Question about gravity and the 'rubber sheet' demonstration

[Zylstra]

So, if we visualize spacetime as a rubber sheet and put a bow,ling ball (earth ion it)...


I don't see how the problem is solved. On Earth, it is gravity that causes the next, smaller ball o 'fall' towards the heavier ball as it is 'pulled towards' earth itself by gravity and rolls along the rubber sheet.




Even if Earth creates a 'bend' in spacetime, what causes matter to still move towards such depressions? What is 'under the sheet'?

 

[scikidus]

So, if we visualize spacetime as a rubber sheet and put a bow,ling ball (earth ion it)...


I don't see how the problem is solved. On Earth, it is gravity that causes the next, smaller ball o 'fall' towards the heavier ball as it is 'pulled towards' earth itself by gravity and rolls along the rubber sheet.




Even if Earth creates a 'bend' in spacetime, what causes matter to still move towards such depressions? What is 'under the sheet'?

You've found one of the problems with the rubber sheet analogy: it's projecting a 4-D environment into a 2-D/3-D world. In actuality, there is no "under the sheet", as all four dimensions of space-time curve from the presence of mass, and everything gets bent accordingly.

 

[Zylstra]

You've found one of the problems with the rubber sheet analogy: it's projecting a 4-D environment into a 2-D/3-D world. In actuality, there is no "under the sheet", as all four dimensions of space-time curve from the presence of mass, and everything gets bent accordingly.

...


and why would matter move towards the center of such 'impressions' or bends? Is it some take on nature seeking to level out? Does the matter 'rush into a void' like gas entering a low-pressure zone? But gas does that due to pressure and the particles bouncing around... water seeks to even out because of gravity....

I still don't see why matter should move into such 'gravity wells' :?: :facepalm:

 

[scikidus]

Because the objects are attempting to move in straight lines but spacetime itself is warped, bending the strait path fo the mass into an orbit.

 

[Ozymandyus]

...


and why would matter move towards the center of such 'impressions' or bends? Is it some take on nature seeking to level out? Does the matter 'rush into a void' like gas entering a low-pressure zone? But gas does that due to pressure and the particles bouncing around... water seeks to even out because of gravity....

I still don't see why matter should move into such 'gravity wells' :?: :facepalm:

You are confusing yourself by thinking there is any other option OTHER than moving into the wells. The problem lies partially in the visualization of the bowling ball, you have to visualize the indentation the ball makes but the ball itself is IN the space time sheet. EVERYTHING is in the sheet, there is no above or below.

Things are not rolling around on TOP of the sheet, they are travelling along the sheet, IN the sheet. Because of the bending, there are points on the sheet where many paths intersect, where there is a lot of matter. Anything travelling along a line that directly intersects these gravity wells will often transfer its energy to other objects and will not continue on its straight 'curved' path. It didn't get 'sucked' into that path or anything, it was travelling along a straight (curved by spacetime) path dictated by its velocity and then hit something gigantic that changed its direction.

 

[Icefire9atla]

Things normally travel in a strait line relative to the space- time fabric. When the fabric is bent, so is the path of the object. So a massive body would bend the paths of thing moving near it towards it.

 

[Master_Ghost_Knight]

F=ma
Fg=GMm/r^2
a=dv/dt
v=dx/dt
The gravity in this model is nothing else then a precieved forced due to the change of the second derivative of spaces over time. When in fact the force is not really there, he just follows straight the natural shape of space that in our preception of the cartesian space it apears like it is being pulled.
Think of it like the coriolis force, in a rotating reference it apears that the body is subjected to a particulr force that pushes away when in fact the object is just moving straight.

 

[Pulsar]

The rubber sheet analogy has its limitations. It's useful to get an idea how space (and time) can be deformed, but that's it. The main problem is that you get the impression that a particle is merely following the geometry of space-time, like a train on rails. But that's not entirely accurate. More precisely, the curvature of space-time causes a particle to accelerate. In other words, the Newtonian concept of force (expressed as the derivative of a gravitational potential) is replaced by the relativistic concept of space-time curvature (expressed as the derivative of a metric). A particle in a gravitational field follows a geodetic line, given by the equations

• Tau is the comoving, proper time for the particle
• Mu, alpha and beta are the four space-time coordinates:
  Mu/alpha/beta = 0 -> time coordinate
  Mu/alpha/beta = 1 -> x space coordinate
  Mu/alpha/beta = 2 -> y space coordinate
  Mu/alpha/beta = 3 -> z space coordinate
• Gamma is the Christoffel symbol, which contains derivatives of the metric tensor of the gravitational field. Note that this Christoffel symbol has 4x4x4=64 values, for every combination of 3 space-time coordinates.

