Gravity: How Does Spacetime Bend?

[cueball B]

This is a layman question, so hold your temper. :)

If gravity is the effect created by a mass that bends space time, how (in what fashion) does space time bend? I have seen it represented in 2d with a 3d sphere in the middle. But wouldn't spacetime be bended over the entirety of the mass (earth if you will)? Wouldn't a sphere envelloped in some kind of space time bubble be a more accurate representation of this?

 

[Janus]

When you talk about space-time curvature, what is really meant is that the geometry of space-time is non-Euclidean. Unfortunately, humans have trouble directly visualizing non-euclidean geometry and resort to modeling it as a space "curved" through a higher dimension.

With gravity, that would be modeling a 3-d space being curved through a 4th dimension.
However, since we cannot visualize a 4th dimension either, representations of this idea involve dropping one dimension to show a 2-d surface curved through 3 dimensions. The practice of showing the mass as a three dimensional object itself, isn't accurate for that model, and is more artistic license.

 

[cueball B]

Thank you for the awnser. Now i can get my head around it. The 2D representation seemed off to me. Good to know it is but an artist rendering.

 

[mjacobsca]

Well, I'd say it's more than a simple artist's rendering. It's an accurate mathematical representation of gravity's affect on space-time as seen through a lower dimensional framework. It's far more accurate than an artist's rendering of an exoplanet, for example.

 

[Burnerjack]

One Question about gravity: Does time pass quicker or slower in close proximity of a gravitational field? The 2D map works well for me, as I can see that matter causes the effect of a gravity well and matter "falls" downhill into the well. Time on the other hand is a more ellusive concept for me.

 

[mjacobsca]

One Question about gravity: Does time pass quicker or slower in close proximity of a gravitational field? The 2D map works well for me, as I can see that matter causes the effect of a gravity well and matter "falls" downhill into the well. Time on the other hand is a more ellusive concept for me.

Correct. Time moves slower near a gravitational field.

Remember that a person moves at "C" through space-time. If you add up their movement across all three spatial dimensions and their movement through the time dimension, you get "C". Near a large gravity well such as a black hole singularity, a person's movement through space is accelerated near "C" as they fall down the well in the spatial dimension. This spatial movement down the well takes away from some of the movement through the time dimension, hence time runs slower.

This is all a gross simplification to your question, and is the visualization I like to use, but I think it gives you the general idea.

 

[cueball B]

Yes, maybe more than a simple artist rendering. Yet not a true representation. I had problems with the 2D representation, because it did not seem logical that mass would only effect space time round the equator

They rarely explain more than meets the eye in those horrid Discovery Channel documentaries. I knew it to be off somehow, but could not explain why, because they failed to mention what Janus said about it. If they would have explained it like he (Janus) did, I wouldn't have been asking this question.

This reminds me. Janus, send your CV to Discovery Channel, they co

 

[twistedspark]

One way that helps me deal with gravity's effect on time is to imagine the grid fabric being time and as mass creates a pocket into this fabric, either tiny like that from an atom or gigantic like from a black hole, not only does the well get deeper, but also the rungs of the fabric get stretched further and further apart. Each rung being one unit of time. As something approaches or passes by the gravity well how long it takes to get to the next rung is increased more and more the closer the object gets. Hence time slows down for the object from an outside observer's viewpoint. Time remains at it's normal pace from the object's viewpoint, it's just taking longer and longer to get where it's going.