Using the rubber sheet gravity well model of gravity, is space a 3-dimensional sheet sinking into the fourth dimension of gravity, or a 4-dimensional (spacetime) sheet sinking into the fifth dimension of gravity? Or am I misinterpreting it altogether?
Chronos or Phobos might be better at answering this but I believe that it is three dimensions poking into the fourth.
So, our three dimensional earth is sitting in (on?) a 4-D spacetime that it warps by virtue of it mass.
I’m not an expert on this stuff, but I believe that the problem is that the rubber sheet analogy is a little flawed.
I DO know that it’s at least POSSIBLE to think of some spacetimes as, say, 4D objects embedded in 5D (or higher) surfaces, the same way that the surface of the rubber sheet is 2D object in our 3D world. However, I think there’s a distinction that has to be made (and correct me if I’m wrong).
The rubber sheet model actually has 3 physical spatial dimensions to work with. I believe that, at least in conventional GR (let’s ignore string theory), there isn’t a PHYSICAL 5th dimension that spacetime bends in; you can certainly write things as if there were an extra dimension (and sometimes it makes the math simpler to do it that way, I’ve heard), but the extra dimension is just a mathematical construct.
So I think the answer to your question is that if you mean what do people who work in relativity think is physically true, you’re just misinterpreting things. If you mean how do they mathematically interpret things, the answer is (I think) that it depends. If, for example, time doesn’t warp, then you could have three spatial dimensions bending into a 4th, plus time. If it does warp, you’d have a 4D spacetime ALL bending into a 5th dimension. But it’s just a mathematical device to make things easier.
Since there are only three spatial dimensions space cannot curve into some other dimension…… there is no other spatial dimension for it to curve into.
When scientists refer to the curvature of spacetime they are talking about an intrinsic change in the geometry of space
**From Einstein: The Life and Times (R. W. Clark, 1971) - **
“because curvature, in the sense of bending, is a meaningless term except when the space is immersed in another space, whereas the property of being non-Euclidean is an intrinsic property which has nothing to do with immersion. However, nothing can be done but to utter a warning that what mathematicians understand by the term “curvature” is not what the word connotes in ordinary speech; what the mathematician means is simply that the relations between the mutual distances of the points are different from the relations which obtain in Euclidean geometry. Curvature (in the mathematical sense) has nothing to do with the shape of the space - whether it is bent or not - but is defined solely by the metric, that is to say, the way in which “distance” is defined. It is not the space that is curved, but the geometry of the space.”
Ring is right. And so is g8rguy. Gravity is not a dimension, it’s a force. And spacetime doesn’t ‘curve’ in the way that the rubber sheet does. Rays that pass through spacetime curve as a result of gravitational distortion of spacetime, but the spacetime doesn’t.
Perhaps a better way to envision it is as a compression or contraction. Imagine a 3-dimensional grid of lines representing ‘virgin’ spacetime. Now put in a star. The gridlines will move closer together in the vicinity of the star, getting closer and closer as they approach the star. That’s a better mental image than a rubber sheet. I never liked the rubber sheet.
Course, truth be known, we aren’t really sure what (if anything) a force is… especially in regards to gravity.
We got a pretty good handle on quantum stuff (we think) and interactions of quantum particles causing forces but no one has yet to observe the graviton (although there’s a number of nice theories that can be tested from its conjectured existence). Part of the problem is the scale of gravity. The reason dim. analysis works so well is that gravity is such a massive thing that it’s easy to comprehend (it’s acting over large distances rather weakly and thus can be modeled in a n+1 dim. vector space). Actually, you can do that with any force, but quantum scales have problems with interference, non-classical behavior, etc. The relativity non-classical behavior is (as far as we can tell) much different in that regard and so…
there is no grand unified theory.
Round about, but, best I can do to get at the parent issue.
Any of you read the tesseract by Alex Garland?
I like the bit about the 2d man trying to imagine a 3d shape, i thought that was relivent here. MAybe it aint. What do i know???
Hell, just shoot me now, i pro’lly missed the point of the book, i pro’lly missed the point of this thread, i prolly missed the poin in life ( it has a point?) and i pro’lly just made a huge fool of myself.
SHOOT ME NOW!
I should never have posted that now.
- FEELS REALLY STUPID *
LOOK, I’M AN IDIOT, THAT AINT NO CRIME! GO FLAME SOMEONE WHO CARES!
( i really do care, but i aint gonna show that here am i! )
Night Night Everyone
…and space is “expanding” or “contracting,” what is it expanding through? Space isn’t exactly like water, water has mass, when it expands its molecules get farther apart, that’s an expansion in 3D. But space, by definition, is mostly empty, except for the odd stray molecule and background radiation, which relativity notwithstanding is not matter. What, exactly, is expanding or contracting? A mathematical curve may not be the same as a normal curve (though they never said anything about that in calculus… then again, I couldn’t really do multivariable calc, which is why I dropped my chem major… I can handle the theory but not the math with quantum crap… anyway…), but, I’m fairly sure it’s not just a matter of two stars moving closer together or farther apart, if the actual distance between them is being warped by gravity. I have been given to understand that gravity DOES warp time, especially around black holes and other supermassive stars, and that astronauts on the space shuttle even experience a (slight, but present and detectable nonetheless) difference from “earth time” due both to their speed and their distance from the earth’s surface. So if we include time as a 4th dimension in addition to the three of space being warped by gravity, wouldn’t that make it 5th-dimensional? Sorry if this is confusing.
Kenny Rogers sang for the Fifth Dimensions.
I thought I’d throw that in so that I could be the third post in a row that didn’t make much sense and we could be the Moe, Larry and Curly of the SDMB.
