Curved space

[Anilkumar]

No.

 

Difficult questions have simple, easy-to-understand, wrong answers.

 

To understand any theory, and general relativity is no exception, you must invest intellectual capital, and that includes mastering the language in which it is formulated.

I suppose Albert Einstien did not know differential geometry when he descerned the Theory of relativity, an unknown theory then. But why would we need mathematics to just understand what is already known.

 

But I don't want to drift into an off-the-subject argument.

[timo]

I suppose Albert Einstien did not know differential geometry when he descerned the Theory of relativity, an unknown theory then.

You probably don't speak German, but by visual inspection you may realize that the way Einstein introduced relativity in his original publication is surprisingly similar to the way it is introduced in some modern physics textbooks. As a matter of fact, the abstract says

The mathematical tools required for General Relativity already existed in the form of differential calculus (footing on the research of Gauss, Riemann, and Christoffel) for non-euclidean manifolds that was rewritten by Ricci and Levi-Civita and brought into a form that has already been applied successfully to other problems in theoretical physics.

(and "yes", such terribly long sentences are the default style choice in this work of Einstein )

[Anilkumar]

You probably don't speak German, but by visual inspection you may realize that the way Einstein introduced relativity in his original publication is surprisingly similar to the way it is introduced in some modern physics textbooks. As a matter of fact, the abstract says

 

(and "yes", such terribly long sentences are the default style choice in this work of Einstein )

 

Yes, I have no acquaintance with German language. But I don't think that would be a hindrance. Every word Einstein has uttered or written has been translated into English, I suppose. I have read that translation earlier. The mathematical tools no doubt existed. But Einstein did not have those tools with him when he imagined the ‘Theory of Relativity’. He always stressed that ‘IMAGINATION IS MORE IMPORTANT’. He did not arrive at the ‘Theory of Relativity’ because he knew Differential geometry. He could imagine what was not known till then, because he was Einstein. Why can’t we explain & understand that which is known already in simple terms. When he could discern an unknown thing without the help of mathematics, why can’t we discern what is known already without the help of mathematics.

 

 

 

Einstein said & I quote “If you can't explain it simply, you don't understand it well enough”.

 

Anyway, I have begun to learn Differential geometry.

[divinum1]

Hi everybody,

 

How and why does mass curve space?

 

Thank you.

 

Hi Anilkumar:

Let me try to explain in layman terms as why space around a mass is curved.

It is gravitational field that establishes this so called curvature around a mass. And the reason is because gravitational field is composed of two forces. Which coexist and cooperate at 180 degrees relative to one another. And these two forces divided the space equally between themselves, while at the same time they have to remain perpendicular to one another at all the times. And as a result, at both polar ends they become subtracted, and this subtraction results in the curvature of space at both poles. Which makes the curvature of the field something similar to magnetic field lines.

[ajb]

I suppose Albert Einstien did not know differential geometry when he descerned the Theory of relativity, an unknown theory then.

 

I don't think Einstein was an expert in differential geometry when he formulated general relativity. My understanding is that he realised that differential geometry was likely to be important, so he made the effort to learn what he could.

 

Differential geometry at the time was the realm of pure mathematicians, only later has it become a standard part of the physicists tool kit.

 

But why would we need mathematics to just understand what is already known.

 

Well, mathematics is the framework of all physical theories.

 

Einstein said & I quote “If you can't explain it simply, you don't understand it well enough”.

 

Simply is a very subjective and this is an idealisation. To really explain general relativity "simply" one does require some knowledge of differential geometry. Maybe one does not need all the details to get the idea, but some elementary understanding of manifolds, metrics and connections is needed.

 

We all have recommendations on what books to read, I suggest Sean M. Carroll, Lecture Notes on General Relativity, arXiv:gr-qc/9712019v1.

[IM Egdall]

Thank you for your interest.

 

OK, I will learn Differential geometry, and also read Gravitation. But till then to make things easier, isn't there a simplified theoretical explanation to it?

 

Thank you

 

 

At the risk of oversimplifying, I will try to answer your question with no mathematics. The presence of mass (and energy) causes space and time to warp. This is at the heart of general relativity. Let's look at examples of each:

 

 

Space warp: Imagine two points in space where all objects are so far away that gravity is virtually zero. Now imagine placing the Earth near these two points. As seen from far away, the two points will now be a different distance apart. This in essence is space warp or space curvature.

