Need Help Understanding Mass/Bent Space-Time

[sirnamemr]

Hello, I am new to the forum and have a question that has been bugging me for some time that I hope someone can help me with.

In the following image is a typical example used in documentary's to try to show how Einstein's theory of relativity explains how mass effects time. Uselly they will show a heavy object, in this case the Earth, on a flat and level plane like this grid. They go on to say that a heavy object will sink down stretching space-time with it making an impression in space and this is also why objects orbit heavier objects. An example being the Earth orbits the sun because it "falls" into this impression around the sun from its mass like the silver sphere around the Earth in the image below.

http://www.freeimagehosting.net/t/kiy9c.jpg

What I don't understand is if this explaintion was true then space would have to be flat and all galaxies in the universe on a single plane but we know this to not be true in the sense that objects orbit other objects in every imaginable direction and angle like in this image below. I hope I am explaining this right...

http://www.freeimagehosting.net/t/92svz.jpg

How is it posible for mass to pull in one direction for one solorsystem/galexy and in a different one for another? I hope someone can help me understand this because so far every single documentary I have seen does not explain it and it's really frustrating.

Thanks so much for taking the time to read this, I hope it makes sense.

 

[yenchin]

The rubber sheet analogy is only that, an analogy, it is in fact quite misleading. It is only meant to convey the concept that the presence of mass can curve an another flat spacetime. The real spacetime is of course 3 dimensional of space and 1 dimension of time, not a flat 2 dimensional rubber sheet! It is presented that way because not many people, if any, can visualize 4 dimensional shapes. Also, the analogy misses out on the fact that spacetime curvature has curvature in the whole *spacetime* and not just *space*. Ultimately, any analogy is limited, and the full wonders of general relativity requires the full understanding of the mathematics [though analogies do help if used correctly].

 

[yenchin]

A better way to visualize is probably to use a three-dimensional grid instead of a two-dimensional rubber sheet, something like http://www.zamandayolculuk.com/cetinbal/KO/k_Gravity_worlds.jpg, but again it is only an analogy and doesn't show the full time *spacetime* curvature.

 

[salvestrom]

As Yenchin says, the bending happens in all directions, so start by imagining those images overlaid in all sorts of angles. Also, these images are exaggerations of the amount of curvature.

 

[Fuzzy Logic]

I think that the stretchy trampoline analogy is actually a backward representation.
Spacetime would actually be pinched into the center of the mass, not expanded away. If it is stretched around, it implies that mass makes spacetime less dense.

 

[alt]

Yes, the rubber sheet analogy isn't a good representation. The above several posts now suggest the analogy being extended to rubber sheets at many planes, and by logical inference, to all possible planes around the sphere.

Whereas the rubber sheet however, suggested one unique plane and path, now the analogy suggests an infinite number of paths, with presumably, the same strength, or curvature .. or whatever.

The question this brings to my mind then, is wouldn't they cancel each other out ?

 

[Janus]

What adds to the confusion with this analogy are illustrations such as that shown in the first post, with a spherical Earth shown "sitting" inside the dimple. The point is that the whole universe is represented by that sheet, reduced to two dimensions. The viewer is seeing it from an "imaginary" third dimension(one that doesn't actually exist for the shown universe).

In this analogy, the whole surface of the Earth should be represented by a circle on the surface of the "dimple".

As pointed out, a more correct analogy would be the viewer looking at a 3-d universe from a 4th dimension, but you can't really draw a 4 dimensional picture.

And even even the 4 dimension analogy would just be an analogy, as there is no 4th physical dimension for our 3-d universe to curve into. It is just a way of modeling the non-euclidean nature of space-time. Is it no wonder that it is confusing?

 

[sirnamemr]

Wow thank you so much, I have a much better mental image of what's going on now. The pic that showed the grid all around the Earth with the lines bending/warping into the center area helped a lot so thanks for posting that "yenchin" and thanks to everyone else who replied.

http://www.zamandayolculuk.com/cetinbal/KO/k_Gravity_worlds.jpg

It's still hard to grasp how the suns gravity can be strong enough to affect the outer planets our planet and closer ones not be "sucked" right in. In a more "accurate" diagram showing space bending/warping from the sun enough to hold the far out planets would the area around the Earth not be extremely warped? How can it be strong enough to hold the outer planets and us the same? Now I'm really confused. lol

Also on a side note I was watching a doc last night called something like "The Elegant Universe" based on Brain Greene's book and he said something that I don't understand. According to him Einstein had proved that gravity is just as fast as light so. An example they used was if the sun disappeared in an instance all of a sudden that, contrary to what Newton thought, gravity would not instantly disappear for us but rather it would dissipate like a wave outward and we would feel the effect of no sun at the same time we seen it disappear. But what happened to nothing being faster then light? The doc clearly states that gravity is the same speed as light so I don't get it... Anyone?

 

[DaveC426913]

But what happened to nothing being faster then light? The doc clearly states that gravity is the same speed as light so I don't get it... Anyone?

Both are correct. Nothing is faster than light. Including gravity waves.

It is better to look at it this way:

c is the speed limit of the universe.
No thing with mass can move at or reach c.
All massless things travel at c - including light, radio waves and gravity waves.

 

[sirnamemr]

Both are correct. Nothing is faster than light. Including gravity waves.

It is better to look at it this way:

c is the speed limit of the universe.
No thing with mass can move at or reach c.
All massless things travel at c - including light, radio waves and gravity waves.

Of course, thanks for helping me understand that and thanks again to everyone else! This thread can be closed if you do that here.