# Gravity and Curves in Space **URL:** \ **Category:** Factual Questions\ **Created:** [July 3, 2008, 4:58pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204 "2008-07-03T16:58:49Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Critical1](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@Critical1](https://boards.straightdope.com/u/Critical1)\ **Post date:** [July 5, 2008, 6:23pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/41 "2008-07-05T18:23:32Z")
try this, take 2 guys in space suits and fling them into space moving at identical speed on perfectly parallel lines. now remove every thing else in the entire universe, just the 2 dudes zooming along through space. in universe A there is no gravity, so in universe A there is no curvature thus they will never ever get closer or farther apart. universe B on the other hand is the one we live in, it has gravity. eventually the gravitational pull even as tiny as it is at the scale of the human body will pull them together until they bump. that is gravity curving space. (note its early, and I aint no physics person so this could be a total load of crap) ---
**Author:** ![Oy](https://avatars.discourse-cdn.com/v4/letter/o/bc8723/32.png) [@Oy](https://boards.straightdope.com/u/Oy)\ **Post date:** [July 5, 2008, 6:53pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/42 "2008-07-05T18:53:19Z")
[QUOTE=Mathochist] Maybe I could have phrased that better. When I said “accept” I meant more like “understand”, though not quite that either. I blame my training. Mathematicians presenting an argument will use “accept” in this sense. We know there’s a difference between “believe it’s true” and “accept the line of reasoning”, but we just gloss over it in our own language. [/QUOTE] I understand your usage of the word “accept” - I did college level math, and I understand the concept of “given that.” It’s this particular “given” that I have a problem with. I’m sure if I learned the equations I could do the math. But because I can’t understand it at gut level, because it doesn’t make sense to me at a profound level, I can’t hold on to it. It will be pure symbol manipulation, and once forgotten, not recoverable except by re-learning. Whereas with low level algebra or basic Euclidean geometry, I can return after twenty years, practise for half an hour, and have it down as well as ever. **Critical1** , why doesn’t universe B’s gravity simply imply that objects with mass attract one another? Why does their drawing together imply curvature of space? You see, that’s where I intellectually know the answer, but at gut level can’t get it. I apparently am not capable of grasping beyond Euclidean geometry and Newtonian physics. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [July 5, 2008, 7:02pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/43 "2008-07-05T19:02:46Z")
[QUOTE=Critical1] try this, take 2 guys in space suits and fling them into space moving at identical speed on perfectly parallel lines. now remove every thing else in the entire universe, just the 2 dudes zooming along through space. in universe A there is no gravity, so in universe A there is no curvature thus they will never ever get closer or farther apart. universe B on the other hand is the one we live in, it has gravity. eventually the gravitational pull even as tiny as it is at the scale of the human body will pull them together until they bump. that is gravity curving space. (note its early, and I aint no physics person so this could be a total load of crap) [/QUOTE] This is true, but the question is how to interpret that observed effect as a curvature. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [July 5, 2008, 7:16pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/44 "2008-07-05T19:16:07Z")
[QUOTE=Mathochist] This is true, but the question is how to interpret that observed effect as a curvature. [/QUOTE] A question: Would it be accurate to say that interpreting it as curvature simply amounts to successfully applying to it geometrical equations that are used to describe things on curved surfaces? If that’s true, then IMO it is actually not necessary to make the metaphysical claim that “space is curved” but rather simply the practical claim that “space can be described using these equations” where it just so happens that “these equations” are equations originally designed to deal with curved surfaces. From that, we might _hypothesize_ that space is curved, but that would be a seperate step, wouldn’t it? I’m starting to think that the claim “space is curved” is misleading unless interpreted as jargon. Do you think I’m wrong to think that, though? -FrL- ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 5, 2008, 7:20pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/45 "2008-07-05T19:20:43Z")
Well, I think the whole perspective of viewing curvature intrinsically, rather than as arising from some embedding, is tied to interpreting “curvature” as mathematical jargon, as you put it; that is, taking “curvature” as being just particular standard terminology for describing the behavior of straight lines and such. What would a separate, stronger claim that “space is curved” amount to? ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [July 5, 2008, 7:29pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/46 "2008-07-05T19:29:49Z")
[QUOTE=Indistinguishable] Well, I think the whole perspective of viewing curvature intrinsically rather than extrinsically is fundamentally tied to interpreting curvature as jargon, as you put it; that is, taking discussion about curvature as being just particular terminology for describing the behavior of straight lines. What would a separate, stronger claim that “space is curved” amount to? [/QUOTE] I think that in “average everyday english,” “space is curved” would have to mean that the space you’re talking about–I guess three dimensional space–is embedded in a higher-dimensioned space, and is extrinsically curved in that higher dimensional space. But I think what scientists “really mean” when they say space is curved is that the movements of objects in four dimensional space-time can be accurately described using non-euclidean geometrical equations. (And a related fact is that non-euclidean geometrical equations can–or often can?–be used to describe relations between figures in extrinsically curved surfaces, but this is just one use to which they might be put.) And if that’s what they “really mean,” then when heard by a layperson, the claim “space is curved” is sure to be misleading. In fact, I’m starting to think it’s so misleading that when scientists are talking about this kind of thing to non-scientists, they ought immediately to say something like “But we don’t really mean it’s curved! That’s just a word we use for historical reasons.” -FrL- ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [July 5, 2008, 7:47pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/47 "2008-07-05T19:47:58Z")
