Experiments Reveal That Deformed Rubber Sheet Is Not Like Spacetime 264
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!"
The earth orbits the sun... (Score:2, Funny)
like a car looking for a parking place.
Um... (Score:5, Insightful)
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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I have never like it as an analogy either. In the classic classroom rubber-sheet demonstration the marble rolls toward the bowling ball because the EARTH's gravity causes it to roll down hill. This is nothing at all like the way general relativity works.
General relativity requires a curvature of space-time, not just space. The best analogy I've seen comes from Kip Thorne (I think); Imagine 2 ants on the surface of an orange, both walking towards the "north" pole. Walking is an analogy to moving forward in t
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what exactly did the experimental physicists test? did they test the behavior of marbles on rubber sheets? science is awesome!
I like it as an analogy because it captures the "gravity well" idea pretty good. also, I don't understand that ant thing at all.
Re:Um... (Score:5, Interesting)
The dented rubber sheet (done in earth's gravity) is a not too bad analogy for Newtonian gravity.
Let me try the "ant" analogy in a bit more detail:
The "orange" is curved space time. here we have 1 space like dimension and one time like dimension, curved into 3d.
The "ants" walk forward. This walking is the analogy to moving forward in time.
On a big flat surface, two ants that started near each other walking on parallel paths (both moving forward in time and at rest relative to each other) would stay the same distance apart.
On the curved orange though as the ants walk forward, they wind up getting closer: Imagine they start at the equator and both head due north. The start out parallel, and both walk in as straight a line as is possible on the surface. After a while they find themselves closer together - as if some mysterious force (gravity) is attracting them. (this is as they get to the north pole.
The orange analogy isn't all that great either because the curvature isn't shaped right for GR. Unfortunately humans aren't good at imagining curved 4-dimensional space.
If the rubber-sheet demo is done without earth's gravity it isn't a terrible analogy, but I don't think I've ever seen it show that way. It seems to always be shown as this curved surface where the EARTH's gravity causes the marbles to roll to the center.
Re:Um... (Score:5, Informative)
If the rubber-sheet demo is done without earth's gravity it isn't a terrible analogy, but I don't think I've ever seen it show that way. It seems to always be shown as this curved surface where the EARTH's gravity causes the marbles to roll to the center.
If it's done without the Earth's gravity then nothing happens, the ball just fucking sits there, and nothing makes a "dent" in the rubber because... there's no gravity.
It's an analogy, not a physical model. You're supposed to ignore the presence of Earth's gravity when you look at it, and understand that the way the balls deform the surface is in some respects similar to how an object deforms space-time.
I can't say this enough: An ANALOGY is not the same thing as a MODEL. It's not supposed to be a physically accurate representation, you should NOT expect to roll a ball across the surface and get results that match actual real-world physics. That's why we call it an ANALOGY.
Rubber sheets for bed wetting physicists (Score:3)
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 gre
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I actually *really like* that analogy. You can imagine your left side struggling more than your right side, and this ultimately turning you.
Since I must be pedantic, I think in practice, to a degree, denser water would be easier to swim through, since it gives you more substance to push against. This is similar to how even if you lay on a low-friction surface (eg. a big skateboard) in air (considerably less dense than water), making the motions of swimming* doesn't get you nearly as far as it does underwa
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The good thing about the rubber sheet analogy is it makes sense for Joe average - your example is obscure and makes no sense, it doesn't provide a readily understandable visual experience to give the viewer an idea of what's going on.
Re:Um... (Score:4, Interesting)
In the analogy of the rubber sheet, the earth's gravitational acceleration is the passage of time.
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I have never like it as an analogy either. In the classic classroom rubber-sheet demonstration the marble rolls toward the bowling ball because the EARTH's gravity causes it to roll down hill. This is nothing at all like the way general relativity works.
General relativity requires a curvature of space-time, not just space. The best analogy I've seen comes from Kip Thorne (I think); Imagine 2 ants on the surface of an orange, both walking towards the "north" pole. Walking is an analogy to moving forward in time. After a while some "force" has brought them closer together (because they are near the pole).