 

Time warp: Imagine a clock also in space where all objects are so far away that gravity is virtually zero. Now again imagine placing the Earth near this clock. The clock now runs slower. due to the Earth's presence. This is called time warp or curvature of time.

 

Together time warp and space warp are called spacetime curvature. And this spacetime curvature determines the path of the Moon around the Earth, and all the planets around the Sun etc., and holds us to the surface of the Earth. Spacetime curvature IS gravity.

 

I hope this helps.

[Anilkumar]

Hi Anilkumar:

Let me try to explain in layman terms as why space around a mass is curved.

It is gravitational field that establishes this so called curvature around a mass. And the reason is because gravitational field is composed of two forces. Which coexist and cooperate at 180 degrees relative to one another. And these two forces divided the space equally between themselves, while at the same time they have to remain perpendicular to one another at all the times. And as a result, at both polar ends they become subtracted, and this subtraction results in the curvature of space at both poles. Which makes the curvature of the field something similar to magnetic field lines.

 

Hello Divinum1,

 

great many thanks for connecting;

 

• 'gravitational field is composed of two forces' - I did not know this clearly. Is this what they say, that - One component is directed towards the center & the other is in a direction tangential to the cirular orbit?---------------------------------------------------------------------------------------------------
• 'polar ends' - Does this mean; the polar ends of the earth or any body [the north/south pole]?------------------------------------------------------------------------------------------------------------------------------------------------------------
• 'they become subtracted' - Vector subtraction?----------------------------------------------------------------------------------------------------------------------------
• 'Which makes the curvature of the field something similar to magnetic field lines' - So due to the curvature of the the Gravitational field, things moving through that field, tend to follow the curved lines of Gravitational field, like a magnetic compass needle gets deflected along the magnetic lines in a magnetic field?

Edited December 1, 2011 by Anilkumar

[DrRocket]

I suppose Albert Einstien did not know differential geometry when he descerned the Theory of relativity, an unknown theory then. But why would we need mathematics to just understand what is already known.

 

But I don't want to drift into an off-the-subject argument.

 

Einstein went out of his way to seek help from Marcel Grossmann, who helped him with Riemannian geometry and tensor analysis. It was ony because Riemann had invented differential geometry that Einstein was vable to formulate genersal relativity. Einstein was vrather clear in acknowledging his debt to Riemann.

 

Mathematics is the language of physics. If you do not understand the requisite mathematics you are effectively illiterate. That appplies to all of physics -- relativity, quantum theory, mechanics, electrodynamics, the whole enchilada.

 

The mathematical tools no doubt existed. But Einstein did not have those tools with him when he imagined the 'Theory of Relativity'. He always stressed that 'IMAGINATION IS MORE IMPORTANT'. He did not arrive at the 'Theory of Relativity' because he knew Differential geometry. He could imagine what was not known till then, because he was Einstein. Why can't we explain & understand that which is known already in simple terms. When he could discern an unknown thing without the help of mathematics, why can't we discern what is known already without the help of mathematics.

 

This is just plain wrong.

 

It was specifically the application of differential geometry and tensor analysis that enabled Einstein to formulate general relativity. That is embodied in Einstein's notion of "general covariance" which in reality is just the coordinate-free formulation permitted by differential geometry. Because he initially lacked understanding of much of the mathematics necessary, he sought out help and learned the mathematics.

 

Einstein's quote that "Imagination is more important" is widely misunderstood and quoted by the mathematically illiterate. It is true in the sense that imagination is the most important ingredient of good research. But imagination wihout an understanding of both existing theory and the tools of mathematics is useless and results in nothing but fantasy. Good researchers first come to understand the existing theory and the language, mathematics, in which it is expressed and only after establishing a solid foundation do they apply imagination to further the body of knowledge by means of disciplined research.

Edited December 1, 2011 by DrRocket

[Anilkumar]

At the risk of oversimplifying, I will try to answer your question with no mathematics. The presence of mass (and energy) causes space and time to warp. This is at the heart of general relativity. Let's look at examples of each:

 

 

Space warp: Imagine two points in space where all objects are so far away that gravity is virtually zero. Now imagine placing the Earth near these two points. As seen from far away, the two points will now be a different distance apart. This in essence is space warp or space curvature.

