I've never really understood this visualization. It's a cheat in so many ways (wrong dimensionality, reliance on actual gravity to work, etc.). While such "gee-whiz" demonstrations are great at getting people excited about science, I worry that they create false expectations. They often produce the feeling of understanding without conveying actual understanding (and the limitations thereof).
The unfortunate truth is that many subjects in physics, including general relativity, are impossible to visualize in the conventional sense. I learned GR from Kip Thorne at Caltech and wrote my Ph.D. dissertation on the dynamics of rotating (Kerr) black holes, and my intuition for the subject is still fuzzy and inchoate. The best you can do is have a cobbled-together half-picture that kind-of, sort-of works, some of the time. Human brains simply are not designed to understand, at a deep intuitive level, things like the geometry of four-dimensional pseudo-Riemannian manifolds.
I agree that the demo is mixing concepts (esp.: relies on actual gravity to work) and tempting confusion. As a teacher, you'd have to be careful to clarify this so you don't confuse students.
I note that he says the demo is about GR, but then uses his rig and two handfuls of marbles to explain how almost all solar system orbits go in the same direction. (He doesn't need GR for that.) In this context, the rubber-sheet model is a very nice testbed for what is in effect a demonstration of stochastic initialization with positive or negative net angular momentum determining how it plays out.
I liked that a lot. It also hooks up with various strands of current research: use of numerical gravitational simulations, solar system dynamics at long time scales, and the surprising discovery of many exoplanets with retrograde motion relative to their host star.
If you'll grant that that is OK, you might have really lost it when he stuck the plastic strut underneath the sheet and said that was like dark energy!
So that makes me want to re-think his rig in a more granular way. It seems like one key question is: does the curvature you get with a mass in the 2d sheet have the same local properties as the curvature you get via GR in Minkowski space? Is this what is really driving the paths of objects in the simulation to be ellipses, hyperbolas, etc.? What is a notable example of some GR prediction that is NOT accounted for by his rig?
The height as a function of position of the elastic sheet is a solution to Poisson's equation, which is the same equation that gives you the (classical) gravitational potential. So the demonstration is an analogue computation that solves the analogous problem in gravity.
Thanks! This visualization has frustrated me for many years, for many of the same reasons you list above, but I don't have the Ph.D. to back up my skepticism, so it's good to know that my bad understanding of gravity wasn't taken in by this.
Wow, you sound very confused to me. Your "false expectations" bit is nonsense. Using your logic, kids shouldn't be told to wash their hands before they eat because it creates the "false expectation" that by washing their hands they're getting rid of all harmful germs. (re: They often produce the feeling of understanding without conveying actual understanding (and the limitations thereof)
Reality is complicated and kids already know that. Its just that they're way better than adults at being comfortable with not knowing everything.
> Human brains simply are not designed to understand, at a deep intuitive level, things like the geometry of four-dimensional pseudo-Riemannian manifolds.
"Hey kids ! Lets get real.. you won't understand this stuff at a "deep intuitive level" but please choose physics as a career." - Doesn't sound motivational to me.
You're not giving the above comment the respect it deserves.
Whenever you offer up an analogy, you want to choose it carefully, and be sure to convey its limitations. The video didn't discuss its limitations (which is OK, it's just a video showing off a rig). So we're left to do it here. And trust me, learning GR with Kip Thorne (http://en.wikipedia.org/wiki/Kip_Thorne) makes the above commenter qualified to offer an opinion.
>Whenever you offer up an analogy, you want to choose it carefully, and be sure to convey its limitations.
Yes, maybe if you're presenting at a conference or a lecture or something like that. Not if you want to get a bunch of kids motivated/interested in a topic. In the case of this video, the limitations can only be understood by people in that field. Sure, You can hand-wave a general clarification like "this isn't actually how it is, because <insert boring text that nobody will remember>" - which would be pointless (IMO) and convey no real information. Because the "real" information takes several years of academic training to understand and comprehend.
Sorry but it changes nothing in my mind. If the OP had said "Hey I would have said it this way and guess what I've successfully used it to motivate X, Y and Z into taking up science" - I'd have been way more impressed and given the "above comment the respect it deserves".
Mr. Burns the best science teacher ever. I remember he introduced the concept of Hertz to a half a sleep class by introducing the Avis and proceeding to casually talk about frequencies of Avis. After about 30 seconds he could tell which of us had read the chapter assigned the night before and which hadn't based on the laughter... His classes were the best.
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.
>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 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.
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?
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 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:
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'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'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.
What an amazing way to explain this concept. I'm a visual thinker, and I always preferred these kind of explanations of concepts. I just wish I had teachers who taught more like this in my science subjects during Secondary School.
This is definitely a nice, intuitive way to introduce people to the theory of gravity. However, I was a little confused about how he tried to model dark energy.
I think his dark energy illustration doesn't work. Dark energy is the inflation of spacetime, not mass warping spacetime (well at least we don't know what is causing the inflation). To make the illustration work, he needs to pull the whole sheet out along the rim, making the whole sheet bigger.
Indeed. It was particularly interesting how he described the "emergent" nature of the direction in which the celestial bodies finally conform to (clockwise/anticlockwise if applied to a 2d space). Wouldn't it be possible for a few planets to escape a collision and orbit in an opposite direction? Is collision necessary imminent from a stochastic perspective?
The unfortunate truth is that many subjects in physics, including general relativity, are impossible to visualize in the conventional sense. I learned GR from Kip Thorne at Caltech and wrote my Ph.D. dissertation on the dynamics of rotating (Kerr) black holes, and my intuition for the subject is still fuzzy and inchoate. The best you can do is have a cobbled-together half-picture that kind-of, sort-of works, some of the time. Human brains simply are not designed to understand, at a deep intuitive level, things like the geometry of four-dimensional pseudo-Riemannian manifolds.