So, even if the initial velocity of a particle is zero (dx_alpha/dtau = 0 for alpha = 1,2,3 and dx_beta/dtau = 0 for beta = 1,2,3), it still has an acceleration due to the terms Gamma^mu_00 (dx_0/dtau)^2.

 

[Zylstra]

F=ma
Fg=GMm/r^2
a=dv/dt
v=dx/dt

I have no idea what any of that is :?: :?: :?: :?: :?: :?: :?: :?:

The gravity in this model is nothing else then a precieved forced due to the change of the second derivative of spaces over time. When in fact the force is not really there, he just follows straight the natural shape of space that in our preception of the cartesian space it apears like it is being pulled.

So it follows the 'wells'' in order to follow the shortest (straightest) path and travels the least amount of space possible? Would it be accurate to imagine a grid on the sheet and the bends of the lines in the grid showing how the 'shortest distance' (straight line) will bend into the well?, due to the curvature of spacetime? Would such an image be representative of the phenomenon in question?

So, basically it still follows a 'straight line' in the sense that a straight line is the shortest distance between two points?

 

[Zylstra]

http://img12.imageshack.us/img12/1135/geodeticlatex.gif[/img]

• Tau is the comoving, proper time for the particle
• Mu, alpha and beta are the four space-time coordinates:
  Mu/alpha/beta = 0 -> time coordinate
  Mu/alpha/beta = 1 -> x space coordinate
  Mu/alpha/beta = 2 -> y space coordinate
  Mu/alpha/beta = 3 -> z space coordinate
• Gamma is the Christoffel symbol, which contains derivatives of the metric tensor of the gravitational field. Note that this Christoffel symbol has 4x4x4=64 values, for every combination of 3 space-time coordinates.

So, even if the initial velocity of a particle is zero (dx_alpha/dtau = 0 for alpha = 1,2,3 and dx_beta/dtau = 0 for beta = 1,2,3), it still has an acceleration due to the terms Gamma^mu_00 (dx_0/dtau)^2.

\

....

my education is nowhere near sufficient to understand any of that :

Please, people... you're speaking to someone w/ a GED... anything beyond algebra and basic geometry will be completely lost on me, so I need to be able to picture it conceptually, as I will not comprehend mathematical proofs


If I add an imaginary grid to the 'sheet' and use the lines of the grid to represent the straightest paths, will that be 'accurate'?


I still don't understand the idea of the acceleration towards to center iof the well, but the bending of light and the effect on moving objects makes sense, if I'm correct in stating that 'the object continues to move along the strightest possible path by seeking to trravel the shortest actual distance (to an 'outside' observer) thorugh spacetime

 

[Pulsar]

Sorry

So it follows the 'wells'' in order to follow the shortest (straightest) path and travels the least amount of space possible? Would it be accurate to imagine a grid on the sheet and the bends of the lines in the grid showing how the 'shortest distance' (straight line) will bend into the well?, due to the curvature of spacetime? Would such an image be representative of the phenomenon in question?
So, basically it still follows a 'straight line' in the sense that a straight line is the shortest distance between two points?

Yes, that's basically it. The particle travels along a geodesic, which can be calculated using the equation I posted. The curvature of space-time causes an acceleration of the particle, which also depends on its position and velocity. So at every point, the particle keeps changing direction, seeking the shortest path.

 

[Zylstra]

Thanks, all


btw, what field of mathematics is that?

 

[Master_Ghost_Knight]

Thanks, all


btw, what field of mathematics is that?

I believe you can learn that on a general mathematical analysis class.
Most particularly on diferential analysis and diferential equations.
It is probably one of the most important mathematical classes in science, you won't go very far if you don't know it, and as our futil atempts of explaining the subject transpiered it is a bit hard to demonstrate whatever we are saying if you don't know any of it.

 

[Zylstra]

Do you know of any online sources where one either study these mathematics or get a list of recommended books?

