A question about gravity

[mreddie1611]

I've been trying to wrap my head around Einstein’s explanation of gravity. I'd like some input to see if they way I'm visualizing could be correct, because it's a little different than what I've been seeing.

 

In typical illustrations of Relativity and the force of gravity, Space-Time is a shown as a two dimensional grid. Mass (a planet) is pictured as forcing the grid down, warping the plane like a heavy weight on a pliable surface, or re-shaping it into a sort of cone-like funnel.

 

What I see (on those iritating nights that thoughts of Relativity are keeping me awake) is the same two dimensional grid drawn on a thin sheet of rubber. The mass is a small rubber ball. Instead of forcing the ball down onto the grid, the ball is inserted into a tiny pin pricked hole in the rubber sheet. The mass displaces the area of the grid where it is inserted, and the lines of the grid are dramatically compressed around the ball. The further away from the mass, the less compression.

 

Even while I'm writing this I see holes in the idea (no pun intended), but bear with me: The sheet of rubber has no tension, or pull, until the rubber ball has been inserted. The strongest "pull" would be at the very edge of the hole. The further away from the displacement, the weaker the pull.

 

 

 

Does mass displace Space-Time? If so, does this also occur as mass moves though space, causing Space-Time compression? Would that mean that mass is affecting Space-Time at near light speeds?

 

 

[Schrödinger's hat]

I've been trying to wrap my head around Einstein's explanation of gravity. I'd like some input to see if they way I'm visualizing could be correct, because it's a little different than what I've been seeing.

 

In typical illustrations of Relativity and the force of gravity, Space-Time is a shown as a two dimensional grid. Mass (a planet) is pictured as forcing the grid down, warping the plane like a heavy weight on a pliable surface, or re-shaping it into a sort of cone-like funnel.

 

What I see (on those iritating nights that thoughts of Relativity are keeping me awake) is the same two dimensional grid drawn on a thin sheet of rubber. The mass is a small rubber ball. Instead of forcing the ball down onto the grid, the ball is inserted into a tiny pin pricked hole in the rubber sheet. The mass displaces the area of the grid where it is inserted, and the lines of the grid are dramatically compressed around the ball. The further away from the mass, the less compression.

 

Even while I'm writing this I see holes in the idea (no pun intended), but bear with me: The sheet of rubber has no tension, or pull, until the rubber ball has been inserted. The strongest "pull" would be at the very edge of the hole. The further away from the displacement, the weaker the pull.

 

 

 

Conceptually, I think this is somewhat of an improvement over the traditional pop-science interpretation. The idea that the stretching/curvature of the surface is intrinsic to it rather than merely as a result of embedding is more aparrent. I like the metaphor of there being more space piling up near a dense object. It gels well with the way things take infinite time cross event horizons in the types of coordinate frame that we're accustomed to.

You'd have to be careful what you meant by inertial motion here though, it's not really at all apparent in this metaphor, and I think a straight line (outside the sheet) would represent acceleration not only of the wrong amount, but in the wrong direction. If you consider a line that is straight with respect to a grid you drew before stretching the sheet then things are still somewhat off.

Without some way of representing the temporal direction you're unlikely to do well in this regard

 

This being said, this is just a metaphor, and bears only a passing relation to the full theory.. Maybe if your sheet looked like this to begin with, you might make some progress in making some of the numbers line up. But then you'd have to supress another spatial dimension and just have one direction as distance, and one as time.

 

Does mass displace Space-Time? If so, does this also occur as mass moves though space, causing Space-Time compression? Would that mean that mass is affecting Space-Time at near light speeds?

Not quite sure how to answer this, or interpret displacing space-time.

The presence of matter will mean that distances and straight lines or still/inertial paths will change.

Mass does effect space-time. I don't know what you mean by 'at near ligh speeds'

[DrRocket]

I've been trying to wrap my head around Einstein's explanation of gravity. I'd like some input to see if they way I'm visualizing could be correct, because it's a little different than what I've been seeing.

 

In typical illustrations of Relativity and the force of gravity, Space-Time is a shown as a two dimensional grid. Mass (a planet) is pictured as forcing the grid down, warping the plane like a heavy weight on a pliable surface, or re-shaping it into a sort of cone-like funnel.

 

What I see (on those iritating nights that thoughts of Relativity are keeping me awake) is the same two dimensional grid drawn on a thin sheet of rubber. The mass is a small rubber ball. Instead of forcing the ball down onto the grid, the ball is inserted into a tiny pin pricked hole in the rubber sheet. The mass displaces the area of the grid where it is inserted, and the lines of the grid are dramatically compressed around the ball. The further away from the mass, the less compression.