 

Time warp: Imagine a clock also in space where all objects are so far away that gravity is virtually zero. Now again imagine placing the Earth near this clock. The clock now runs slower. due to the Earth's presence. This is called time warp or curvature of time.

 

Together time warp and space warp are called spacetime curvature. And this spacetime curvature determines the path of the Moon around the Earth, and all the planets around the Sun etc., and holds us to the surface of the Earth. Spacetime curvature IS gravity.

 

I hope this helps.

 

Hello IM Egdall,

 

thank you for trying to help-out,

 

So now,

 

In the example of Space warp:

 

If there was a Rocket, shuttling between those two points at a fixed uniform velocity, prior to our bringing Earth near them;

 

will now take less time or may be more time, to reach between the points, after we place Earth near them?

 

for the person observing from far away.

 

If this is so; {I know that there are no WHYs in physics, but still}

is there a reason for this?

 

i.e.

 

What TOOLS does Gravity have in its pockets, to change that distance? &

 

What are the,

 

OR

 

Where are the,

 

nuts & bolts placed in the 'BODY' of "THE 'EMPTY' SPACE", that the Gravity 'tightens' or 'loosens' to bring a STRUCTURAL change in the STRUCTURELESS STRUCTURE of the empty Space?

 

Thank you

[Anilkumar]

Thank you DrRocket,

 

for your interest.

 

Mathematics is the language of physics.

 

I feel, a language can not invent theories. It is the mind that invents theories. And languages are usefull in expressing it to others.

 

Also, I am unable to decide which one of the following two statements are true, as they are contradictory:-

 

. . . . .It was ony because Riemann had invented differential geometry that Einstein was vable to formulate genersal relativity . . . .

. . . . It was specifically the application of differential geometry and tensor analysis that enabled Einstein to formulate general relativity.

 

------------------------------------And

 

I don't think Einstein was an expert in differential geometry when he formulated general relativity. My understanding is that he realised that differential geometry was likely to be important, so he made the effort to learn what he could.

 

Differential geometry at the time was the realm of pure mathematicians, only later has it become a standard part of the physicists tool kit . . . .

 

Anyway I am not an authority on this and moreover I am very-less interested in knowing HOW & much-more interested in knowing WHAT, Einstein invented.

 

I started this thread to get a glimpse of the Space-time warp phenomenon. To know the HOWs & WHATs of it. I want to get to know about it as much as possible. I do not wish to become an expert or an advocate of SR/GR. I want to know about it.

 

I would appreciate if anybody could help me in this regard.

 

Thank you.

 

I don't think Einstein was an expert in differential geometry when he formulated general relativity. My understanding is that he realised that differential geometry was likely to be important, so he made the effort to learn what he could.

 

Differential geometry at the time was the realm of pure mathematicians, only later has it become a standard part of the physicists tool kit.

 

 

 

Well, mathematics is the framework of all physical theories.

 

 

 

Simply is a very subjective and this is an idealisation. To really explain general relativity "simply" one does require some knowledge of differential geometry. Maybe one does not need all the details to get the idea, but some elementary understanding of manifolds, metrics and connections is needed.

 

We all have recommendations on what books to read, I suggest Sean M. Carroll, Lecture Notes on General Relativity, arXiv:gr-qc/9712019v1.

 

Hello ajb,

 

I am trying to learn differential geometry. But till then I think I can surely, get to know about it theoretically as much as possible.

 

Nice meeting you.

Edited December 1, 2011 by Anilkumar

[ajb]

Also, I am unable to decide which one of the following two statements are true, as they are contradictory:-

 

I don't see there is a contradiction. Einstein was not an expert in differential geometry when he first worked on developing general relativity. Grossmann introduced Einstein to differential geometry and collaborated with Einstein on several papers. It was Levi-Civita who suggested to Einstein that differential geometry, and in particular tensors and the idea of general covariance could be useful in his formulation of a relativistic theory of gravity.

 

The earliest works of Einstein on gravity, well really acceleration and free fall in special relativity (1908) and then later the equivalence principle and the prediction of gravitational time dilation (1911) all pre-date the proper formulation of general relativity.

 

 

The point being, Einstein realised that general relativity requires differential geometry to be formulated properly. The motivation for this is that Einstein believed physics to be described by local fields and that covariance is fundamental. Grossmann played a big role in helping Einstein with geometry.

