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Comment by danellis | Hacker News Reader

This visualization always bothered me. The marbles 'stick' to the surface, but only because of the gravity pulling them from underneath. In the absence of gravity, marbles coming in from the outside could just continue in a straight line parallel to the ground, unaffected by the mass in the middle.

The only way I've been able to reconcile this in my mind is to think that this is a visualization of gravity warping spacetime in a 2D universe, and that is why the masses are stuck to the surface, but I've never seen that said in any of the explanations.

Am I right in thinking about it that way?

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>The only way I've been able to reconcile this in my mind is to think that this is a visualization of gravity warping spacetime in a 2D universe, and that is why the masses are stuck to the surface

Yes, that is correct. The sheet models a 2D universe, so objects are not allowed to "leave" the sheet, just like the Earth can't leave the three spatial dimensions it inhabits in the real universe.

For the same reason, an object on the sheet universe can't see (or even imagine) the concept that its sheet is bending. After all, the sheet is bending in a dimension that it cannot know about.

The analogy breaks down when you try to think where the force pulling the object down the bent spandex comes from. The objects on the sheet get pulled down a bend because of the Earth's gravity, but in the actual universe there's no 4D Earth that's pulling objects down a 3D slope.

... there's no 4D Earth that's pulling objects down a 3D slope.

What is pulling it then?

There is no answer to this question. Relativity simply allows one to calculate how much curvature is created in a particular mass configuration, and what the resulting gravitational forces are. It doesn't try to explain why the curvature occurs.

This link explains it better than I did: http://www.thenakedscientists.com/forum/index.php?topic=3887...

Just wondering, if acceleration == gravity (equivalence principle), how would this be visualized in this model?

I suppose it's possible that mass interacting with the higgs field could give rise to motion in the way an object will be pushed from a high density area of liquid to a low density area as mentioned in another comment here..

Those answers are so vague and abstract and far from a conceptual understanding from most people that have them told to me, that one comes to wonder how much they resemble the mystic explanations of the universe by priests and samans of yore in functionality.

E.g. a lot of big words that many repeat but few are supposed to understand (and even those, not that good).

Gravity is the result of a mass warping the structure of spacetime, but it's hard to imagine how the structure of spacetime being altered.

I think it helps in addition to the 2D curving sheet illustration by imagining 3D space with "liquid-density." In an empty system, the space liquid-density is uniform and an object with certain inertia just moves straight ahead. When another object B is placed near object A, object B's mass alters the space-density near it to be thinner. Object A moving pass object B will slip toward B because the space near it is thinner. The closer A to B, the thinner space gets and the faster it slips. There is no force involved. It's just objects slipping toward the thinnest density region. The "thinning" of space is mass warping spacetime, which is what we called gravity.

That analogy only seems to work in a system where everything is moving. If two objects are at rest relative to each other they are still attracting each other right?

Even stationary objects will feel pressure to move towards the lower density region, so ww520's analogy still works.

It would even refract light. I'd never heard of this mental model, very interesting.

Maybe it works if you imagine everything moving, and stasis is simulated by running in circles?

I see your point, but still find it to be a very nice visualization, and I think the 2D interpretation is actually quite close. I really like that pupils can play with this themselves. Yes, you'd be more exact with showing bending space/time curves, but that's already an abstraction many people won't be able to follow (see also: http://xkcd.com/895/).

I don't have a lot of confidence in my own understanding of relativity, gravity, etc., but I think you're taking the analogy too literally. In spacetime the object isn't warping the 'surface' because of something pulling on it, and the demonstration is not about explaining why matter warps spacetime, only demonstrating the effects of that warping.

I've always had trouble with this visualization too.

A better way of thinking about it might be to think of space as a 3d grid of springs. Matter pulls in the nearest springs, but this cause other springs in the grid to stretch out, creating tension.

Think of a relaxed spring stretched between two points. If you pull in just one part of the spring, the other side goes under tension.

   /\/\/\/\/\  (a relaxed spring)
   |||/-\_/-\  (a spring with the left parts of the coil pulled in, the right side is stretched out and thus under tension)

If you have two objects with mass in this "space" the "springs" between them act kind of like springs under tension. A simple model would be two weights on a table connected by a spring. If you pull them away from each other, the tension causes them to want to move towards each other. In the 3d grid of springs the same is true.

   x - a mass


   /-\_/-\_/|||x|||/-\_/-\_/ - a mass in space, notice space is pulled in around the mass, putting the rest of space in tension
   

   x|||/-\_/-\_/|||x - two masses in space, notice space is pulled in around both masses, putting the space in between in tension

Nature wants to move towards an equilibrium, but it can't relax the springs around the mass, so to make this happen, the masses are pulled towards each other to remove the energy in the intervening space.

   x|||/-\_/\_/|||x - starting to pull

   x|||/-\/\_/|||x - more

   x|||/-\/\|||x - more

   x|||/\/|||x - more

and so on

except there's no physical spring in between, so while in the analogy, you'd finish with x||||||x, in the real world, the masses can keep moving towards each other and you end up with

   x||||||x

   x|||x - more

   xx - the final resting state

We call this spring energy "potential energy" in physics, but it's caused by mass's necessary warping of space-time.

I think this is easier and more intuitive to visualize in true 3d. The warped 2d fabric is very hard to visualize in 3d and the way it functions (an outside force of gravity pulls objects down the slope towards the notional masses) isn't quite accurate.

I haven't studied GR, but I too have always had the same problem with this analogy. It is a crude analogy perhaps suitable for a 1 minute introduction.

As far as I can tell, this video gives a far better intuitive insight:

http://youtu.be/jlTVIMOix3I

I have no comments about the demo in the video. However, from what I understand about GR, the important concept is that mass bends space-time (3D space and 1D time). Time and space in GR is inseparable. This is an important concept.

So the next question is why in GR, the two mass objects gravitated each other. It is because in GR, object follows the geodesics (i.e. straight line, shortest path) in space-time. So imagine, if there is only 1 object, it will follow the geodesics of spacetime with space coordinates being constant and time coordinate is changing with a constant rate.

However, if another object is placed near it, it will bend the space time surrounding it. So now, the geodesic is not "straight" anymore. The new geodesic will include changes in the space coordinates ( object moving nearer to each other).

So there is actually no pull force of gravity, it justs that the spacetime is curved thus the "straight line" now appears "curved" in our perspective.

So gravity is helpful here in two ways as far as I can see:

  * it causes the marbles to warp the sheet
  * it causes the marbles to move in a direction that approximates how an object in spacetime will take the shortest routes between two points, taking into account curvature.

The limitations are:

  * it's 2d
  * the marbles lose energy to friction with the sheet
  * the marbles lose energy to the elasticity of the sheet

So the exact orbital paths aren't accurate since they're losing energy. The warped sheet sets up a situation in which the marble's behavior of seeking the lowest energy position (downward) happens to emulate the behavior of objects in space seeking to travel the shortest distance between two points.

I'm also curious to learn the answer to your question. The way I've always seen space-time modeled in illustrations, and now this video, is like a single plane. I've always imagined that plane as one of infinite planes that form a sphere surrounding the mass whose gravity is warping the space-time. If I'm wrong, I'd appreciate being corrected.

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