Three dimensional gravity paradox

[madsquid]

i have encountered a problem with gravity, acording to logic gravity should not be able to work as it does in our universe or any other that has spatial dimensions that work in an identical way (even if said universe has less dimensions than our own). you are probobaly aware of a paradigm that allows us to visualise exactly how gravity works. the precise nature of this concept varies but it goes along the lines of this. if four people held up a sheet, and a fith then places a basketball (representing a planet or star) in the center of the sheet, it will create a dip in the sheet. if the fith person places a marble (representing say, an asteroid) on the sheet, it will roll toward the ball. this is all very well, the only problem is that in reality objects are not sitting on a flat sheet or film of space-time that can be warped and manipulated, rather they exitst in space with three dimensions (excluding the additional dimensions the existence of which is implyed by string theory). objects are pushing outward on space-time in all directions so objects should repulse not attract

 

[xAxis]

I don't think you can say that objects are pushing outward on space-time. Where did you get that?

 

[Nugatory]

you are probobaly aware of a paradigm that allows us to visualise exactly how gravity works. the precise nature of this concept varies but it goes along the lines of this. if four people held up a sheet, and a fith then places a basketball (representing a planet or star) in the center of the sheet, it will create a dip in the sheet. if the fith person places a marble (representing say, an asteroid) on the sheet, it will roll toward the ball

That "paradigm" is a deeply misleading model that has nothing to do with any past or current theory of gravitation. It's one of those things that just isn't true, but that the non-technical press just won't give up.

 

[A.T.]

i have encountered a problem with gravity, acording to logic gravity should not be able to work...

Then you have encountered a problem your logic, not with gravity.

you are probobaly aware of a paradigm that allows us to visualise exactly how gravity works.

What you describe is the flawed marble-on-rubber-sheet-model of General Relativity. There are many threads here explaining what is wrong with it.

 

[sophiecentaur]

The rubber sheet thing is only a loose analogy and not a serious model. The Maths describe what is going on pretty well - so stick to that for any meaningful conclusions.

 

[Damo ET]

As Sophiecentar has said, the rubber sheet analogy is just that, a very basic way to explain how gravity acts on different masses in 2 dimensions! You must realize that the universe we are in doesn't exist in 2 dimensions. And if you are not looking at the situation from directly above, the analogy becomes irrelevant. It is a 2d representation (loosely) of 3d gravity.
Your argument would be like me saying that I have discovered a flaw with maps, the fact that they don't represent what is actually on the ground when you are standing on the top of a mountain (or any other place). A map is a 2d representation of a 3d surface.

Everything with mass in the universe sits inside the space/time of the universe, and that space/time IS bent and distorted by the mass. I don't understand your take on mass pushing against space/time?

Also, you can't use a bed sheet for your explanation, as gravity doesn't increase or decrease at a linear amount from any mass, the square of the distance is used, which means even the 2d gravity analogy needs a 'rubber sheet' to mimic this.Damo

 

[A.T.]

It is a 2d representation (loosely) of 3d gravity.

Gravity in GR is 4d, not 3d. And the 4th dimension (time) is crucial to the model. But the sheet analogy just shows 2 space dimensions, which doesn't explain anything. You can provide much better analogies by using 1 space and the time dimension:
http://www.relativitet.se/spacetime1.html

 

[Damo ET]

Gravity in GR is 4d, not 3d. And the 4th dimension (time) is crucial to the model. But the sheet analogy just shows 2 space dimensions, which doesn't explain anything. You can provide much better analogies by using 1 space and the time dimension:
http://www.relativitet.se/spacetime1.html

I understand that, but I wasn't talking of gravity in GR, I was talking of gravity in the sheet model that the OP suggested, which is still a 2d model of how gravity effects 3d space.


Damo

 

[madsquid]

i understand that the sheet model is only a two dimensional representation, i am stating that when we add the third dimension, the dip created in the sheet, would exist in all directions.

 

[Nugatory]

i understand that the sheet model is only a two dimensional representation, i am stating that when we add the third dimension, the dip created in the sheet, would exist in all directions.

Yes, but so what? The sheet model and the entire concept of a "dip" has very little to do with gravity.

 

[sophiecentaur]

Yes, but so what? The sheet model and the entire concept of a "dip" has very little to do with gravity.

Exactly. The force that pulls marbles down into dips in a rubber sheet is only symbolic / analogous. The dip in the sheet is a graph of potential and not a distortion of space time which is what GR is about. Making the model in 3D, with some contrived central force law would not make it more real; in fact, it would be more confusing because of the apparent parallel when there is none.

 

[Low-Q]

i understand that the sheet model is only a two dimensional representation, i am stating that when we add the third dimension, the dip created in the sheet, would exist in all directions.

That is correct. However, in addition to be a 2D model it also has another "flaw". If you push a small "planet" towards the "sun" in the middle of the rubber sheet, the deflection in the sheet which represent the gravitational force from the sun let's the small "planet" also deflect as it approach the "sun", and finally hit the "sun" at the botton rather than at the "equator". In a 4d universe the "planet" would more likely move towards the "sun" in a straight line.

An important thing to notice with the rubber sheet, is that the deflection is increasing closer to the "sun", representing the increased gravity that does not increase linear, but exponential to the distance. A useful experiment to understant the basics, even if it will for most people confuse more than educate if not explained "with a tweezer".

Vidar

 

[ZapperZ]

i understand that the sheet model is only a two dimensional representation, i am stating that when we add the third dimension, the dip created in the sheet, would exist in all directions.

Please pay attention to the comment that this 2d sheet that you are obsessed with is merely a CARTOON representation of gravity in General Relativity. You cannot claim something is wrong based on that type of understanding.

You only saw the shadow of the animal. You haven't seen the animal itself.

Zz.

 

[jbriggs444]

That is correct. However, in addition to be a 2D model it also has another "flaw". If you push a small "planet" towards the "sun" in the middle of the rubber sheet, the deflection in the sheet which represent the gravitational force from the sun let's the small "planet" also deflect as it approach the "sun", and finally hit the "sun" at the botton rather than at the "equator". In a 4d universe the "planet" would more likely move towards the "sun" in a straight line.

Ummm. A 2d model will not show a planet hitting the "bottom" of the sun. It's a 2d model. It does not model "top" or "bottom". Or equator.

An important thing to notice with the rubber sheet, is that the deflection is increasing closer to the "sun", representing the increased gravity that does not increase linear, but exponential to the distance.

Actual gravity is inverse square, not linear. I believe that gravity as modeled with a rubber sheet is, to a first approximation, inverse square.