[Anilkumar]

I don't see there is a contradiction. Einstein was not an expert in differential geometry when he first worked on developing general relativity. Grossmann introduced Einstein to differential geometry and collaborated with Einstein on several papers. It was Levi-Civita who suggested to Einstein that differential geometry, and in particular tensors and the idea of general covariance could be useful in his formulation of a relativistic theory of gravity.

 

The earliest works of Einstein on gravity, well really acceleration and free fall in special relativity (1908) and then later the equivalence principle and the prediction of gravitational time dilation (1911) all pre-date the proper formulation of general relativity.

 

 

The point being, Einstein realised that general relativity requires differential geometry to be formulated properly. The motivation for this is that Einstein believed physics to be described by local fields and that covariance is fundamental. Grossmann played a big role in helping Einstein with geometry.

 

Yes, even I too had read something similar to what you mentioned.

[IM Egdall]

Hello IM Egdall,

 

thank you for trying to help-out,

 

So now,

 

In the example of Space warp:

 

If there was a Rocket, shuttling between those two points at a fixed uniform velocity, prior to our bringing Earth near them;

 

will now take less time or may be more time, to reach between the points, after we place Earth near them?

 

for the person observing from far away.

 

If this is so; {I know that there are no WHYs in physics, but still}

is there a reason for this?

 

i.e.

 

What TOOLS does Gravity have in its pockets, to change that distance? &

 

What are the,

 

OR

 

Where are the,

 

nuts & bolts placed in the 'BODY' of "THE 'EMPTY' SPACE", that the Gravity 'tightens' or 'loosens' to bring a STRUCTURAL change in the STRUCTURELESS STRUCTURE of the empty Space?

 

Thank you

 

As to the rocket, once the earth is put in place near the two points, both space and time are affected (warped.) The rocket would then follow the shortest path in the warped spacetime or what is called the geodesic.

 

As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that. Maybe the combining of general relativity and quantum mechanics in a new theory of so-called "quantum gravity" will someday tell us why.

Edited December 2, 2011 by IM Egdall

[Anilkumar]

As to the rocket, once the earth is put in place near the two points, both space and time are affected (warped.) The rocket would then follow the shortest path in the warped spacetime or what is called the geodesic.

 

As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that. Maybe the combining of general relativity and quantum mechanics in a new theory of so-called "quantum gravity" will someday tell us why.

 

OR

simply,

 

are we interpreting the effect of the Gravitational field on Matter & Time as Space-time warp? i.e.;

 

When an object or light is passing through a Gravitational field it is forced to behave differently due to its influence and we are attributing this change in behaviour to a change in the structure of the Space.

 

To make my point clear, I would like to give the following illustration:-

 

"Let us suppose there is a Bar-magnet and a Magnetic-needle, in empty space, devoid of any influence of any other kind. The Magnetic-needle is placed far away from the Magnet & there is negligible or no deflection of the needle.

 

Now the Magnetic-needle slowly starts moving towards the Magnet. As it gets closer to the Magnet, we start seeing deflections in the needle.

 

Now we know that the deflections are due to the influence of the magnetic field of the Bar-magnet.

 

But instead of saying that the deflections are due to the influence of the magnetic field of the Bar-magnet; we say the Space arround the Bar-magnet is warped due to its Magnetic-field & the warp is the cause for the deflections".

 

Is this similar to Space warp due to Gravity. The difference being that, the Magnet deflects the Magnetic-needle, whereas Gravity deflects everything with mass & even Time.

 

Like saying;

 

if there is a Ball on top of a Table. Instead of saying 'The Ball is on the Table' we say 'The Table is under the Ball'.

 

Instead of saying 'Gravity influences Motion' we say 'Gravity warps Space'.

 

With all this writing as above;

 

Am I anywhere near interpreting the phenomenon of Space-Time warp?

 

[dimreepr]

Hi everybody,

 

How and why does mass curve space?

 

Thank you.

 

Hi anilkumar I see you've posted on my thread that "theory" explains it. As for the maths I'd need alot of help 2 express.

[Anilkumar]

Hi anilkumar I see you've posted on my thread that "theory" explains it. As for the maths I'd need alot of help 2 express.

 

I feel 'Theory' gives a feel of whats happening.

 

And Mathematics gives a proof of it.