 

[Master_Ghost_Knight]

Do you know of any online sources where one either study these mathematics or get a list of recommended books?

Unfortunatly for you to learn this on your own will take a while, even though they are not as complicated as they apear they need complex bases, it may take a year or 2 to grasp it with a real education.

Some of my institue advised bibliography in order to understand math are:
Linear Algebra and Its Applications , G. Strang, 1988, 3rd ed. Academic Press (Not very important but linear algebra may come in handy)
A First Course in Real Analysis , Murrey H. Protter and Charles B. Morrey, 1993, Springer-Verlag (Introduction to mathematical analysis and diferential analysis, this is probably what is going to make understand of what is going on)
Complex Analysis , L. Ahlfors, 1979, 3rd ed. McGraw Hill (analysis of the complex plane, it has some interesting results, but not has important to understand what was presented)
Diff. Equat. and their Applic.? An Introduction to Apply Mathematics , M. Braun, 1993, 4th ed. Springer-Verlag (diferential equantion, one area of diferential analysis, not necessary to understand what the equations means, but you can solve them with this)

 

[Zylstra]

I went to
I believe you can learn that on a general mathematical analysis class.
Most particularly on diferential analysis and diferential equations..

the local library to ask about that....

the 'librarian' seemed very confused :roll:c

Unfortunatly for you to learn this on your own will take a while, even though they are not as complicated as they apear they need complex bases, it may take a year or 2 to grasp it with a real education.

Well, that sucks. If it's as important as you say, though, i don't have much choice if I want to understand any of this stuff. Noq, what level of math *(calc, trig, etc) do i need to make sure to master before delving into this?

Some of my institue advised bibliography in order to understand math are:
Linear Algebra and Its Applications , G. Strang, 1988, 3rd ed. Academic Press (Not very important but linear algebra may come in handy)
A First Course in Real Analysis , Murrey H. Protter and Charles B. Morrey, 1993, Springer-Verlag (Introduction to mathematical analysis and diferential analysis, this is probably what is going to make understand of what is going on)
Complex Analysis , L. Ahlfors, 1979, 3rd ed. McGraw Hill (analysis of the complex plane, it has some interesting results, but not has important to understand what was presented)
Diff. Equat. and their Applic.? An Introduction to Apply Mathematics , M. Braun, 1993, 4th ed. Springer-Verlag (diferential equantion, one area of diferential analysis, not necessary to understand what the equations means, but you can solve them with this)

[/quote]

THANK YOU!!

Now to see whether the library can get these on loan

 

[ImprobableJoe]

...


and why would matter move towards the center of such 'impressions' or bends? Is it some take on nature seeking to level out? Does the matter 'rush into a void' like gas entering a low-pressure zone? But gas does that due to pressure and the particles bouncing around... water seeks to even out because of gravity....

I still don't see why matter should move into such 'gravity wells' :?: :facepalm:

Do you wonder why a rock rolls downhill? If you don't? It is time for you to STFU.

 

[e2iPi]

the local library to ask about that....

the 'librarian' seemed very confused

If you have a local university or college, try one of the off-campus bookstores (they typically have better deals than the campus bookstore) and of course there is always Amazon.com

Noq, what level of math *(calc, trig, etc) do i need to make sure to master before delving into this?

You should have at least a firm grasp of differentiation and integration before delving into the more advanced topics. (Not strictly necessary for linear algebra, but still recommended if you want to understand some proofs)

Happy learning!

-1

 

[e2iPi]

Do you wonder why a rock rolls downhill? If you don't? It is time for you to STFU.

Somebody piss in your Cheerios, Joe?

The nature of space-time IS a rather difficult thing to try to wrap your skull around, at least beyond an intuitive "rubber sheet" understanding, especially if you don't have the requisite mathematical background. Chill, man.

-1

 

[ImprobableJoe]

Somebody piss in your Cheerios, Joe?

The nature of space-time IS a rather difficult thing to try to wrap your skull around, at least beyond an intuitive "rubber sheet" understanding, especially if you don't have the requisite mathematical background. Chill, man.

-1

hey "person who I mistook for someone else", if you don't like my posting style then feel free to stop reading my posts, instead of following me around and complaining about them.

*** stuff in quotes is AN EDIT!!