[QUOTE=Frylock] A question: Would it be accurate to say that interpreting it as curvature simply amounts to successfully applying to it geometrical equations that are used to describe things on curved surfaces? If that’s true, then IMO it is actually not necessary to make the metaphysical claim that “space is curved” but rather simply the practical claim that “space can be described using these equations” where it just so happens that “these equations” are equations originally designed to deal with curved surfaces. From that, we might _hypothesize_ that space is curved, but that would be a seperate step, wouldn’t it? I’m starting to think that the claim “space is curved” is misleading unless interpreted as jargon. Do you think I’m wrong to think that, though? -FrL- [/QUOTE] This is actually a very deep question in the philosophy of physics. At what point, and to what extent, can we identify physical reality with a sufficiently-successful model? I don’t have a good answer to this question. I _will_ say that I’m willing to talk about “forces” – specifically gravitation – as if they’re real when I deal with Newtonian mechanics. Sure, there’s no such thing in GR as the “force of gravity” like there is in classical mechanics, and sure GR is far more accurate. But I still say that the Earth’s gravity “pulls down” the cinder thrown out from my weber kettle onto the deck.. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 5, 2008, 7:51pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/48 "2008-07-05T19:51:04Z")
> [@](#): > > On the other hand, in the Honor Harrington sci-fi series, they use gravity waves as a considerable aid to propulsion, and I suspect there they may be postulating areas where gravity itself is more powerful than elsewhere. Don’t take Honor Harrington too seriously. The science is a little better than in _Star Trek_, but not by all that much. I think that Harrington’s universe just might be completely self-consistent, but it’s not ours, and terminology like “gravitational wave” has completely different meanings in her world and ours. > [@](#): > > I’m starting to think that the claim “space is curved” is misleading unless interpreted as jargon. Do you think I’m wrong to think that, though? I’m having a hard time understanding how statements can be interpreted as anything other than jargon. The word “curvature” has a very precise meaning in mathematics, which is related to but not identical with the common meaning of the word. When we say “space is curved”, we mean that in the precise technical meaning of “curved”. That is to say, the jargon meaning. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [July 5, 2008, 9:01pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/49 "2008-07-05T21:01:00Z")
[QUOTE=Chronos] I’m having a hard time understanding how statements can be interpreted as anything other than jargon. [/QUOTE] I’m having a hard time understanding how you are having a hard time understanding how statements can be interpreted as anything other than jargon. 😛😉 See my post #46. “Curved,” as you pointed out, means something different in “average everyday English” than it does in an astrophysical context, and if I am not familiar with the astrophysical meaning of the term, then I am very likely to come away from a statement like “space is curved” with a bad misunderstanding of what the physicists are saying. -FrL- ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [July 5, 2008, 9:03pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/50 "2008-07-05T21:03:15Z")
The cylinder is an intuitively clear case of extrinsic curvature without intrinsic curvature. Are there any intuitively relatively straightforward examples of surfaces that are intrinsically curved without being extrinsically curved? Also, an a one dimensional space be intrinsically curved? What does this amount to? -FrL- ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [July 5, 2008, 9:59pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/51 "2008-07-05T21:59:49Z")
[QUOTE=Frylock] Are there any intuitively relatively straightforward examples of surfaces that are intrinsically curved without being extrinsically curved? [/QUOTE] I don’t think so. I can put whatever metric I want on a flat plane, but that’s hard to come up with, and it’s not exactly what you want. > [@](#): > > Also, an a one dimensional space be intrinsically curved? What does this amount to? No, it can’t. Curvature is (in a sense) inherently two-dimensional. It measures how much “coordinate parallelograms fail to close” or “triangles have an angle surplus or deficit” or “circles have longer or shorter circumferences than their radii would indicate”. You need two distinct directions to move in before you have any effects of curvature. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 5, 2008, 11:31pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/52 "2008-07-05T23:31:12Z")
> [@](#): > > See my post #46. “Curved,” as you pointed out, means something different in “average everyday English” than it does in an astrophysical context, and if I am not familiar with the astrophysical meaning of the term, then I am very likely to come away from a statement like “space is curved” with a bad misunderstanding of what the physicists are saying. The problem isn’t just that terms mean different things to professionals and laymen; it’s also that they mean different things to different laymen. This is why we need the technical meanings in the first place, so that it’s absolutely clear (to someone else who knows the jargon, at least) what it is we’re talking about. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [July 5, 2008, 11:41pm UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/53 "2008-07-05T23:41:22Z")
