accelerate any further.

Otherwise see the video below, and note how the straight world line the starts along time, and then becomes more and more along space. That is acceleration in space.

 

[Christine88]

Photons falling vertically at light speed, do stay at a constant velocity, and do not accelerate any further.

Otherwise see the video below, and note how the straight world line the starts along time, and then becomes more and more along space. That is acceleration in space.

Yes I understand that light speed is always constant in a vacuum, slows down in a medium, but I'm afraid I don't get that video.

 

[A.T.]

I'm afraid I don't get that video.

I'm afraid one cannot simplify it much more than that video. Try the other one, with more explanation:

 

[ShayanJ]

Why do objects accelerate when falling as opposed to a constant velocity?

Well, in some way they do accelerate but in the way we prefer to state it, there is no acceleration!
I think this is a good explanation:
Just consider the sun-earth system. When you look at the whole Earth's world-line, from some other place with a different gravitational field-maybe a vanishing one-you see there that the world-line is curved, because its the geodesic of the space-time in that part of it and is generally different from the geodesic of the space-time in a different part of it. But space-time is always locally(when you only pay attention to your near vicinity) flat(Minkowskian) and locally the world-line is a straight line in space-time. This way, the object is going with constant velocity at every point of space-time and so we should accept its always going in constant velocity. The only point is, because of the curvature of space-time, the distance the object travels and the time in which the object travels that distance, are changing through its world-line only because of the change in space-time through the object's world-line, i.e. as the object goes in its world-line the rods and clocks change because space and time themselves change.

 

[DrGreg]

Why do objects accelerate when falling as opposed to a constant velocity?

Like lots of other things, in relativity acceleration is relative. Suppose you throw a ball up in the air while you are stood on the ground. The ball accelerates relative to you, but, equally, you accelerate relative to the ball. If I am nearby, jumping on a trampoline, then while I am in the air I see you accelerating upwards relative to me, and I see the ball moving at a constant velocity relative to me.

In general relativity we measure acceleration (or more accurately "proper acceleration") relative to falling objects, i.e. "inertial" means falling freely under gravity.

 

[jerromyjon]

I think one more piece is required to fully comprehend "why": Gravity is virtually indistinguishable from acceleration through space which nicely removes the time factor for simplified comprehension. Imagine standing in a rocket in empty space on a floor perpendicular to acceleration. If you hold a ball, your hand is accelerating it and if you let go it stops accelerating with you and the floor accelerates to reach it. I hope that helps!

 

[Christine88]

I think one more piece is required to fully comprehend "why": Gravity is virtually indistinguishable from acceleration through space which nicely removes the time factor for simplified comprehension. Imagine standing in a rocket in empty space on a floor perpendicular to acceleration. If you hold a ball, your hand is accelerating it and if you let go it stops accelerating with you and the floor accelerates to reach it. I hope that helps!

I think I've heard that called the law of equivalents?

 

[Christine88]

I'm afraid one cannot simplify it much more than that video. Try the other one, with more explanation:

The guy in the video lost me when he retuned the graph back to zero gravity and then proceeded with his explanation as though there was still gravity. How could that be if the graph was returned to zero gravity? So this is how I understand it. Let us imagine a little moon sitting out in space all by itself and absolutely motionless relative to the rest of the universe. No gravitational influences effecting it. In fact it is the only object in the universe so it's at absolute equilibrium. I assume from what I have gathered here that our little moon is still moving through time and since space and time are equivalent it's moving through space as well. So I guess a rest state is just an illusion. Anyway God decides to give the lonely little moon a companion and creates a large planet right next to it. Since the little moon is already in motion through space-time it falls toward the large planet without the need of an external force to get it moving because it's already in motion. Does that sound right? I still don't get the acceleration though.

 

[jkl71]

You may find this useful, but as a warning in some ways this analogy is a bit deceptive, I’ll explain why later.

Imagine two people are at the Earth’s equator, fairly close together and both decide to walk due North (their paths are lines of longitude and are geodesics). They start off on parallel paths and both are traveling on straight lines. However, if they make careful measurements they’ll find that they are approaching each other. From the outside perspective it’s pretty clear what’s happening, the surface of the Earth is curved and parallel lines can converge. If the people walking don’t know about this, they might conclude there is a force causing them to accelerate towards each other.

In general relativity bodies that are not acted upon by any force (in this context by force I mean what Newton might call a non-gravitational force) travel on space-time geodesics. Since space-time can be curved, initially parallel geodesics can converge. So two observers moving on geodesics can seem to accelerate towards each other although neither is accelerating. For example, a body in free fall in the Earth’s gravitational field will seem to accelerate towards the Earth, but a better perspective is that the world lines of this body an the Earth, which are both geodesics, are converging because of space-time curvature.

Why is the analogy a bit deceptive? In the first case it’s just a curved spatial surface and time is taken as an external parameter (basically it’s the usual Newtonian point-of-view). In the case of GR, it’s space-time itself that’s curved and there is no external time.

