Doubt on Gravitation

[Sooryakiran]

Hello Friends,

 

Please forgive me for asking such a crazy doubt.

 

Relativity explains gravity as curvature of space-time and all objects under the influence of a mass follows a straight path in 4D space time which can be visualised as curved in 3D perception .

 

Now my doubt is, of gravitation was not a force and just a curvature in space-time , why does a small mass ( at rest with respect to another larger one ) get attracted to each other. Since the mass was at rest, it doesn't have to follow any path in modified space-time , right ?

[KipIngram]

The small mass (well, both masses really, but its effect on the large mass is negligible) "want" to follow a geodesic path through space time. But if the small mass is sitting on the surface of the large mass that surface is blocking that geodesic (i.e., it's applying an "upward" force on the small mass which prevents it from moving along its free-fall geodesic.) So the point is that it would follow a geodesic, if it were not being subjected to a contact force with the large mass's surface.

[imatfaal]

... Now my doubt is, of gravitation was not a force and just a curvature in space-time , why does a small mass ( at rest with respect to another larger one ) get attracted to each other. Since the mass was at rest, it doesn't have to follow any path in modified space-time , right ?

 

It is travelling through space-time - even if it is not travelling through space. It it moving along a worldline through space-time - and if space time is has a curvature then it it will follow the shortest route; the geodesic

 

https://en.wikipedia.org/wiki/World_line

[MigL]

It is impossible to visualize 4dimensional space-time, so to simplify and allow for visualization, lets reduce it to 2 dimensions.

 

Say you and I are 2dimensional people living on the surface of a plane ( ever read Flatland ? ) and we both decide to travel North. We would be travelling in parallel directions, so our paths would never meet.

 

If we now introduce curvature, such that we are not on a plane but on the surface of a sphere, and again, you and I start at the equator and travel straight North ( in what seem to be parallel paths ), we find ourselves approaching each other, and eventually bump into each other ( at the North pole ). We have been travelling parallel paths, but, on this curved surface, 'straight' is dependent on the curvature, and parallel paths do meet.

 

If we did not know that we were living on a 'curved' surface we might call this tendency, for objects to move towards each other and meet, a force, or gravity.

Extending this to 4dimensions ( mathematically of course ) is how GR models gravity.

[studiot]

Like it, MigL +1

[koti]

Very elegant analogy MigL.

 

Edit: This will most probably end up in me admiting to being dense but in the name of "there are no stupid questions" I have to ask...

If the 2D beings start off traveling parallel to each other on their plane in a direction - say we call it north, they will never meet each other. Say they are 1m apart from each other and being situated parallel to each other, the distance between them will stay to be 1m forever.

If we add the 3rd dimention and we start off at the equator again 1m appart from each other and travel to the north pole direction, we will pass the north pole exactly 1m appart from each other - just like when we started off. Again the distance between us will stay to be 1m forever.

Assuming we start off in the 2D world or the 3D world parallel to each other but the goal of our travel is a certain point at a distance, in both worlds we will and up meeting at that point - we are not travelling parallel to each other in both these cases.

 

So is your analogy not as elegant as I initially thought it was or am I just missing something trivial here? It is 2am and I'm very tired so it might be the latter.

Edited June 9, 2017 by koti

[MigL]

Try it on a globe, Koti.

All lines of longitude go north/south, are parallel at the equator and meet at the North pole.

[koti]

MigL, forget it... I havent been sleeping much lately, its horrible what sleep depravation can do to you.

[Eise]

An argument that helps me to understand it:

 

Imagine this small mass infinite far from any masses. It travels through spacetime along the time axis only, because it stays where it is in space. Now add a mass. It will curve spacetime, which means that now the small mass will deviate from the timeaxis, so it moves in space.

 

This video explains it pretty good (and I wonder why physicists still try to explain spacetime curvature with the rubber sheet analogy):

 

https://www.youtube.com/watch?v=jlTVIMOix3I

[studiot]

An argument that helps me to understand it:

 

Imagine this small mass infinite far from any masses. It travels through spacetime along the time axis only, because it stays where it is in space. Now add a mass. It will curve spacetime, which means that now the small mass will deviate from the timeaxis, so it moves in space.

 

This video explains it pretty good (and I wonder why physicists still try to explain spacetime curvature with the rubber sheet analogy):

 

https://www.youtube.com/watch?v=jlTVIMOix3I

 

Once again this analogy is fatally flawed as is implies there is some absolute reference underlying both the gridlines and the object's 'true ' position.