And yet, to someone like me (a non-physicist) the rubber sheet analogy makes a lot of sense to me, while the orange analogy....well, I'm not exactly sure where you are going with that because it helps me understand nothing. Maybe you just didn't explain it fully or correctly, but I'm not finding it very useful
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I'm with you -- an ant walking on a sphere as metaphor for a 1d ant travelling in 3d is just a trick of plotting.
It adds nothing to the understanding of space/time -- "see, it's curved, just like space
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I have never like it as an analogy either.
It was never meant as more than an illustration of 'curved space' and how that might affect motion, which would be easy for lay-people to follow intuitively.
Also, all theories are 'fundamentally flawed'; we all know that. The best we can hope for, using the scientific method, is that we can discover more and more of the flaws and get rid of them. That is the fundamental insigt one needs to understand science: we knows we are wrong, but we have a method that brings us a little closer to the truth, if just we
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I agree, the marble will still follow a curve if it sticks to the rubber in zero-g - so the curvature does change its trajectory. Usually when this is shown though ,it is done in earth gravity and that is the largest effect on the marble. Even in zero-g, the analogy with GR is very thin because the curvature of the rubber sheet doesn't involve the time coordinate, so the effect on the marble's path doesn't really look like gravity in GR.
Done right the rubber sheet can be a barely OK analogy, as it is usual
Re:Um... (Score:5, Interesting)
The problem is the rubber sheet is a 2D surface. It can represent two dimensions. It can be two of space (as is normal), one space and one time, etc.
Real spacetime is a 4D entity - 3 (elongated) space, 1 time. The reason we use the rubber sheet analogy is because visualizing the distortions in spacetime (a 4D entity) is quite... difficult. Even visualizing a 3D representation is quite hard (pick your mix of space and time dimensions you want to show).
However, a 2D representation is quite easy to demonstrate and show to a class so they can visualize that happens. Sure, gravity is the biggest reason why the rubber sheet curves and what causes the marble to follow the curves, but it's a remarkably intuitive image of the warping of spacetime. (Then again, gravity is what causes the warping to begin with, and while we're using the earth to warp a rubber sheet because it's convenient...).
To be honest, it isn't a rigorous mathematical model, but it was never supposed to be. It's a practical demonstration on the weirdness of spacetime and gravity, illustrated on a 2D plane because we, despite being 4D entities have a hard time imagining it.
No one's going to derive equations for general relativity based on the rubber sheet analogy (or model - our physics class had a real model and we all had a chance to play with it). But it's certainly a great "a ha!" style of demonstration to solidify what is happening from dozens of equations and dry text.
And face it - modern physics is really damn hard to show people what is happening - either things are too big (relativity) or too small (quantum physics) that most people do not have any sort of grasp of it. At best, you have a model or an analogy. And never mind gravity is an extremely weak force to deal with.
So no, you aren't going to be mathematically correct. You are, however, going to get a lot of "I get it now!" reactions. Because in normal everyday life, gravity is not like what the theory says it is. We experience gravity like what Newton said it is. We don't see gravitational lensing or other such things
I say the rubber sheet model is more adept at getting the public to understand relativity than anything else.
infinite sheets in all directions (Score:2)
right...when I used to explain this, I introduce the she
Re:Um... (Score:4, Insightful)
Re:Um... (Score:5, Insightful)
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.
^this, many analogies in science are made to give a layperson a general/basic understanding of the concepts at work. They were never meant to be or expected to be working mathematical models.
Re:Um... (Score:4, Insightful)
^this, many analogies in science are made to give a layperson a general/basic understanding of the concepts at work. They were never meant to be or expected to be working mathematical models.
But how can we claim to be more smarter than the next person if we can't take a useful analogy and utterly destroy it by being overly pedantic?