Also consider a person standing on the surface of the Earth. From the Newtonian perspective one would usually say that person is not accelerating. From the GR perspective it’s more natural to say that the person is accelerating, in other words deviating from a space-time geodesic, because of the force from the ground on their feet (imagine a rocket in deep space traveling at a constant acceleration).

 

[pervect]

Yes I understand that light speed is always constant in a vacuum, slows down in a medium, but I'm afraid I don't get that video.

What part don't you get?

Let's break it down into xxxxx four parts. The first part is understanding that one can represent space-time via a diagram, a space-time-diagram.

The second part is that if you have 1 space and one time dimension, your space-time diagram is a two dimensional diagram.

The third part, is to understand that you can draw a two-dimensional space-time diagram on a curved 2d surface (which we will visulaize as being the 2d surface of some 3d object).

The fourth part is to understand the consequences of drawing this, by interpreting the results of the diagram (which is basically a map) physically. This entails a bit of geometry, and also the ability to go back from the abstract space-time diagram to what it represents.

Which of the above parts do you get, and which do you not get?

 

[Christine88]

You may find this useful, but as a warning in some ways this analogy is a bit deceptive, I’ll explain why later.

Imagine two people are at the Earth’s equator, fairly close together and both decide to walk due North (their paths are lines of longitude and are geodesics). They start off on parallel paths and both are traveling on straight lines. However, if they make careful measurements they’ll find that they are approaching each other. From the outside perspective it’s pretty clear what’s happening, the surface of the Earth is curved and parallel lines can converge. If the people walking don’t know about this, they might conclude there is a force causing them to accelerate towards each other.

In general relativity bodies that are not acted upon by any force (in this context by force I mean what Newton might call a non-gravitational force) travel on space-time geodesics. Since space-time can be curved, initially parallel geodesics can converge. So two observers moving on geodesics can seem to accelerate towards each other although neither is accelerating. For example, a body in free fall in the Earth’s gravitational field will seem to accelerate towards the Earth, but a better perspective is that the world lines of this body an the Earth, which are both geodesics, are converging because of space-time curvature.

Why is the analogy a bit deceptive? In the first case it’s just a curved spatial surface and time is taken as an external parameter (basically it’s the usual Newtonian point-of-view). In the case of GR, it’s space-time itself that’s curved and there is no external time.

Also consider a person standing on the surface of the Earth. From the Newtonian perspective one would usually say that person is not accelerating. From the GR perspective it’s more natural to say that the person is accelerating, in other words deviating from a space-time geodesic, because of the force from the ground on their feet (imagine a rocket in deep space traveling at a constant acceleration).

Ok so does that mean that the acceleration of gravity is basically just an illusion? Or a quirk of geometry?

 

[Nugatory]

Ok so does that mean that the acceleration of gravity is basically just an illusion? Or a quirk of geometry?

No, the acceleration (as we're using the word here) is real. Release an object above the Earth's surface, and it and the the Earth's surface will move closer together. We choose to interpret that as the object falling towards a stationary Earth with some speed. That speed will increase with time - and that's more or less by definition acceleration.

Be aware that there is something else called "proper acceleration" which the falling object is not experiencing. But as I said... That's something different.

 

[Christine88]

What part don't you get?

Let's break it down into xxxxx four parts. The first part is understanding that one can represent space-time via a diagram, a space-time-diagram.

The second part is that if you have 1 space and one time dimension, your space-time diagram is a two dimensional diagram.

The third part, is to understand that you can draw a two-dimensional space-time diagram on a curved 2d surface (which we will visulaize as being the 2d surface of some 3d object).

The fourth part is to understand the consequences of drawing this, by interpreting the results of the diagram (which is basically a map) physically. This entails a bit of geometry, and also the ability to go back from the abstract space-time diagram to what it represents.

Which of the above parts do you get, and which do you not get?

I don't get any of it. I don't know enough about all of this to understand a graph like that.

 

[Dale]

I don't get any of it. I don't know enough about all of this to understand a graph like that.

Do you mind me asking what is your background? Usually by the time someone can ask the question you started with they have seen "position vs time" diagrams, which is pervect's point 1 and 2.

 

[A.T.]

The guy in the video lost me when he retuned the graph back to zero gravity and then proceeded with his explanation as though there was still gravity. How could that be if the graph was returned to zero gravity?

He merely switches between two different interpretations of gravity:

Einsteins interpretation: The free falling worldline is straight (force free), while the space-time coordinates are curvilinear.

Newtons interpretation: The free falling worldline is curved (bend by the force of gravity), while the the space-time coordinates are Cartesian.

Since the little moon is already in motion through space-time it falls toward the large planet without the need of an external force to get it moving because it's already in motion. Does that sound right?

Yes, the space time distortion changes the directions w.r.t the space & time axes, which manifest itself as accelerations in space.

I still don't get the acceleration though.

If you get why a free falling object starts moving in space, do you get the acceleration. To start moving from rest it needs to accelerate.