 

There is no absolute reference to say that 'it moved'.

[Strange]

 

Once again this analogy is fatally flawed as is implies there is some absolute reference underlying both the gridlines and the object's 'true ' position.

 

 

It doesn't require an absolute reference. You can define any coordinate system and the example still works. It is simplest when, as in the example, the coordinate system is initially stationary with respect to the mass. But that doesn't make it an absolute reference.

 

 

There is no absolute reference to say that 'it moved'.

 

Indeed. It moved relative to where it was before.

[studiot]

 

 

It doesn't require an absolute reference. You can define any coordinate system and the example still works. It is simplest when, as in the example, the coordinate system is initially stationary with respect to the mass. But that doesn't make it an absolute reference.

 

Indeed. It moved relative to where it was before.

 

Both your statement "where it was before" and Eise's It will deviate from the time axis imply an absolute axis.

 

In Eise's case the phrase 'the time axis'

 

In your case where 'it was before'

 

give the game away.

 

 

Ignoring the fact that you cannot simply 'add a mass' think of it this way

 

There are two different situations being compared and measurements in one system cannot be subtracted from measurements in the other to say 'it moved'.

 

The system with one mass has a different coordinate system from the system with two masses, they can never be the same.

 

There will be a third system to which you can reduce both the original scenarios, and in which you can say 'it moved'

 

But then again there will be many others in which 'it moved differently' is appropriately

 

and finally possibly one in which 'it did not move at all'

 

All these systems are equally valid, that is the point of relativity.

 

Gauss' Theorema Egrerium says that the measure of the projection of the comparison is invariant in all manifolds.

Edited June 9, 2017 by studiot

[Eise]

I only wanted to show the OP that there is a difference between space and spacetime. 'Standing still' in space does not mean 'standing still' in spacetime.

 

I don't think the OP understands what you are discussing now. Trying to have all details right will not lead to at least a bit understanding of lay people. It possibly will shy them away.

 

And as I said, the analogy as shown in the video is much better than the rubber sheet. But of course, still an analogy.

Edited June 9, 2017 by Eise

[DParlevliet]

Say you and I are 2dimensional people living on the surface of a plane ( ever read Flatland ? ) and we both decide to travel North. We would be travelling in parallel directions, so our paths would never meet.

But the question of Sooryakiran was about the situation where there is no movement (in 3D), no travelling to North.

[Strange]

But the question of Sooryakiran was about the situation where there is no movement (in 3D), no travelling to North.

 

 

The lines of longitude are supposed to represent the time dimension in this analogy. And "north" is the future. So you are always travelling "north" even when stationary in space.

[DParlevliet]

The lines of longitude are supposed to represent the time dimension in this analogy. And "north" is the future. So you are always travelling "north" even when stationary in space.

Indeed, but that supposes there is a movement in the time axis, like in the video. I agree with you answer earlier but oppose MigL and Studiot. Their explanation supposes movement in the time axis and that is the analogy they don't agree.

Edited June 12, 2017 by DParlevliet

[studiot]

But the question of Sooryakiran was about the situation where there is no movement (in 3D), no travelling to North.

 

Actually he doesn't say anything of the sort, however since I know that neither you nor he have English as a first language I will explain a best I can.

 

He actually said

 

 

at rest with respect to another larger one

 

He did not say the system was at rest, just that any motion of the large mass is follwed by a comparable motion of the small one.

 

One of the tenets of Relativity is that there is no such thing as absolute rest.

 

I'm quite sure MigL can answer for himself but just remember he was trying to reduce an extremely difficult problem (visualisation in 4 dimensions) to a simpler one to promote understanding.

Yes his model is not perfect, but it is very clear.

[DParlevliet]

Indeed Sooryakiran was more accurate then me, but that does not change the subject. If both masses (and observer) does not move relative to each other there is gravitation. That cannot be explained by (relative) movements in space-3D.

 

Multidimensional systems can be simplified to 2D dimensions without any change in effects as long there are no movements in the other dimensions. So that is no model, it is a simplification with follows all relativistic rules.

[studiot]

Indeed Sooryakiran was more accurate then me, but that does not change the subject. If both masses (and observer) does not move relative to each other there is gravitation. That cannot be explained by (relative) movements in space-3D.

 

Multidimensional systems can be simplified to 2D dimensions without any change in effects as long there are no movements in the other dimensions. So that is no model, it is a simplification with follows all relativistic rules.