The main way in which we acquire new knowledge is by relating it to old knowledge. We introduce concepts progressively, building on primitives and emerging with complex models. Geometry can be reduced to a finite set of axioms (with an optional postulate) yet results in a near-infinite number of complex interactions. When we describe how computers work, we discuss in terms of layers of abstraction, from transistors and resistors, to APIs and data flows.
Yet at every level and skill level, I can find people who scoff at those who continue to conceptualize things based on a earlier or lower level of abstraction. These people are what I call petty intellectuals: They aren't actually smart or gifted, they just read a lot of books and memorized a bunch of shit, and think this makes them "better" than others. The truly gifted will make you feel like you, too, can be gifted. This is the real lesson out of this article -- people who pick apart analogies for being "wrong" are usually simple-minded folk of average to below-average intelligence who desperately want to be "better" than you.
The rubber sheet analogy works because it gives us a way to visualize a natural phenomenon; Not everyone has an aptitude for complex math, or the patience for it. The essentials of the theory of relativity can be relayed without resorting to complex math -- ie, describing space time as a "rubber sheet". It may not be as accurate, but accuracy is not the goal: Understanding is. It is also why we talk about "strings" in string theory, despite them having not much to do with a ball of yarn. It's why Heisenburg's black cat is forever dying in internet memes. It's why quarks have some rather strange names ... owing to leading a decidely charmed existance. Communicating concepts and relationships is what analogies are good for: They build a foundation for later learning to be given context and meaning.
This is not a small problem in the scientific community either: Richard Feynman was laughed at for years for Feynman diagrams. He was told in no uncertain terms that visualizing these complex interactions couldn't be done, shouldn't be done, and was an abomination and a sin against those who practiced "proper" science. It wasn't supposed to be simple, dammit.
Today, the Feyman diagram is one of the most recognizable images in quantum physics. The pedantics lost... but it was a bitter fight.
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Ah, so you too don't know the difference between a model and an analogy. In your car "model" of a Linux computer, what counts as the wheels?
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Sure he does. The analogy is unsatisfying because an analogy is being drawn between gravity and gravity. It just removed one space dimension. A bunch of posters here have commented that they don't see how it explains gravity in a relativistic sense any more than it does in a Newtonian sense, since we're mapping time to time and not making it clear that it's part of the time-space continuum.
That analogy never really worked for me either (to be fair, nobody ever tried to formally present this to me; it's an a
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What would start the marble moving?
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It may be accurate, but you'll never find a theoretically ideal rubber sheet.
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After all, it's an analogy, not a model.
Analogies are like glass: if you push them too far, they break.
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The analogy is good enough to show the effects, but since it's a 2D effect visualized in 3D while the actual effect is in 3D it is bound to have errors. And the rubber itself isn't infinitely flexible but offers drag which in turn means that the rubber sheet presentation is just a rough approximation and not useful from a mathematical point of view.
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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.
Could you explain this using a car analogy?
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And there was a spherical cow
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And there was a spherical cow
... in a vacuum.
Dyson or Hoover?
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And there was a spherical cow
... in a vacuum.
Dyson or Hoover?
Clearly it's a Dyson Spherical Cow, given we might as well assume a large amount of free energy, too.
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Besides, the theoretical model is a frictionless and massless rubber sheet, not a real rubber sheet.
Physicists getting paid (likely tax money, too) for playing with marbles, to show that an analogy is only... an analogy.
I think I want that job.
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I think this is one for the Journal of Irreproducible Results.
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So physicists should come up with a better analogy, and stop using one with obvious flaws.
Taxes aren't needed to fund the government. The lesson of QE is that the Fed can create money to buy bonds and keep the loans rolling over forever without consequence.
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"Taxes aren't needed to fund the government. The lesson of QE is that the Fed can create money to buy bonds and keep the loans rolling over forever without consequence."
Haha. Hardly. QE and inflation both eventually have very harsh consequences. As a nation, our economy is no better off than it was in 2008, the people in general are poorer, the Fed has no more tricks up its sleeve, and unemployment is still high.
And we haven't seen the worst of the consequences yet (depite the fact that my food costs are pretty close to twice what they were 4 years ago). If the economy continues to recover on its own, it might not get too bad.
