Gravity is really curves in space time

[michael879]

so according to relativity, gravity is rly curves in space time. I imagine this in a 2d context, with a 2d world wrapped around a "balloon". Gravity would be like pushing in part of the balloon. If you think about the way this curvature distorts "quantized" space-time, it makes sense that something moving towards a planet would accelerate, and something moving away would slow down. However, this only works for small object vs. large objects. How do two dents in space-time fall into each other? and why would something with no velocity move into a large gravitational source?

 

[selfAdjoint]

so according to relativity, gravity is rly curves in space time. I imagine this in a 2d context, with a 2d world wrapped around a "balloon". Gravity would be like pushing in part of the balloon. If you think about the way this curvature distorts "quantized" space-time, it makes sense that something moving towards a planet would accelerate, and something moving away would slow down. However, this only works for small object vs. large objects. How do two dents in space-time fall into each other? and why would something with no velocity move into a large gravitational source?

If you imagine two of the dents in your balloon approaching each other, they would first become a compound dent with a single lip but two pits, and then the pits would combine, becoming deeper than either by itself, so we have now the gravity curvature of one body that is the sum of the masses of the two original ones.

If something with no velocity is close enough to another body to be on the slope of that body's dent, it would slide down that slop toward the pit. In Newtonian terms we would say it felt a weak gravitational force which drew it into the region of stronger gravitation.

 

[michael879]

If you imagine two of the dents in your balloon approaching each other, they would first become a compound dent with a single lip but two pits, and then the pits would combine, becoming deeper than either by itself, so we have now the gravity curvature of one body that is the sum of the masses of the two original ones.

If something with no velocity is close enough to another body to be on the slope of that body's dent, it would slide down that slop toward the pit. In Newtonian terms we would say it felt a weak gravitational force which drew it into the region of stronger gravitation.

see that's how it was explained to me, however I have two major problems with it.
Your first answer: what makes them compound? the dent is supposed to describe gravitational attraction, so we should be able to visualize why two dents would move towards each other. I can't and ur explanation doesnt.

second answer: doesn't work at all. Your explaining this acting as if there is some force in the center of the sphere universe pulling everything towards it. Without that, there is no reason for an object to "slide" down the curve. With it, we have another problem as to what the force is and what causes it. I agree this would explain gravity but I have never heard anyone talk about it, and I think people use this explanation because we are all so used to a downward force. Its easier if you think of the dents facing upward (which would be the same thing in a universe with no extra forces).

anyone else have any ideas? can't figure this out.

 

[yogi]

Take an elastic sheet in free space and put two balls on it having masses m1 and m2. Space the balls apart - now grab the sheet at all for corners and accelerate it in a direction normal to the surface upon which the balls are at rest - the sheet will deform because of the inertia of the balls - they will roll toward each other - no other force is required.

 

[selfAdjoint]

see that's how it was explained to me, however I have two major problems with it.
Your first answer: what makes them compound? the dent is supposed to describe gravitational attraction, so we should be able to visualize why two dents would move towards each other. I can't and ur explanation doesnt.

second answer: doesn't work at all. Your explaining this acting as if there is some force in the center of the sphere universe pulling everything towards it. Without that, there is no reason for an object to "slide" down the curve. With it, we have another problem as to what the force is and what causes it. I agree this would explain gravity but I have never heard anyone talk about it, and I think people use this explanation because we are all so used to a downward force. Its easier if you think of the dents facing upward (which would be the same thing in a universe with no extra forces).

This is the problem with the rubber sheet example (or your balloon). The problem has often been expressed on this forum, that these models make use of exterior gravity, whereas in GR the curvature IS the gravity. What can I say but that the math of Einstein's field equations is consistent and its predictions have been confirmed and no experiements exist that firmly contradict it, so it is the best theory of gravity we have. If the baby visualisations don't satisfy you then you have to step up and learn at least a little bit of the real theory.

 

[Honorable_Death]

so selfadjoint why don't u step it up and explain the real thing, because your explanations are utterly usless and don't explain the question, your right they are baby visualisations, so show us one that actually explains it.

 

[michael879]

Take an elastic sheet in free space and put two balls on it having masses m1 and m2. Space the balls apart - now grab the sheet at all for corners and accelerate it in a direction normal to the surface upon which the balls are at rest - the sheet will deform because of the inertia of the balls - they will roll toward each other - no other force is required.

o yea... I was thinking that that requires gravity but now that I think about it even without gravity inertia would have the same effect. However, I still don't understand how two planets can be attracted to each other with this representation of gravity.

 

[pervect]

so selfadjoint why don't u step it up and explain the real thing, because your explanations are utterly usless and don't explain the question, your right they are baby visualisations, so show us one that actually explains it.

There are a few good online resources like

Baez's GR tutorial

that offer a short intro to how GR really works, because it actually explains Einstein's equation (G_uv = 8 Pi T_uv).

This is probably about as simple as a short, fully mathematical explanation can get, it at least gives the flavor of what is really going on in the theory. To really understand even the basics of GR takes more than a few posts on a BBS, or even a paper. It takes a textbook and some dedicated study. Baez's paper is still a good resource for the interested student - if nothing else, it gives an idea of what sort of material is required to understand GR as it is actually formulated.

When used properly, the rubber-sheet analogies are not quite as useless as they sometimes appear, but they are often not used properly. For instance, people often forget that space-time should be considered to be curved, rather than space only. Thus useful things can be (and are) done by comparing the space-time plots of an observer with 1 space and 1 time dimension on a flat sheet of paper vs a sphere.

 

[yogi]

michael - the rubber sheet analogy is only metaphorical - it gives a pictorial - if you consider the rubber sheet as spacetime, the inertia of masses would oppose any acceleration thereof - now you will say - but spacetime is not accelerating. And I will say, yes it is.

 

[selfAdjoint]

Honorable_Death, I can just endorse what pervect said. Another good introduction is Thorne's book Black Holes and Time Warps. If anyone skilled enough wants to try to do a clear derivation of the Schwartzschild metric, feel free.

 

[michael879]

michael - the rubber sheet analogy is only metaphorical - it gives a pictorial - if you consider the rubber sheet as spacetime, the inertia of masses would oppose any acceleration thereof - now you will say - but spacetime is not accelerating. And I will say, yes it is.

it is? so is that why they think there is some external force besides the original big bang expanding the universe?

 

[yogi]

Well - the apparent acceleration that has been deduced from the 1a supernova data is not explained - in fact there is no agreement on why the universe is expanding - whether it be a constant radial dilation - or an accelerating dilation - we don't have a good theory or a good model - all we have is educated guess work. But most folks in the physics community do agree that the universe is expanding - and if you consider the universe to be the Hubble sphere centered upon your own location - the volume of that sphere will accelerate if the radial increase is uniform (recall a sphere's volume is (4/3)pi(R^3) so if the radius doubles, the volume goes up by a factor of 8. In other words the volume of space is accelerating. Now look at the units of the gravitational constant G. (cubic meters per second squared )/kgm In other words, the constant that determines gravity has units of volumetric acceleration per unit mass

 

[Zanket]

How do two dents in space-time fall into each other? and why would something with no velocity move into a large gravitational source?

The answer to the 2nd question, because gravity attracts objects to one another, answers the 1st question too. The curvature of spacetime, misleadingly demonstrated by the rubber sheet analogy, describes the degree to which gravity is working at each place. It doesn't explain how gravity works, i.e. how objects attract one another.

 

[Enos]

I know how gravity works but proving it is the hard part.

 

[michael879]

I get how it works, it attracts mass together. Is there any theory why it works? I thought the rubber sheet analogy did that.