Trying to make sense of gravity

[Mark R]

My question regarding Gravity and spacetime.

 

I have seen example of the Trampoline effect when explaining gravity and 3 dimensional cube models. Here is what I thought was happening and I wondered if anyone can shed some light to where or not I am making any sense.

 

In the trampoline diagram we see something entering an orbit due to the curve create in the spacetime grid. Kind of like something going down a drain so to speak. I picture a 3 dimensional grid, let’s say it’s made of a liquid sponge. I take an object like my fist for example and place it into the grid. The fist would be forcing the liquid sponge away from its self which would create pressure back towards the fist. I thought that this pressure or force would be gravity. So like on earth if one jumps they are jumping up into in the pressure of the compressed spacetime pushing back to earth.

 

Each planet or object in space would be creating a pressure in the spacetime grid creates a friction and prevents it from speeding out of control.

 

Ok that’s my thought......anyone?

 

Cheers, Mark

 

 

[lemur]

There's no friction or action/reaction in the interaction between objects and the 'spacetime' they travel through. Objects take the path of least resistance as long as they are uninfluenced by outside forces. When an object follows a curved path through space, it is only moving under its own inertial momentum. It's not like something rolling on a curved track that experiences force as it is impeded in a straight-line path. There's no centrifuge effect pulling Earth away from the sun while the sun's gravity holds it in orbit like a rope. Earth is simply in free-fall in a curved path around the sun.

 

edit: I believe this explanation illustrates the meaning of spacetime curvature but I always have to mention I'm not a licensed physicist because otherwise someone might think I was and allow me to spread false information (so I'm told, anyway)

Edited April 25, 2011 by lemur

[ajb]

I have seen example of the Trampoline effect when explaining gravity...

 

Ok, so the bowling ball on the trampoline is an analogy to the situation in general relativity. The analogy demonstrates that a large object changes the local geometry of space-time and that the path of test particles is changed as compared to the flat case.

 

and 3 dimensional cube models.

 

What is a 3 dimensional cube model?

 

In the trampoline diagram we see something entering an orbit due to the curve create in the spacetime grid. Kind of like something going down a drain so to speak.

 

Sure, we see that the "straight line" path followed by the test particle is not really flat due to the non-trivial geometry of the underlying space-time. The trampoline analogy demonstrates this and the fact that a test particle will be attracted to the large mass.

 

I picture a 3 dimensional grid, let’s say it’s made of a liquid sponge. I take an object like my fist for example and place it into the grid. The fist would be forcing the liquid sponge away from its self which would create pressure back towards the fist. I thought that this pressure or force would be gravity. So like on earth if one jumps they are jumping up into in the pressure of the compressed spacetime pushing back to earth.

 

You want to think of gravity as some kind of restoring force driving the tendency of space-time to want to be flat?

 

I don't know how far you will be able to follow that interpretation. It is not an interpretation of general relativity that I have heard of before. Really you will want to think 4-d or just consider "time slices".

 

The usual interpretation is that gravity is the local geometry.

[DrRocket]

My question regarding Gravity and spacetime.

 

I have seen example of the Trampoline effect when explaining gravity and 3 dimensional cube models. Here is what I thought was happening and I wondered if anyone can shed some light to where or not I am making any sense.

 

In the trampoline diagram we see something entering an orbit due to the curve create in the spacetime grid. Kind of like something going down a drain so to speak. I picture a 3 dimensional grid, let's say it's made of a liquid sponge. I take an object like my fist for example and place it into the grid. The fist would be forcing the liquid sponge away from its self which would create pressure back towards the fist. I thought that this pressure or force would be gravity. So like on earth if one jumps they are jumping up into in the pressure of the compressed spacetime pushing back to earth.

 

Each planet or object in space would be creating a pressure in the spacetime grid creates a friction and prevents it from speeding out of control.

 

Ok that's my thought......anyone?

 

Cheers, Mark

 

 

 

 

 

The trampoline analogy usually creates as much or more confusion as enlightenment. That is clearly the case here.

 

Objects under the influence of no force other than gravity follow geodesic paths in spacetime. They do NOT follow geodesic paths in space -- an elliptical orbit is not a spatial geodesic, not by a long shot.

 

Unfortunately there is no simple intuitive explanation of the curvature tensor. I don't know of any good explanations outside of real no-kidding texts on general relativity or texts on differential geometry.. The best is probably Gravitation by Misner, Thorne and Wheeler. It requires quite a bit of background.

[ajb]

Unfortunately there is no simple intuitive explanation of the curvature tensor.

 

It is not hard to understand curvature in 2d via parallel transport of vectors. You can think of vectors as little arrows and parallel transport along a curve just means "not changing the direction of the vector" , other than that due to following the curve. If you follow a close path, a loop and the vector is not the same as when you started, the space is curved.

 

Draw a closed path on a ball or balloon. Take a pencil to be a vector and parallel transport it around the closed path. Try not to introduce any change in direction other than that demanded by the loop. You will see the vector is not pointing in the same direction as you started. The ball (i.e. the sphere) is curved. (It is easier than I make it sound.)

 

Try it on (a piece of) the cylinder, i.e. a toilet roll tube.

 

The idea is the same in higher dimensions, but a lot more work is needed to understand vectors and parallel transport.

[Mark R]

Ok, so the bowling ball on the trampoline is an analogy to the situation in general relativity. The analogy demonstrates that a large object changes the local geometry of space-time and that the path of test particles is changed as compared to the flat case.

 

 

 

What is a 3 dimensional cube model?

 

 

 

Sure, we see that the "straight line" path followed by the test particle is not really flat due to the non-trivial geometry of the underlying space-time. The trampoline analogy demonstrates this and the fact that a test particle will be attracted to the large mass.

 

 

 

You want to think of gravity as some kind of restoring force driving the tendency of space-time to want to be flat?

 

I don't know how far you will be able to follow that interpretation. It is not an interpretation of general relativity that I have heard of before. Really you will want to think 4-d or just consider "time slices".

 

The usual interpretation is that gravity is the local geometry.

 

Thanks for the information, Ok

lets start again in a sense.

 

Would I be correct in saying that if there was nothing in the universe (hypothetically) there would be no force, pressure...etc

Only when something is present in spacetime would you have an effect? Actually only if you have 2 objects since they would then have something to react with (each other).

 

I may be saying this (hard to explain).... Is it the object that has an effect on spacetime and the other objects react to this change in spacetime?

 

Thaks for your patience, I would have replied earlier but did not turn on the send email button to responded messages.

[ajb]

Is it the object that has an effect on spacetime and the other objects react to this change in spacetime?

 

This is the difference between the idealised situation of a source and a test particle. In electromagnetism we have to also distinguish between a source charge and a test charge.

 

So, a source of gravity is a massive object, or more correctly we need something with energy-momentum. Such an object is understood as influencing the space-time around it. Say for a massive, non-rotating, spherically symmetric object (a good model of a star) the local geometry of the space-time around the object is described by the Schwarzschild metric.

 

A test particle is a particle that is assumed to be "near massless" in the sense that the particle is only influenced by gravity but itself does not act as a source of gravity. One can also consider beams of light in this way. In essence such test particles "map out" the local geometry (assuming they are not acted upon by other forces) but do not change the geometry.

 

This is an idealised situation, but for example it is ok to consider the planets orbiting the Sun as test particles as they are so much lighter than the Sun.

 

Of course test particles are idealised and in truth they will effect the local geometry. This is quite complicated to deal with as the fundamental equations of general relativity, the Einstein field equations are highly non-linear. That is one cannot simply "add solutions".