But note that this is just coordinate acceleration, a geometrical effect. A free falling object doesn't experience proper acceleration. A free falling accelerometer measures zero. In terms of proper acceleration, the apple is not accelerating down, but the branch and surface are accelerating up.

 

[jkl71]

Ok so does that mean that the acceleration of gravity is basically just an illusion? Or a quirk of geometry?

I wouldn't use the words illusion or quirk. In the approximation that you can ignore other forces objects move on geodesics. Space-time can be curved (the source being the stress-energy tensor) and this can make the geodesics "accelerate" (I'm using quotes because I'm using terms pretty roughly, the concepts and terminology can be made more rigorous) towards each other, e.g. they can start off parallel and then converge and intersect.

Consider an object in free fall in the Earth's gravitational field (of course the Earth is also in the gravitational field of this object). From the Newtonian point of view there is a force between the two objects and that causes them to accelerate towards each other. From the GR point of view the object and Earth still accelerate towards each other (again being a bit rough with terms), but there is no force. The acceleration arises from the way the object and Earth space-time geodesics converge.

In a sense there is acceleration of gravity in GR, but it's not the result of a force. It's the result of the way space-time geodesics converge. Typically the term acceleration in GR is used for forces that cause objects to not follow geodesics.

 

[Christine88]

Do you mind me asking what is your background? Usually by the time someone can ask the question you started with they have seen "position vs time" diagrams, which is pervect's point 1 and 2.

I just started Engineering school this year.

 

[Christine88]

He merely switches between two different interpretations of gravity:

Einsteins interpretation: The free falling worldline is straight (force free), while the space-time coordinates are curvilinear.

Newtons interpretation: The free falling worldline is curved (bend by the force of gravity), while the the space-time coordinates are Cartesian.


Yes, the space time distortion changes the directions w.r.t the space & time axes, which manifest itself as accelerations in space.If you get why a free falling object starts moving in space, do you get the acceleration. To start moving from rest it needs to accelerate.

But note that this is just coordinate acceleration, a geometrical effect. A free falling object doesn't experience proper acceleration. A free falling accelerometer measures zero. In terms of proper acceleration, the apple is not accelerating down, but the branch and surface are accelerating up.

Acceleration as I understand it is constantly changing velocity. Velocity is distance over time.

 

[Christine88]

I wouldn't use the words illusion or quirk. In the approximation that you can ignore other forces objects move on geodesics. Space-time can be curved (the source being the stress-energy tensor) and this can make the geodesics "accelerate" (I'm using quotes because I'm using terms pretty roughly, the concepts and terminology can be made more rigorous) towards each other, e.g. they can start off parallel and then converge and intersect.

Consider an object in free fall in the Earth's gravitational field (of course the Earth is also in the gravitational field of this object). From the Newtonian point of view there is a force between the two objects and that causes them to accelerate towards each other. From the GR point of view the object and Earth still accelerate towards each other (again being a bit rough with terms), but there is no force. The acceleration arises from the way the object and Earth space-time geodesics converge.

In a sense there is acceleration of gravity in GR, but it's not the result of a force. It's the result of the way space-time geodesics converge. Typically the term acceleration in GR is used for forces that cause objects to not follow geodesics.

So acceleration of gravity is a phenomenon that no one really understands and can only be explained by mathematical representation?

 

[Christine88]

He merely switches between two different interpretations of gravity:

Einsteins interpretation: The free falling worldline is straight (force free), while the space-time coordinates are curvilinear.

Newtons interpretation: The free falling worldline is curved (bend by the force of gravity), while the the space-time coordinates are Cartesian.


Yes, the space time distortion changes the directions w.r.t the space & time axes, which manifest itself as accelerations in space.If you get why a free falling object starts moving in space, do you get the acceleration. To start moving from rest it needs to accelerate.

But note that this is just coordinate acceleration, a geometrical effect. A free falling object doesn't experience proper acceleration. A free falling accelerometer measures zero. In terms of proper acceleration, the apple is not accelerating down, but the branch and surface are accelerating up.

Coordinate acceleration. Yes I think that is where I'm running into problems. I'm thinking in terms of actual acceleration as opposed to theoretical acceleration.

 

[Dale]

I just started Engineering school this year.

You may want to hold off on your questions for a few months. In that time your classes should teach you about position vs time graphs. Then pervects comments should be clear.

 

[Dale]

So acceleration of gravity is a phenomenon that no one really understands and can only be explained by mathematical representation?

No. For many people the mathematical representation leads directly to understanding. Just because you don't understand it after a day or two of study doesn't mean that nobody does, nor even that you won't be able to eventually.

 

[A.T.]

Acceleration as I understand it is constantly changing velocity.

That is "coordinate acceleration" while "proper acceleration" is what an accelerometer measures.

I'm thinking in terms of actual acceleration as opposed to theoretical acceleration.

No idea what you mean by "theoretical acceleration". I would suggest you learn the commonly used terms above, instead of inventing your own. And "actual acceleration" usually refers to "proper acceleration", not to the "acceleration as you understand it".