 

Now that we have agreed the conditions which the OP set, we can move on to the question he actually asked, and MigL offered an analogy in a simplified situation.

 

The question that was asked boils down to

 

Why do objects subject to gravity experience an apparent force if gravity is due to (some form of) curvature?

 

Well Migl offered a situation where objects would indeed experience an apparent attractive force, although none really exists, due to the curvature of the 2D manifold and not due to any gravity.

 

You come from the land of imaginary forces (D'Alambert) so you should not be so suprised at this.

 

As to your last line, we are discussing the classical mechanics of angular momentum in another thread here and are approaching the point we we can deduce that even the simplest multidimensional system (3D) have properties that do not exist in 2D, so perhaps you would like to reconsider or rephrase this?

Edited June 12, 2017 by studiot

[DParlevliet]

There is a curvation in 2D, but without movement there will be no approaching each other. The approaching is caused by the travel North (combined with curvation), so by a movement. Wich movement?

 

I don't think a 3D has properties that do not exist in 2D as long as there are no movements in the 1D which is disregarded. That follows also from the relativity. Properties does not change is a 4D rotated of displaced. That can only be true if all properties exist equal for all axis of subset of axis.

[studiot]

 

 

I don't think a 3D has properties that do not exist in 2D as long as there are no movements in the 1D which is disregarded. That follows also from the relativity. Properties does not change is a 4D rotated of displaced. That can only be true if all properties exist equal for all axis of subset of axis.

 

This is off topic here so I shall not refer to it again, just refer you to this article in Poinsot's Theorem and Wrenches in Mechanics.

If you wish to pursue the difference between 2D and 3D please start another thread where it can be discussed at leisure.

 

http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/lecture14.pdf

 

Yet other French Mathematicians associated with differences between 2D and 3D are Varignon and Poincarre.

 

 

 

There is a curvation in 2D, but without movement there will be no approaching each other. The approaching is caused by the travel North (combined with curvation), so by a movement. Wich movement?

 

 

You have already accepted movement is available in the OP.

I know of nothing in General Relativity to suggest that movement is necessary to establish the apparent force of gravity.

If there is I would be very grateful if you would point it out.

Edited June 12, 2017 by studiot

[Strange]

Indeed Sooryakiran was more accurate then me, but that does not change the subject. If both masses (and observer) does not move relative to each other there is gravitation. That cannot be explained by (relative) movements in space-3D.

 

 

Indeed. But we re talking about movement in 4D space-time. The movement is in the time dimension - which is reduced to one of the two dimensions in the analogy, the other being the spatial separation.

 

You can say "there is no movement in time" but if so you are just rejecting the entire model based on this analogy and then no one can answer your question.

[DParlevliet]

You can say "there is no movement in time" but if so you are just rejecting the entire model based on this analogy and then no one can answer your question.

It was a reply to studiot, not to you. Indeed if two objects does not move relative to each other then gravitation (by curvation of spave) can only be explained in a model with movement in time. Thats is what the video showed. That is what Migl showed if one of its axis is time. But studiot did not agree with the video.

I know of nothing in General Relativity to suggest that movement is necessary to establish the apparent force of gravity.

Then explain how gravity exist in the case Sooryarikan proposed.

[studiot]

It was a reply to studiot, not to you. Indeed if two objects does not move relative to each other then gravitation (by curvation of spave) can only be explained in a model with movement in time. Thats is what the video showed. That is what Migl showed if one of its axis is time. But studiot did not agree with the video.

Then explain how gravity exist in the case Sooryarikan proposed.

 

You know you are completely right about one thing and it was a very good question.

 

The model proposed by MigL does indeed require motion in order to develop an apparent force and offers no answer as to why there might be one between objects with zero relative motion.

 

Interestingly Einstein in his paper submitted in 1915 to the Prussian academy says at greater length than this shortened translation:

 

"What we perceive as gravity is nothing more than objects moving in the geometry of spacetime"

 

I was rather concentrating on the geometry of spacetime part, which is in some ways much easier for me.

 

It is good to have separated this into two questions, one about motion and the other about geometry.

 

I am therefore searching for a model to demonstrate the attraction.

 

I would be grateful for help from anyone who knows more about the Einstein Field Eqautions than I do (not difficult).

 

Perhaps MigL has another, better model up his sleeve cigar?

Edited June 13, 2017 by studiot

[MigL]

Sorry, no more models.

 

But, then again, no model is perfect.

The only perfect model of reality, is reality itself, as even GR fails at some boundaries.

And that doesn't negate its usefulness.