See, the problem is that you’re still thinking about this from the wrong perspective. You’ve probably seen the analogy that says that “space is like a balloon,” where you inflate it and points on the surface get farther apart as the balloon expands. The problem is that the balloon is actually expanding into a PHYSICAL dimension, and that’s a flaw of the analogy. I suspect that it’s just impossible to visualize this, but I’m pretty sure that the answer to the question you asked is that the question itself doesn’t really have a meaning. On a very large scale, the universe is growing; that doesn’t mean that it’s growing into some higher dimension, it just means that the distance between any two points in space (were space to be completely empty) is increasing.
Oh, I loathe trying to explain this, because I always do a miserable job. Anyone out there want to take a stab at a clearer explanation? Really, that quote
sums things up quite nicely, only unless you spend a whole lot of time reading and going through the maths, the quote probably also is fairly unenlightening.
The “fabric of spacetime,” to be all metaphorical about it. Very helpful, I’m sure.
<blatant hijack>No no, the idea is that when we think of curvature in every day life, we think of something that doesn’t LOOK flat. We look at something like a can of coke and say that it appears to be curved. This is an example of what relativists (people who do GR for a living) call “extrinsic curvature,” and it absolutely depends on the surface of the can being a 2D object in our 3D world. What a relativist (or a mathematician) normally means by “curvature” is intrinsic curvature, which actually depends on the geometry of the surface. The surface of a sphere has intrinsic curvature, and in principal, you could actually detect this. But our example of a cylinder is actually flat, counter-intuitive though that may be.
It might help to think about it this way: if you wanted to cover a bowling ball with plastic wrap, you’d have to stretch it in some places and not in others, or else you’d have to crumple it, or it’d have to have places where it’s double layered, or some such. But you couldn’t just roll it on. By contrast, you could wrap a rolling pin in plastic wrap without stretching the stuff (assuming you were careful enough). This is because the plastic wrap and the cylinder are flat, and the bowling ball is not.</blatant hijack>
No, you’d have 3 for space and 1 for time, and that’s all there is. I suppose there’s nothing to prevent you from saying that there is this mysterious 4th spatial dimension that we can’t access and that has no effects on anything and whose sole purpose in life was to provide the geometry of space with something to look curvy in, but why would you do that?
Hey, I’m a grad student in physics, and some of these concepts confuse me, too! So no worries.
I am honored to be a recommended source on this subject…and in the same breath as Chronos, nonetheless! thanks! But g8rguy, Ring, and Whack-a-Mole already did a gr8 job explaining it.
As has been said, the rubber sheet analogy is a helpful visual tool, but it is not an accurate description. Space is not curving into anything or expanding into anything, as far as we know. I say “AFAWK” because we have no way of examining anything that is “outside” of this universe, if such a place exists at all.
But remember that the “fabric” of the universe is not just space, it’s “spacetime” (3 dimensions of space and 1 of time). So in a sense, you may be able to say that Space is curving/expanding into Time. This may be the best way to grasp the concept, but it may be stretching it (sorry, bad joke).
Einstein essentialy showed that gravity is the same thing as the geometry of spacetime and not some separate force. Although gravity certainly acts like a force, what we perceive as gravity is actually just movement along “curved” space. But gravity is not fully understood, so there is probably more to it.
But cosmology is way more complicated than all of what we’re discussing. Most cosmological discussions seem to end with “we don’t know”. Here are some great websites if you have free time…
I was gonna ask a question about gravity today myself, so I am glad this topic is already open. It is a slight hijack, so please forgive me. As always, please correct me and please fogive my ignorance. I think Einstein basically stated that gravity was the result of matter warping space-time, but I always wondered if this warping was just a result, and not actually the cause of gravity. I guess this might be where the discussions of gravitons and gravity waves might fit in. Lastly, I used to have a copy of an insert to the Houston Chronicle (it wasn’t Parade; I can’t remember exactly what it was - Texas, maybe) where the search for the Theory of Everything was discussed. Anyway, I could have sworn that in the article that a scientist mentioned that it was now considered possible that gravity might be in the high end of the electromagnetic spectrum, and that it might actually have frequency, amplitude, etc. I mentioned that in a post here once, and the guy after me said I was nuts. Did I confuse some Bob Lazar kooktech I read once with something I read in that article?
Thanks for any clarification you can provide.
Almost correct. Gravity IS the warping of spacetime. The way I’ve best seen it explained is “matter tells spacetime how to curve; the curvature of spacetime tells matter how to move.” We interpret the fact that, for example, the earth falls towards the sun as gravitational attraction, but really, it’s all a result of spacetime being warped.
Well, gravitons are what pops out when you try to “quantize” general relativity, and as I understand it (here I’m starting to get out of my depth), they’re basically the MEANS by which matter tells spacetime how to curve. There’s also all sorts of problems with them, mostly that we’ve never seen them and that while there’s no problem with writing down the equations for quantum gravity, we don’t know how to solve them.
Gravity waves are just a natural consequence of general relativity. Quick aside: I haven’t kept up with this, since I’m not a relativist, but I don’t think that we’ve directly seen a gravitational wave yet. Is this true?
I’m pretty sure that you must have, the biggest reason being that electromagnetism is what’s known as a vector field (hence the spin 1 photon) and gravity isn’t; it’s a tensor field (hence the spin 2 graviton). Gravity interacts with light, but if someone is saying that they’re really the same thing, he’s probably one of these odd types who believes that his Gumby variables approach to physics explains everything without even having to (gasp!) do math.
That said, if you believe the string theorists, gravity and electromagnetism are related on a deep and fundamental level. But they’re not the SAME. (I could, of course, be misinterpreting what the string theorists are saying, but then, I don’t particularly think they’re right anyway.)