 

Even while I'm writing this I see holes in the idea (no pun intended), but bear with me: The sheet of rubber has no tension, or pull, until the rubber ball has been inserted. The strongest "pull" would be at the very edge of the hole. The further away from the displacement, the weaker the pull.

 

 

 

Does mass displace Space-Time? If so, does this also occur as mass moves though space, causing Space-Time compression? Would that mean that mass is affecting Space-Time at near light speeds?

 

 

 

The pop-sci analogies often create as much confusion as enlightenment.

 

1. Space-time is static. Nothing moves through it. The spacetime manifold embodies all of space and all of time -- past, present and future. Movement of a body is reflected in the world line of that body, which is a curve in the spacetime manifold. It can roughly be said that the body moves through "space" but not through spacetime. Even that requires a bit of thought as there is no such thing as a global notion of "space" (nor of "time"), and you need to understand the real meaning of local charts (What physicists call coordinates).

 

2. Curvature in higher dimensions is something that is a bit difficult to portray, so what you see in pop-sci are cartoons that depict curvature of surfaces. To really understand what is going on in relativity you will have to invest the effort to understand how curvature is handled in (pseudo) Riemannian geometry -- i.e. understand what a metric and curvature tensor really are. There is no simple explanation, despite the pop-sci cartoons that you see, and talk of the number of degrees in a triangle. .

 

3. As noted in 1), mass does not affect spacetime. But you can consider so-called gravity waves as an effect on the curvature of space, and those are predicted to propagate at the speed of light. This effect is not particularly straightforward, as it involves the non-linear nature of the Einstein field equations and an effect of gravity itself on curvature. It is not straightforward because gravitational energy does not occur directly in the stress-energy tensor that determines curvature, but rather enters through non-linearities in the field equations.

 

 

The bottom line is that if you are going to think deeply and seriously about general relativity you will have to go beyond the pop-sci analogies. Probably the best source for a rigorous exposition of general relativity is Gravitation by Misner, Thorne and Wheeler. Another excellent book is General Relativity and the Einstein Field Equations by Yvonne Choquet-Bruhat, but to read that one you should probably first read something like Analysis, Manifolds and Physics by Yvonne Choquet-Bruhat and Cecile Dewitt-Morettte.

 

Or you can stick with the pop-sci explanations. But in that case many questions that arise will be the result of the confusion that naturally arises from over-simplified and misleading ideas, and they will not have answers that are comprehensible in the language in which the initial "explanation" was presented.

[mreddie1611]

I suppose what it all comes down to for me is an attempt to explain Einstein’s concept of gravity in an accessible metaphor. Space-Time contraction when approaching the speed of light may take a while to understand, but the concept (if not the math) is not outside the ability of an interested pedestrian high-school graduate. Like me. So why not gravity? It may be “pop-sci” cartoons that help the understanding, but I’m a big fan of cartoons. And pop-sci, come to think of it. Aren’t you? How can anybody not like “Futurama”?

 

Einstein’s ideas regarding gravity don’t seem as simple and straight forward as his ideas on time dilation. Yeah, my metaphor is a cartoon, but is it a cartoon that works at least as well as the ones we’ve all seen? Probably not, sure, but I’m certainly not satisfied with what’s out there.

 

 

 

The pop-sci analogies often create as much confusion as enlightenment.

 

1. Space-time is static. Nothing moves through it. The spacetime manifold embodies all of space and all of time -- past, present and future. Movement of a body is reflected in the world line of that body, which is a curve in the spacetime manifold. It can roughly be said that the body moves through "space" but not through spacetime. Even that requires a bit of thought as there is no such thing as a global notion of "space" (nor of "time"), and you need to understand the real meaning of local charts (What physicists call coordinates).

 

2. Curvature in higher dimensions is something that is a bit difficult to portray, so what you see in pop-sci are cartoons that depict curvature of surfaces. To really understand what is going on in relativity you will have to invest the effort to understand how curvature is handled in (pseudo) Riemannian geometry -- i.e. understand what a metric and curvature tensor really are. There is no simple explanation, despite the pop-sci cartoons that you see, and talk of the number of degrees in a triangle. .

 

3. As noted in 1), mass does not affect spacetime. But you can consider so-called gravity waves as an effect on the curvature of space, and those are predicted to propagate at the speed of light. This effect is not particularly straightforward, as it involves the non-linear nature of the Einstein field equations and an effect of gravity itself on curvature. It is not straightforward because gravitational energy does not occur directly in the stress-energy tensor that determines curvature, but rather enters through non-linearities in the field equations.