[guenter]

If there was a Rocket, shuttling between those two points at a fixed uniform velocity, prior to our bringing Earth near them;

 

will now take less time or may be more time, to reach between the points, after we place Earth near them?

 

for the person observing from far away.

Replacing the rocket by radar signals, we talk about the Shapiro Delay. Those signals reflected by mars take more time to return to earth in case they pass near by the sun than compared to an analogous measurement without the sun. The effect is tiny but measurable and demonstrates the spacetime curvature due to the sun.

[IM Egdall]

Is this similar to Space warp due to Gravity. The difference being that, the Magnet deflects the Magnetic-needle, whereas Gravity deflects everything with mass & even Time.

 

Like saying;

 

if there is a Ball on top of a Table. Instead of saying 'The Ball is on the Table' we say 'The Table is under the Ball'.

 

Instead of saying 'Gravity influences Motion' we say 'Gravity warps Space'.

 

With all this writing as above;

 

Am I anywhere near interpreting the phenomenon of Space-Time warp?

 

 

 

You are close. However, it is not quite correct to say "gravity warps space." It is better to say the presence of mass/energy warps space (and time). LIke the presence of the Sun warps space and time in its vicinity.

 

And this warping or curvature of space and time (spacetime curvature) is what causes planets to orbit the Sun and holds us down to the Earth. We call this effect gravity. So spacetime warp or curvature IS gravity.

 

Physicist John Archibald Wheeler said something like "mass/energy grips spacetime and tells it how to curve -- and curved spacetime (gravity) grips mass/energy and tells it how to move."

Edited December 4, 2011 by IM Egdall

[Anilkumar]

You are close. However, it is not quite correct to say "gravity warps space." It is better to say the presence of mass/energy warps space (and time). LIke the presence of the Sun warps space and time in its vicinity.

 

And this warping or curvature of space and time (spacetime curvature) is what causes planets to orbit the Sun and holds us down to the Earth. We call this effect gravity. So spacetime warp or curvature IS gravity.

 

Physicist John Archibald Wheeler said something like "mass/energy grips spacetime and tells it how to curve -- and curved spacetime (gravity) grips mass/energy and tells it how to move."

 

If it is right to say that;

 

"Gravity influences Motion & Time"

 

Why are we creating unnecessary misunderstanding by saying, the other way round, that;

 

"Presence of mass/energy warps space &Time. And this warped space affects motion. This effect is called gravity".

 

While we very well know that;

 

• Space is a structureless entity. And so altering the structure of that entity which does not have any structure does not arise.
• We do not know how it can be done.

 

As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that. Maybe the combining of general relativity and quantum mechanics in a new theory of so-called "quantum gravity" will someday tell us why.

 

Replacing the rocket by radar signals, we talk about the Shapiro Delay. Those signals reflected by mars take more time to return to earth in case they pass near by the sun than compared to an analogous measurement without the sun. The effect is tiny but measurable and demonstrates the spacetime curvature due to the sun.

 

I have no objection in the fact that the path & duration of the signals are altered.

 

But I have objection in how we say that.

 

We say that;

 

"mass/energy warps Space & Time and so, the Signals take the altered path".

 

I object this method of its interpretation, because, Space is a structureless entity. And there is no way, the structure of a structureless entity can be altered.

 

So instead I want us to say that;

 

"Mass has Gravity. And this Gravity alters the Direction and Duration of anything that is moving, in its vicinity"

Edited December 5, 2011 by Anilkumar

[guenter]

"mass/energy warps Space & Time and so, the Signals take the altered path".

 

I object this method of its interpretation, because, Space is a structureless entity. And there is no way, the structure of a structureless entity can be altered.

 

There is a way, Anilkumar. The Friedmann-Robertson-Walker cosmological model is derived from the einsteinian equations. Here the mass density is thought homogeneous like sugar in the tea. Being perfectly structureless, the curvature as expressed by the sum of the angles in a triangle can be hyperbolic, euclidian or spherical. Depending on the mass density.

 

 

@IM Egdall: "As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that."

 

Why? There is no need, as long as the predictions of the theory are in excellent agreement with the observation. The problem of General Relativity is the singularity.

[Anilkumar]

Thanks Quenter,

 

for your concern.

