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I always had a bit of difficulty completely grasping the concept of curved space-time. To simplify it for myself, I think of a 2-dimentional universe with no time. Let's say this universe is sphere-shaped. If I were to plaster this universe onto the surface of a 3-dimentional sphere, it implies that the 3rd dimension must exist for the 2d universe to exist in this shape.Am I thinking about his in the right manner? Does this example extrapolate correctly to 4d space-time? Does our universe require a 5th dimension to be curved?

I always had a bit of difficulty completely grasping the concept of curved space-time. To simplify it for myself, I think of a 2-dimentional universe with no time. Let's say this universe is sphere-shaped. If I were to plaster this universe onto the surface of a 3-dimentional sphere, it implies that the 3rd dimension must exist for the 2d universe to exist in this shape. Am I thinking about his in the right manner? Does this example extrapolate correctly to 4d space-time? Does our universe require a 5th dimension to be curved?

Depends on what you mean by a curved universe? As far as I get it the universe as such is more or less 'flat', meaning that there is no limit to it that I know.

"not the curvature of space, but of spacetime". Curved spacetime isn't curvature of space and curvature of time. It's a curvature in your plot of measurements of motion through space over time.

you know that when you plot all your clock rates, what you get is a plot like this: GNUFDL image by Johnstone, see Wikipedia [nofollow]

Quote from: yor_onDepends on what you mean by a curved universe? As far as I get it the universe as such is more or less 'flat', meaning that there is no limit to it that I know. You're thinking of space being flat. The spacetime is still curved.

So the vertical "dimension" (not a real dimension) seen in this graph is the time dilation?

Then what are people referring to when they talk about the shape and/or curvature of the universe? Are they talking about the curvature of space or of spacetime?

Quote from: cowlinator on 21/09/2014 23:32:42Then what are people referring to when they talk about the shape and/or curvature of the universe? Are they talking about the curvature of space or of spacetime?IMHO there's quite a lot of confusion about that.

You were responding to a well-known crackpot when you posted opinion.

Quote from: PmbPhy on 27/09/2014 11:06:55You were responding to a well-known crackpot when you posted opinion.He's the only one who answered my question to any degree of detail, and with any degree of clarity. To me, this implies there is some confusion about it.

It could be that “crackpot” has evolved to mean someone who takes the trouble to give more than a dogmatic answer to a question.

Quote from: cowlinator on 27/09/2014 21:40:41He's the only one who answered my question to any degree of detail, and with any degree of clarity. To me, this implies there is some confusion about it. The number of posts a person makes having what appears to be greater detail cannot logically be used to infer that a person isn't a crackpot.

He's the only one who answered my question to any degree of detail, and with any degree of clarity. To me, this implies there is some confusion about it.

Quote from: JohnDuffieldSo you know that when you plot all your clock rates, what you get is a plot like this This will mislead you to misinterpret every embedding diagram that you see from now on to be what he claims it means and thus you'd be misusing them too.

So you know that when you plot all your clock rates, what you get is a plot like this

That's nice. The only thing I was logically inferring was: the lack of posts, having what appears to be greater detail, that anyone makes, infers that there is some confusion on the subject.

So what you're saying is, that because a 3d graph an Earth on it was used to represent certain axes, ...

And should I be offended?

In astrophysics, a gravity well is specifically the gravitational potential field around a massive body. Other types of potential wells include electrical and magnetic potential wells. Physical models of gravity wells are sometimes used to illustrate orbital mechanics. Gravity wells are frequently confused with embedding diagrams used in general relativity theory, but the two concepts are distinctly separate, and not directly related.....Gravity wells and general relativityBoth the rigid gravity well and the rubber-sheet model are frequently misidentified as models of general relativity, due to an accidental resemblance to general relativistic embedding diagrams,[citation needed] and perhaps Einstein's employment of gravitational "curvature" bending the path of light, which he described as a prediction of general relativity. In particular, the embedding diagram most commonly found in textbooks (an isometric embedding of a constant-time equatorial slice of the Schwarzschild metric in Euclidean 3-dimensional space) superficially resembles a gravity well.Embedding diagrams are, however, fundamentally different from gravity wells in a number of ways. Most importantly, an embedding is merely a shape, while a potential plot has a distinguished "downward" direction; thus turning a gravity well "upside down" (by negating the potential) turns the attractive force into a repulsive force, while turning a Schwarzschild embedding upside down (by rotating it) has no effect, since it leaves its intrinsic geometry unchanged. Geodesics following across the Schwarzschild surface would bend toward the central mass like a ball rolling in a gravity well, but for entirely different reasons. There is no analogue of the Schwarzschild embedding for a repulsive field: while such a field can be modeled in general relativity, the spatial geometry cannot be embedded in three dimensions.The Schwarzschild embedding is commonly drawn with a hyperbolic cross section like the potential well, but in fact it has a parabolic cross section which, unlike the gravity well, does not approach a planar asymptote.

You know about gravitational time dilation, and that clocks go slower when they're lower.

JD says:1. You know about gravitational time dilation, and that clocks go slower when they're lower.

4. Curved spacetime isn't curvature of space and curvature of time. It's a curvature in your plot of measurements of motion through space over time. It's a curvature of "the metric", metric being to do with measurement.

Contrary to how JD makes it appear the way he phrased it, all clocks run at the same rate in a gravitational field