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Experiments Reveal That Deformed Rubber Sheet Is Not Like Spacetime
KentuckyFC writes "General relativity is mathematically challenging and yet widely appreciated by the public. This state of affairs is almost entirely the result of one the most famous analogies in science: that the warping of spacetime to produce gravity is like the deformation of a rubber sheet by a central mass. Now physicists have tested this idea theoretically and experimentally and say it doesn't hold water. It turns out that a marble rolling on deformed rubber sheet does not follow the same trajectory as a planet orbiting a star and that the marble's equations of motion lead to a strangely twisted version of Kepler's third law of planetary motion. And experiments with a real marble rolling on a spandex sheet show that the mass of the sheet itself creates a distortion that further complicates matters. Indeed, the physicists say that a rubber sheet deformed by a central mass can never produce the same motion of planet orbiting a star in spacetime. So the analogy is fundamentally flawed. Shame!"
like a car looking for a parking place.
I'm not sure the analogy was ever meant to be a rigorous and exact model, but more of a kind of way of visualizing space-time. All analogies break down if you try to map them exactly to the phenomenon you're trying to explain. After all, it's an analogy, not a model.
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This was figured out more than 100 years ago. A rubber sheet can be mapped to a scalar theory of gravity. If you made it past the first two lectures of a class on General Relativity, you would know that Relativity is a tensor theory. That is why it is so horrendously complicated.
Thought experiments using analogues like the rubber sheet are often useful for visualization, organizing your thoughts, or providing a template to work on, but that doesn't mean that they necessarily provide a picture that is correct in all respects. The fact that they aren't accurate in all respects doesn't mean that they aren't useful representations.
much of left-wing thought is a kind of playing with fire by people who don't even know that fire is hot - George Orwell
Maybe it's just a general analogy for general relativity that's easy to understand, and not to be taken so so literally. Did they bother to come up with another analogy? Didn't think so. What dicks.
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... that anyone who had a grasp of high school phsyics, and who understood the analogy - of 3D matter flattened to represent a 2D metaphor for our real 3D world, which lives in 4D spacetime - or who understood that gravity attracted mass towards mass and not towards the "down" direction perpendicular to the sheet - would think for a second that such a demonstration would create the same exact trajectory as actual interaction between 3D objects in 4D spacetime.
No analogy is perfect. However relativity is sufficiently complex that I don't know if any analogy would be perfect at all. This analogy at least provides a general sense of the way it works, it may not be 100% accurate but's relatively (see what I did there) close enough to provide a general understanding.
Who seriously expected the physics of a marble rolling on a rubber sheet to exactly match the physics of a planetary body in orbit? Who thought the analogy was ever meant to make that statement? It's still a pretty good analogy for giving a layperson the gist of how gravity works, and I seriously doubt it was ever meant to do any more than just that.
All analogies are flawed in some way. They're analogies. They're not the actual thing. If the rubber sheet's characteristics match that of spacetime exactly, it probably is spacetime.
But even if it's not exact, I think it's still a useful way to illustrate to the general relativity-illiterate (yours truly being among them) what the theory is all about, and why it's significant. General relativistic effects are not something that can be demonstrated (easily) in the classroom. Putting a marble on a rubber sheet is.
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No. A rubber sheet is a flawed *model* for the shape of spacetime; as an *analogy*, it's still reasonable...
Analogies help to understand something... up to a certain point.
It only illustrates the basic concepts. After that, one has to go beyond the analogy and do the math.
I remember a poster on a door at the math department of my university (parafrazing from memory): "Do not try to visualize a space with more than 3 dimensions. Nobody can do that, trying will just twist your mind. Just use the formulas with the correct number of variables and leave it at that."
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Next they are gonna to tell me my Fisher Price bath boats are not sufficient for planning naval invasions.
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Suppose that you had a big rubber sheet stretched out, and onto that sheet you place a ball. Now suppose that there's a force that pulls the ball down, creating a depression in the sheet. Well, gravity is a lot like that force. Really a lot like it.
So the analogy is fundamentally flawed. Shame!
The analogy is not fundamentally flawed. The Slashdot summary is. There is nothing wrong with doing this kind of test, it's kind of "mythbusters" semi-science. It's kinda nifty. The problem, as usual, is the over-reporting of science in an attempt to create pithy quotable summaries.
In other news, experts pointed out that rubber sheets provide a two-dimensional surface, while the real spacetime continuum provides three spatial dimensions and one of time. Experts also pointed out that rubber sheets have nonzero friction with rolling marbles, while empty space has zero friction; and that the rubber sheets do not provide the time dilation effects that gravity provides.
Experts also pointed out that the whole rubber sheet thing is what is known as an "analogy" and pretty much by definition is inexact.
Personally, I found the article interesting, but the tongue-in-cheek "Shame!" of the summary a bit over the top.