 

 

The bottom line is that if you are going to think deeply and seriously about general relativity you will have to go beyond the pop-sci analogies. Probably the best source for a rigorous exposition of general relativity is Gravitation by Misner, Thorne and Wheeler. Another excellent book is General Relativity and the Einstein Field Equations by Yvonne Choquet-Bruhat, but to read that one you should probably first read something like Analysis, Manifolds and Physics by Yvonne Choquet-Bruhat and Cecile Dewitt-Morettte.

 

Or you can stick with the pop-sci explanations. But in that case many questions that arise will be the result of the confusion that naturally arises from over-simplified and misleading ideas, and they will not have answers that are comprehensible in the language in which the initial "explanation" was presented.

[DrRocket]

I suppose what it all comes down to for me is an attempt to explain Einstein's concept of gravity in an accessible metaphor.

 

Einstein's ideas regarding gravity don't seem as simple and straight forward as his ideas on time dilation. Yeah, my metaphor is a cartoon, but is it a cartoon that works at least as well as the ones we've all seen? Probably not, sure, but I'm certainly not satisfied with what's out there.

 

 

General relativity is quite a bit more subtle than special relativity.

 

Even with special relativity the heart of the theory is not "time dlation" or "length contraction" or other coordinate effects but rather the invariance of the spacetime interval as measured with the Minkowski metric. This carries over to general relativity, where you discover that special relativity is really just a local approximation to general relativity -- it is general relativity on the tangent space to the spacetime manifold. While this may not yet make sense to you, until it does you are not yet ready to seriously study general relativity.

 

Any successful attempt to explain Einstein's concept of gravity must start with an understanding of the underlying theory, and that involves much more than any metaphor. In short, a metaphor is no substitute for understanding.

 

You are right to not be satisfied with the cartoons that are "out there". But you are extremely naive to think that ANY metaphor will provide you with understanding.

 

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

 

Rather than undertake something for which you do not yet have adequate background, you would be well advised to spend your time in obtaining a deep understanding of those subjects that are within your reach and in learning the necessary material to extend that reach. General relativity requires quite a lot of mathematics, in particular differential geometry. But you are in a position to study special relativity seriously, since that requires little more than elementary algebra (though linear algebra is needed for more advanced study of the geometry of Minkowski space). You are also almost certainly in a position to learn algebra and elementary calculus which is a necessary step in the study of the mathematics needed for general relativity.

Edited December 8, 2011 by DrRocket

[Anilkumar]

Hello there,

 

. . . Space-time is static. Nothing moves through it. The spacetime manifold embodies all of space and all of time -- past, present and future. Movement of a body is reflected in the world line of that body, which is a curve in the spacetime manifold. It can roughly be said that the body moves through "space" but not through spacetime. Even that requires a bit of thought as there is no such thing as a global notion of "space" (nor of "time"), and you need to understand the real meaning of local charts (What physicists call coordinates

 

By this, would it be proper to imply that;

 

The 'Space is a natural entity' but,

 

'Space-time' is a geometrical representation of an event in that 'Space' or,

 

'Space-time' is a mathematical graph, of motion, of an object inside 'space'?

 

. . . there is no such thing as a global notion of "space" (nor of "time"), and you need to understand the real meaning of local charts (What physicists call coordinates

 

Does the point made here, refer to the same position, taken & mentioned, in the post of another thread, shown below ;

 

. . . For special relativity, Einstein came to embrace the notion that nothing exists beyond what we observe, what we can measure. He defined time as simply "what you read on a clock", and space as simply "the distance you measure between two points". The notion of time and space as anything beyond these "operational" definitions were, according to Einstein, simply the creation of the human mind.

In other words, time is relative; how fast it passes depends on the motion of the observer. This is measurable. However, the concept of time we hold in our minds is merely an abstraction. Einstein applied a similar view to "space".

 

But how can space contract? And how can the apparently same space contract differently for two (or more) observers in relative motion? Here Einstein is saying there is no "space" per se; only the distance between two points. The distance between the two points is measurable, albeit differently by the two observers. But "space" itself is again a mere abstraction.

 

In summary, we must "stop thinking about 'space and time' (as) something that is 'given to us', and must instead think about 'measuring positions and times', which is something we can do," writes Morton Tavel, professor of physics at Vassar College. "Only our measurements have real existence. We build up an intuition of something called space and time, which we believe exists beyond these measurements . . . (But) Einstein's first commandment was to pay attention only to your measurements and worry later about the properties of the more abstract notion of space and time." . . .

Thank you.

Edited December 8, 2011 by Anilkumar