[QUOTE=Chronos] The problem isn’t just that terms mean different things to professionals and laymen; it’s also that they mean different things to different laymen. This is why we need the technical meanings in the first place, so that it’s absolutely clear (to someone else who knows the jargon, at least) what it is we’re talking about. [/QUOTE] Yes. -FrL- ---
**Author:** ![Critical1](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@Critical1](https://boards.straightdope.com/u/Critical1)\ **Post date:** [July 6, 2008, 12:52am UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/54 "2008-07-06T00:52:31Z")
[QUOTE=Mathochist] This is true, but the question is how to interpret that observed effect as a curvature. [/QUOTE] well the same scenario would work if you replaced our spacemen with a lightspeed bullet and a laser, eventually they are going to come together. one way i think it helped a friend was to flip the whole thing over and look at it from the point of view of a beam of light. you could say that Light always moves in a perfectly straight line and gravity (and crap like reflections/refraction) makes it appear to be moving in various non straight lines so if you were a beam of light zooming along and looking at the universe go by planets and stars would be very very distorted compared to our human view point where they look like spheres. ug, I hope that made sense, I am going to take a nap. stupid work on the 5th ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [July 6, 2008, 1:44am UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/55 "2008-07-06T01:44:32Z")
[QUOTE=Critical1] well the same scenario would work if you replaced our spacemen with a lightspeed bullet and a laser, eventually they are going to come together. [/QUOTE] Yes, sure. But the question is still, “what does the fact that they converge have to do with curvature?” ---
**Author:** ![Oy](https://avatars.discourse-cdn.com/v4/letter/o/bc8723/32.png) [@Oy](https://boards.straightdope.com/u/Oy)\ **Post date:** [July 6, 2008, 2:11am UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/56 "2008-07-06T02:11:58Z")
[QUOTE=Mathochist] Yes, sure. But the question is still, “what does the fact that they converge have to do with curvature?” [/QUOTE] I’m so glad that at least you and some of the others recognize what I don’t understand. It makes me think that maybe I’m not quite as stupid as all that. Frankly, I can accept “Space lends itself to being described by equations used for describing curves.” better than “Space is curved.” even though the latter is certainly punchier, and I still don’t have a clue \*why \* this is so. I mean, everything was going just fine with Newtonian physics, and then relativity had to come along and ruin everything! And don’t even \*think \* about telling me it feels longer sitting on a hot stove than sitting next to a pretty girl! ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 6, 2008, 2:39am UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/57 "2008-07-06T02:39:32Z")
As long as you’re fine with the “spacetime can be described by these equations” part of it, don’t sweat the rest of it. Science only concerns itself with that which can be observed: There’s no scientific difference between “spacetime is curved” and “spacetime isn’t actually curved, but it behaves just as if it were”. ---
**Author:** ![Critical1](https://avatars.discourse-cdn.com/v4/letter/c/3e96dc/32.png) [@Critical1](https://boards.straightdope.com/u/Critical1)\ **Post date:** [July 6, 2008, 2:51am UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/58 "2008-07-06T02:51:04Z")
[QUOTE=Oy!] I’m so glad that at least you and some of the others recognize what I don’t understand. It makes me think that maybe I’m not quite as stupid as all that. Frankly, I can accept “Space lends itself to being described by equations used for describing curves.” better than “Space is curved.” even though the latter is certainly punchier, and I still don’t have a clue \*why \* this is so. [/QUOTE] well to strip things down as far as I can, in the scenarios I described BOTH are traveling along parallel lines. this is a true statement. its just that with gravity parallel lines happen to meet rather often in ways that a lack of gravity would find very very strange. and trust me, physics is strange as hell, check out a book called “Chaos Theory” by Gleick. (I think thats spelled right) it uses minimal complicated math stuff and mostly just laymans terms to talk about a lot of complicated physics stuff, and its a good read. ---
**Author:** ![Oy](https://avatars.discourse-cdn.com/v4/letter/o/bc8723/32.png) [@Oy](https://boards.straightdope.com/u/Oy)\ **Post date:** [July 6, 2008, 3:13am UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/59 "2008-07-06T03:13:00Z")
Thanks, **Critical1** , but I think I’ll stick to the Euclidean-Newtonian world from here on in. I don’t like it in your world. Hell, as far as I’m concerned, your world can’t _exist_! Yes, I realize that it does, but it makes no _sense_, and I don’t think that to me it ever _can_ make sense. So I’ll accept it the way the religious accept God, except my prophets will be scientists, and I’m not going to attend church at all frequently. Maybe once every few years on Easter or something. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [July 6, 2008, 3:44am UTC](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204/60 "2008-07-06T03:44:42Z")
[QUOTE=Critical1] its just that with gravity parallel lines happen to meet rather often in ways that a lack of gravity would find very very strange. [/QUOTE] No, they’re not parallel, because they do eventually meet. They’re “initially parallel”, but they don’t stay parallel. [Previous page](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204.md?page=2) [Next page](https://boards.straightdope.com/t/gravity-and-curves-in-space/455204.md?page=4)