P.S. From TFA:
lf(1): it's like ls(1) but sorts filenames by extension, tersely
I think most of us grasped this intuitively on some level. If nothing else, a ball rolling on a sheet is always going to experience friction. It doesn't orbit. It spirals in. It's "like" relativity. Then if you get into serious physics you learn the equations that are not merely "like" but *are* relativity.
For all intensive purposes, "whom" is no longer a word. That begs the question, "who cares"?
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... when we use analogies we're dealing with the most relevant information to communicate an idea. There is certainly nothing wrong with the analogy because it was never intended to communicate the whole complexity of the phenomenon, it was always meant as a starting point.
When we use analogy we're talking in ratio's and proportion, we're saying the phenomena is a X percent like this macroscopic phenomenon that everyone knows, but of course it is more complex then that, but that's a rough approximation of what is happening.
Nobody of any intelligence should get pedantic about it because that was never the intent of the communicator to begin with. I hate these ignorant pedants that stupidly misunderstand the intent of the person who originally made the analogy. You're not being smart, you've proven you don't get anything at all about communication of complex ideas.
We 'layer' people in to understanding by giving them basic models to get across general rough approximations and then we ease them into the deeper complexities, contradictions and unknowns.
First, it's an analogy, not a model, so it doesn't need to be mathematically correct, it only has to be conceptually correct. I don't see the problem there. Conceptually, gravity bends the spacetime around the mass, such that objects moving through the distortion appear to an observer to travel along a path that is not straight (it is straight to the object) in space or in time. The rubber sheet is a perfectly good representation of this concept.
If you want it mathematically perfect, you have problems. First, we don't yet know for certain if you should treat a mass as a point source or one with volume. The ternary star system recently found will help there. Second, in order for something to change state, there must be a force. With springs or rubber, this is a restoring force of known value. It not only removes curvature where there is no mass, it prevents the mass stretching the material to infinity and beyond. The nuclear forces play a role in reproducing some of this. The object cannot collapse further than the point where gravity and the nuclear forces all balance out. But as far as I know, the nuclear forces do NOT prevent spacetime bending infinitely, nor remove the distortion when the mass moves elsewhere. This matters. You cannot produce a mathematically-correct simulation with a deformable surface if you don't know the precise rules governing the deformation and restoration.
Let us imagine, though, that we know Hooke's Constant for spacetime. Ok, you get a material (or invent one) with the same constant. Unfortunately, not quite that simple. Relativistic equations are non-linear. You'd need a material where the forces involved reversibly (important!) altered the material in such a way that at any given instant, Hooke's Constant was correct, but that this constant would be purely an instantaneous value.
Ok, that is doable, we've plenty of adaptable materials. Gives you a geometrically correct solution and therefore the right mathematical results. Messy, though.
Is there an alternative?
Well, yes. This is all about reproducing forces. There is absolutely no rule that says you can use only physical shapes to do this. There are plenty of other forces (eg: electromagnetism) which can substitute for one of the others. Have the "fixed" mass as an electromagnet to encapsulate all the details that exist in spacetime that don't readily transpose to a rubber sheet. Let the sheet model gravity alone. That is what it is supposed to do. The other variables are factored in, so the geometry is still correct, only this time by imposing values rather than letting them naturally be correct.
Problem solved. Nobel prize to the usual address, please.
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The only fundamental flaw is with the physicists level of seriousness in documenting this test.
The rubber sheet is used as an analogy to describe the quintessential elements of the space-time theory to people uncomfortable with mathematics. It's not intended to be directly equivalent to an astronomical system! Obviously other effects (like friction and fabric warping) are more dominant on the experiment scales than at astronomical scales.
Reading the paper, there are something like five other references on marbles and spandex to simulate space-time warping. I mean, really? This is probably a good teaching tool for graduate students, but we must have too many underfunded physicists in the world if they are wasting actual research time with spandex and marbles. There are more useful projects that can be investigated cheaply and experimentally.
King; "Look! General Relativity!"
Knights; "General Relativity!"
Minion; "It's only a model."
King; "Shh!"
The rubber sheet (simple thing that 'uneducated' people understand) is a way of explaining the curvature of 4d space/time by mass (complicated thing that really requires a graduate level math degree to do anything meaningful with) by dropping down to 2d space. For what it is intended to do, it is a wonderful tool.
I always imagined 3d space with fluctuating 'density' gradients when I think of relativistic effects. Imagine being in a pool, where some of the water was was really dense or thick, and took great effort to swim through.
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A marble rolling on a rubber sheet will create a gyroscopic effect due to the strict alignment of the plane of rotation with direction of motion.
A planet spinning in space will have it's rotation in a completely different plane, and apparantly aligned (although often observably skewed) with the plane of orbit.
No wonder it's not comparable.