Read what Alan Greenspan has to say on th
This is old news (Score:5, Informative)
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 (Score:3, Insightful)
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.
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The point being made is that if the rubber sheet image only makes sense as a description of gravity when there is gravity causing the motion, then it's not even a useful representation. Turn the sheet up side down to see how well it works if you think you're ignoring the external gravity acting on the ball.
At best it works as a 3-D graph of the Newtonian gravitational field strength, but it's not explaining anything *about* gravity and certainly not General Relativity.
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Well, yes. I should hope so. Einstein did most of his best work imagining cows travelling near or at the speed of light. If relativity had to wait for NASA to modify a cow's digestive system to fuel a ramjet capable of near-light speeds, we would still be waiting. Not that it isn't fun to picture such a cow.
But, yeah, his thought experiments were definitely figurative descriptions, not mathematically precise models and it is not necessary for NASA to engineer a cow capable of making his figurative descripti
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I always thought it was a terribly weak analogy to begin with, because the analogy itself relies on gravity - the very thing it's trying to be an analogy of - which must exist in the world of this hypothetical sheet of rubber in order to pull the marble around the orbit of the mass deforming the rubber.
I can't think of a worse kind of analogy that requires that the entity being described exist within the analogy itself.
Works for the public (Score:4, Insightful)
I don't think .... (Score:5, Insightful)
... 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.
Re:I don't think .... (Score:5, Insightful)
I don't think the scientists did either- I think this was more of a 'fun' experiment to see what happens when you actualize the analogy.
Re:I don't think .... (Score:5, Funny)
actualize
Stop that.
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Asimov's Lesser-Known Fourth Law: Individuals using market-speak or manager-speak no longer qualify as humans and are an immediate threat to all real intelligence. Deal with, as per third law.
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a 2D metaphor for our real 3D world, which lives in 4D spacetime
The 'rubber sheet' model might have helped me a bit, but I think it was more confusion than clarity. It was one day, maybe 5 years ago, when I saw/read/heard(who knows?) it explained that the motion of a planet is a straight line in 4D spacetime that it all suddenly made sense to me.
Stupid (Score:3, Insightful)
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.
Why did they bother? (Score:4, Interesting)
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Flawed, but not useful? (Score:4)
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.
Re:Flawed, but not useful? (Score:5, Funny)
Analogies are like rubber sheets in that they have to be deformed to match their models.
Whiskey. Tango. Foxtrot. (Score:2)
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run your Hotwheels car through a loop (Score:2)
Shape your Hotwheels track into a loop.
Roll a car through it real fast. Notice that the car stays on the track when it's upside down - when gravity is trying to pull the car AWAY from the track.
Notice also when the car is vertical gravity is pulling the car backwards, neither toward the track or away from the track. You now see that gravity has nothing to do with it
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"If you had a "sticky marble" and took the rubber sheet into orbit and deformed it, the marble would still curve toward the divot. Not because gravity pulls it there but because the sheet is curved. That's the whole point of the analogy."
What's the "stickiness"? You've simply introduced another mysterious force to replace the gravity pulling the marble down towards the curve. Why should there be a "stickiness"? What is the stickiness? Where does it come from? Did someone apply glue to the marble, or the she
Analogy vs Model (Score:4, Informative)
All analogies are fundamentally flawed (Score:5, Interesting)
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."
For Pete's Sake! (Score:5, Funny)
Next they are gonna to tell me my Fisher Price bath boats are not sufficient for planning naval invasions.
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Next they are gonna to tell me my Fisher Price bath boats are not sufficient for planning naval invasions.
Of course not, don't be silly. Now Lego, that's another matter entirely. Lego is the stuff of military dominance!
So we should be watching Denmark very closely ...
This article is troll (Score:2, Insightful)
But the truth is that this work cannot diminish the extraordinary utility of this analogy. And so the public love affair with general relativity is safe. Long may it continue!
So what's the damn point?
Rubber sheet analogy explained (Score:5, Funny)
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.