 

There is a way, Anilkumar. The Friedmann-Robertson-Walker cosmological model is derived from the einsteinian equations. Here the mass density is thought homogeneous like sugar in the tea. Being perfectly structureless, the curvature as expressed by the sum of the angles in a triangle can be hyperbolic, euclidian or spherical. Depending on the mass density.

 

@IM Egdall: "As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that."

 

Why? There is no need, as long as the predictions of the theory are in excellent agreement with the observation. The problem of General Relativity is the singularity.

 

To act, one needs 'SOMETHING' to act on;

 

one cannot act on 'NOTHING' ;

 

SPACE is 'NOTHING' ;

 

it is 'EMPTINESS'.

 

Mass or mass density, denotes EXISTANCE of physical material, and Empty-Space denotes NON-EXISTANCE of anything.

 

Then,

 

how can something that 'exists' act on something that 'does not exist'.

 

The very proposition that Space i.e. 'INFINITE - EMPTINESS' has a geometrical shape of its own, is incomprehensible.

 

How can empty space, have a geometrical shape? It is like saying 'The Non-existent', 'THE-ABSENT', or 'THAT WHICH IS MISSING' has a shape of its own.

Edited December 6, 2011 by Anilkumar

[StringJunky]

 

How can empty space, have a geometrical shape? It is like saying 'The Non-existent', 'THE-ABSENT', or 'THAT WHICH IS MISSING' has a shape of its own.

The geometry of space is inferred or extrapolated from the observed behaviour of bodies within it.

[IamJoseph]

Mass or mass density, denotes EXISTANCE of physical material, and Empty-Space denotes NON-EXISTANCE of anything.

 

 

Magestic engineering is seen throughout the universe, as with the human body. However, unlike our engineering values, the starting point [origins] is an enigma.

 

Space is exactly the same matter as all other physical matter. This is the bottom line effect of Einstein's space bending premise. If space was 'nothingness' it could not bend! Space is a rarer form of matter, rarer than atmospheric matter, as in: solids; liquids; atmospheric matter [less rare; air]; non-atmospheric matter [still rarer - but never 'nothing']. Everything contained in the universe is basically the same matter - only their densities vary.

 

The real beguiling question is: where does it end? I don't refer to the horizonal or vertical mediums of space, but what does this bendable space rest upon? Remember that once there was no space - because once there was no universe. The expanding universe says that the space is expanding; the question thus remains, where is the space expanding to - and upon what foundation? The finite factor negates the existence of anything contained in the universe - to exist outside or not within the universe.

 

 

 

My answer: we cannot know the true 'origins' of anything. We do not know the origins of stars, life or pineapples.We get away from this enigma by wrongly accounting the universe as infinite [MV; Parallel Uni's]. But the expanding universe says it was not infinite 10 seconds ago.

 

There is a way, Anilkumar. The Friedmann-Robertson-Walker cosmological model is derived from the einsteinian equations. Here the mass density is There is no need, as long as the predictions of the theory are in excellent agreement with the observation. The problem of General Relativity is the singularity.

 

 

 

There is no singularity in the universe, nor can there ever be according to scientific understandings. Basically, aside from the mathematical and theoretical perspective, a singularity aligns with the premise of one indivisible and irreducible entity, namely a pristine 'one'. A pure, pristine 'one' cannot exist in the universe: if it did it could not produce an action, which requires a minimum of two interactives. A sole and lone pristine one would remain the same at all times, namely it can be seen as an infinite entity, one which requires no other counterpart to exist or cause an action. We know also, that if the universe is finite - it cannot contain an infinite.It takes two to tango applies.

[Anilkumar]

The geometry of space is inferred or extrapolated from the observed behaviour of bodies within it.

 

Why don't we accredit, the observed behavior of bodies, to their 'INHERENT PROPERTIES' ?

 

Why ascribe it to 'NOTHING'?

 

 

-------------------------**********************-----------------------------------

. . . Space is a rarer form of matter, rarer than atmospheric matter, as in: solids; liquids; atmospheric matter [less rare; air]; non-atmospheric matter [still rarer - but never 'nothing'] . . .

 

This does not accord with the definition of Space.

Edited December 6, 2011 by Anilkumar

[swansont]

Why don't we accredit, the observed behavior of bodies, to their 'INHERENT PROPERTIES' ?

 

Because a mass will not move or accelerate on its own. There is an external influence, and in GR, this is geometric in origin.