# Why is spacetime shown on a 2 dimensional plane?

1. Dec 8, 2013

### Crazyhorse2882

I don't have the mathematics down quite yet but one thing I've noticed whenever I watch documentaries about gravity in relativity is that it's always described on a 2 dimensional plane. They show a planet bending space time as if the space time is underneath it but I'm thinking that the space time actually encircles the mass creating almost a bubble of sorts around it. Can someone explain this in laymen's terms to me please? Thank you

2. Dec 8, 2013

### phinds

You are correct. This pop-sci analogy is very poor, really, but it DOES give the basic idea of "bending space-time" to the layman. It just isn't accurate at all in any real sense.

Such analogies are often rather poor once you actually understand what is being explained, they just serve as an introduction for laymen.

3. Dec 8, 2013

4. Dec 9, 2013

### Chalnoth

Because it's really, really hard to visualize three-dimensional curvature (let alone four-dimensional space-time curvature). Drakkith's picture isn't bad, but it's still hard to understand what that means (at least to me).

5. Dec 9, 2013

### julcab12

..... Here is rough indirect approximation and representation of gravity to a point(). A somewhat similar effect. A few pointers thought. It is important to limit yourself to only what the presentation is trying to convey. 2D appears to give the basic and effective illustration for GR. It is simpler when explained in manifolds. Anyways here is the link.

Last edited: Dec 9, 2013
6. Dec 9, 2013

### Chalnoth

Cool. Though I think one thing to bear in mind is that setup has quite a lot of friction, so it doesn't produce orbits much at all like real ones. If you could produce the same sort of setup, but with minimal friction, that might change. But I doubt that's possible because anything placed on there will deform the sheet, which uses energy and acts as a source of friction. Gravity doesn't have this issue because you don't lose any energy when you deform space-time (if the deformation causes a reduction in the energy of the object doing the deforming, then that energy is stored in the fabric of space-time and not lost...the energy from deforming the sheet is lost to heat).

7. Dec 9, 2013

### Chronos

A fun thing to do [if you are really bored] with 2D spacetime diagrams is try to represent them in 3D using isometric projection.

8. Dec 10, 2013

### Clayjay

The universe is three-dimensional therefore when gravity is projected onto a two-dimensional analog plane it is for demonstration purposes. Gravity collapses space around the center of gravity in three dimensional space but in a two-dimensional analog plain gravity bends space. Only in flatland does gravity bend space.

9. Dec 10, 2013

### TumblingDice

That description sounds like the picture Drakkith linked to in post #3, and as he said, " It's a little more accurate than your standard 2d grid."

Yours is the first mention of 'space' in the thread, as opposed to space-time. I don't think gravity collapses space, but it does create different world lines in space-time - geodesics for mass in inertial frames.

I'm posting outside of my limits here, and standing by to learn more from the experts. :uhh:

10. Dec 11, 2013

### Chalnoth

Gravity certainly is a warping of space as well as space-time.

11. Dec 12, 2013

### Chronos

I have no experience in 4D isometric projection. I think I need bigger paper.

12. Feb 17, 2017

### Android Neox

The rubber sheet model is imperfect but still excellent. It shows the curvature of space due to stretching (dilation) in a gravity well. Instead of viewing it from the side, it should be viewed from above because gravitational space dilation is radial... away from the observer. Also, as the sheet is stretched away from the observer, there need to be more lines added, like altitude lines on a topological map. If the lines on the sheet are separated by identical differences in gravitational potential energy, you can relate the difference in time flow between two points as a direct function of how many lines you have to cross to get from one point to the other.

13. Feb 17, 2017

### Staff: Mentor

If everyone understood and presented the rubber sheet model the way you do, we wouldn't have a problem with it. Unfortunately, very few do, so practically speaking it is a source of misconception and confusion, and that makes it a problem.

The correct picture that you describe is found in many decent textbooks because it's one of the better ways of explaining how a surface with Schwarzchild coordinate $r$ is a sphere of surface area $4\pi{r}^2$ and a surface with Schwarzschild coordinate $r+\Delta{r}$ is a sphere of surface area $4\pi{(r+\Delta{r})}^2$, yet the distance between them is greater than $\Delta{r}$. We just make an analogy between the circumference of circles in the "funnel" and the area of the spheres, and we're there. However, these correct presentations are seldom if ever done in terms of the rubber sheet model, and I will bet long odd against anyone who presents the rubber sheet model as an explanation understanding what's really going on.

14. Feb 22, 2017

### Blake Barr

The key is that if you showed a representation of space-time distortion around a body by drawing the three-dimensional spacial representation you get a drawing that is very confusing and hard to understand. Lines and grids all over the place. A bowling ball on a sheet just works better.

15. Jun 14, 2017

### FredKnowsNothing

Can the explanation of earth orbiting the sun but not being pulled in because it is moving perpendicular to the curvature of the sun be visualized like a swimmer that can overcome and undertow if they swim perpendicular to the force of the undertow? Also if anyone can explain the way time slows or speeds up relative to gravity or speed i would love to know. For some reason i cant picture how this is possible. From the moment twins are born they would age the same regardless how could one possible age slower based on gravity or speed. How do either of those variables really affect it?

16. Jun 14, 2017

### phinds

I don't get what you are asking but it doesn't matter since the celestial orbits are well understood and there's no need for that kind of analogy (if that is in fact what you're striving for).

You should read up on it. Google "The Twin Paradox" and really study it. The different paths through spacetime will likely become clear to you after a while.

Also, just FYI, it is bad form here on PF to hijack a thread in this way. If you have a separate question, start your own thread.

17. Jun 14, 2017

### FredKnowsNothing

I agree on the orbit being well understood I was thinking of a way to visualize the forces at play, why the earth would not crash into the sun, how to think of the feeling on our bodies like the pulling force on your body when in an undertow but how you can overcome that force like the earth does by moving perpendicular. But lets forget that one.

I get the twin paradox and its fine if calendars and clocks move slower, but biologically regardless of the movement of a second hand the twins bodies would have to be the same, not one older than the other. Or does speed and gravity change our biology in some fashion.

18. Jun 14, 2017

### phinds

AGAIN, read about and actually study the Twin Paradox. The different paths through space-time fully explain that the twins CANNOT have the same age when they meet back up. It has nothing to do with biological processes slowing down (they don't) it is just what happens because of different paths through spacetime.

And by the way, clocks and calendars do NOT move slower. In their own frame of reference time passes at one second per second just as it does for the stay at home twin. It's just that different paths through space-time take different numbers of seconds.

Last edited: Jun 14, 2017
19. Jun 14, 2017

### Staff: Mentor

I suppose so, assuming:

1. The water is flowing into something like a large hole from all directions such that the swimmer is moving in an ellipse around the hole.
2. The swimmer is moving quickly enough and never exerts a force towards or away from the hole.

It's certainly not the analogy I would go with though.