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Attack the Slashdot summary, not the article (Score:3)
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.
The experts have spoken (Score:4, Interesting)
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:
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The problem is that when physicists present the analogy, they act like the equations for the marble's motions agree with the observations of planetary motion. They make no caveats. They basically ram the analogy down our throats without explaining the shortcomings. Maybe they should start.
That's pretty neat... (Score:2)
Upon thinking about a marble rolling on a rubber sheet I immediately see two big differences between it and a planet moving in space: (i) the marble.. well.. rolls along the sheet, which planets don't do while moving through space; and (ii) the rubber sheet doesn't propagate disturbances at the speed of light (or anywhere close to it).
I think most of us grasped this intuitively (Score:3)
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.
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You could of used irregardless in you're sig to embiggen it's affect.
Obligatory XKCD (Score:5, Informative)
Obligatory XKCD
http://xkcd.com/895/ [xkcd.com]
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Obligatory Young Ones.
Neil: Alright, so most metaphor's don't bear close examination.
The Young Ones: Flood. [menvafan.net]
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Woah... using an analogy containing an analogy of an analogy to explain why analogies are flawed.
Yo dawg.
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Possibly on my bookshelf, or maybe in his office [snopes.com].
Nothing wrong with analogy... (Score:3)
... 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.
It's conceptual (Score:2)
Its like dealing with the mythbusters (Score:2)
The point of the rubber sheet analogy is to discuss the SHAPE of the surface which is a stand in for forces of gravitation.
As such, even if following the analogy you shouldn't use an actual rubber sheet because it will be distorted by the marble itself. Rather, use a hard surface modeled on what a rubber sheet would do with that deformation.
Will that be perfect? Probably not but will be less of a failure then this spandex idea.
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The moving rubber balls will be resisted by the spandex which will slow them down and thus render the experiment useless. Much more useful if the surface is hard but in roughly the right shape. Then the marbles will at least move freely on the surface.
Completely silly. (Score:2)
It was used only as a visual aid to be able to teach mere mortals about gravity.
Will someone please smack these researchers, they obviously have zero social skills or understand you have to find a simple way of explaining things to the normals without their eyes glossing over and wandering away.
Doesn't Hold Water? (Score:2)
In my experience, rubber sheets are actually very good at holding water. I'm guessing one of these guys has a wife who, due to the number of years her husband spent on his Ph.D., is feeling the old biological clock ticking and she's taken a needle to every rubber she can find.
Science centres figured this out decades ago ... (Score:2)
I've seen models created out of hardened plastic that more realistically reflect the curvature of space. It still isn't perfect since you still have friction, but it does a decent job of demonstrating orbits.
The true advantage of stretched rubber sheets is that it is a cheap and easy demonstration to create. That was especially important in the days before computer simulations or even television.
Only possibilities are: (Score:2)
Creationism!
All science is wrong!
Feel free to add other crap. Seriously, how many analogies are exact? An object makes a dent in time/space, and another object reacts to that dent.
Remember, the analogy is there to give an idea on how to understand space/time, not for people who already understand space /time to figure out how rubber sheets work. That's for kinky people and kids with bedwetting problems to figure out.
" . .and yet widely appreciated by the public" (Score:2)
Planets and billiard balls (Score:2)
it doesn't matter until there's a better analogy (Score:2)
A flawed analogy can still be very useful. Very instructive. Even true.
An old planetary clockwork can still give you a very good idea of the movement of the planets, even though it's way off and in some ways misleading.
Anyway, the rubber sheet with the marble still beats "heaven above, hell below and Earth in the center of the universe", or "the stars represent the light of angels". Analogies are either better, or worse. More useful or less useful.
Look up "analogy" (Score:3)
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.
Well it's nothing like that. (Score:2)
.
Monty Python (Score:4, Funny)
King; "Look! General Relativity!"
Knights; "General Relativity!"
Minion; "It's only a model."
King; "Shh!"
Gyroscopic effect (Score:3)
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.
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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. Firs
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