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#1
Aug2804, 03:25 PM

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How can concentrations of mass (such as the Earth) or energy bend space and time? I mean, is there any theory that states what causes spacetime to be bent by these large masses? Aren't space and time just abstract concepts, so how can they be bend?



#2
Aug2804, 03:41 PM

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To highly oversimplify, Einstein said that Newton's concept of gravity as a force acting over a distance should better be expressed in terms of geometry. Masses curve space, so orbits can be expressed as "paths that best conserve momentum". In a flat space with no massive objects nearby, that path would be a straight line, but in space surrounding a massive object like the sun, the path that best conserves momentum is going to be curved. Not necessarily round, mind you  some periodic comets have very eccentric but stable orbits (at least until they pass too close to another massive body and get perturbed out of them).
In the macro world, Einstein's concept of curved space time has had a stellar record. The biggest question facing it today, is how can it be reconciled with quantum physics (VERY small scales). 


#3
Aug3104, 11:35 PM

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Let's start with something simpler. You're probably familiar with three dimensional Euclidean geometry. This is, of course, an abstract mathematical theory. (Though, it may be employed gainfully to model reality in many circumstances)
In Euclidean geometry, we know how to talk about things "bending"; for example, we can talk about how the surface of a sphere is curved. Mathematically, we can generalize to a higher dimensional space; we could talk about 62dimensional Euclidean geometry, and how a 49dimensional surface might curve and bend in that 62dimensional space. Einstein's realization is that our (apparently) 4dimensional spacetime doesn't look like an example of 4D euclidean geometry; it looks more like an example of a 4D surface in some higher dimensional Euclidean geometry. Alternatively, Einstein realized that, while the universe looks like a 4D Euclidean geometry on "human" scales, it doesn't necessarily look like 4D Euclidean geometry on large scales. (Both of the above ways of looking at it are mathematically equivalent; it's called a "manifold"... though it's a pretty deep theorem that the latter concept can always be viewed as the former concept) 


#4
Sep104, 02:03 AM

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Bending of Space and Time
Pete 


#5
Sep104, 04:56 AM

P: 193

In this context, would i be way off base in comparing spacetime to water with an object floating beneath the surface to represent a concentration of mass...
...the water bends around the object. 


#6
Sep104, 06:43 AM

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As for my use of the geometric model of curvature, let me remind you that I said "to highly oversimplify". When someone phases a question in a manner that leads you to believe that they are asking for a basic explanation of a fundamental concept, it is only fair to GIVE them a basic explanation. That's what I did. 


#7
Sep104, 08:49 AM

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#8
Sep104, 09:18 AM

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Pete 


#9
Sep104, 12:16 PM

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Secondly, when we talk about curved spacetime (the Einstein view of gravitation), we cannot ALSO throw in the Newtonian "force of gravity" as an additional force acting on the Earth. We can model Earth's orbit either with Newtonian gravity (force acting over a distance) or with Einsteinian curved spacetime. Either model alone will yield acceptable results, but we cannot talk about the Earth following a geodesic in spacetime AND ALSO being pulled by the Sun's gravity. That doesn't work. 


#10
Sep104, 12:21 PM

P: 2,828

just confusion between angular and linear momentum. You guys are refering to different (both correct) statements.
As for the interpretation of GR : everybody its own. But it is worth trying to understand Pete's interpretation. 


#11
Sep104, 10:55 PM

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This argument was first advanced by Schild BTW. The 4d parallelogram is formed by two consecutive light rays moving upwards in a gravitational field. The redshift implies that clocks further down in a gravitationall field must be ticking slowly, which means that the lorentz interval (the concept of "distance" first introduced by Special relativity, and used throughout General relativity) is different when measured at the top and bottom of this parallelogram. Since we know that this is impossible in Euclidean geometry, Einstein was led to try nonEuclidean geometry. This result implies that spacetime must be curved, but only in a very weak sense. Nowadays, people usually think of curvedspace time as having a nonzero Riemann tensor. The gravitational redshift argument does NOT actually show that. But it does present an argument that there must be varying metric components in the spacetime geometry. 


#12
Sep104, 11:51 PM

P: 283

I’ve been trying to gain a better understanding of what spacetime actually is, and the rubber sheet analogy seems to be misleading, well at least to me because it implies that there is some sort of medium or fabric, which is being bent.
Einstein’s actual quote "Spacetime does not claim existence in its own right, but only as a structural quality of the [gravitational] field" So if we observe a light source from a distance galaxy passing by a closer cluster of galaxies, we’ll notice that the light from the galaxy behind is bent around the nearer cluster. This of course is gravitational lensing, which is merely gravity bending light. Is this right? 


#13
Sep204, 06:37 PM

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I am not comfortable with the concept of "gravitational lensing"  invoking gravitation as the means by which light rays are refracted and distorted. It posits that gravity (an effect of spacetime distortion) is the cause of lensing (another effect of spacetime distortion). Please check this thread.
http://www.physicsforums.com/showthread.php?t=40705 


#14
Sep204, 09:28 PM

P: 283

Cheers for the linked thread Turbo, very interesting read!
Though I’m still not convinced. What I mean is light rays, which are refracted and distorted by gravity, and the apparent curvature of spacetime seem to be one and the same? Am I missing something here? 


#15
Sep204, 10:05 PM

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Light rays, like matter, follow geodesics in spacetime. Well, actually, this statement is only approximately true  it's almost true, but it's only strictly true when the energy of the piece of matter or the light ray is sufficiently low. Fortunately, this is a good enough approximation for typical applications including gravitational lensing (or planetary orbits, for that matter). The ultimate origin of curvature in spacetime is the stressenergy tensor, T_{ab}, which generates a curvature in spacetime according to Einstein's field equations, G_{ab} = T_{ab}. While G_{ab} is zero in regions where T_{ab} is zero, the general curvature tensor, R_{abcd} is not. More specifically, the Ricci component of R is zero when T_{ab}=0, but the Weyl component of R is nonzero. If this does make you feel better, great. If not, why not  what's missing? 


#16
Sep304, 04:09 AM

P: 599

This sounds like total abracadabra to me, could you please elaborate on your post. Is your question "what is missing mass?" or "what do you think about my explanation for missing mass?"?
I also don't understand why you say gravitationational interaction is instantaneous, when the General theory of relativity predicts it moves with the speed of light (not in contradiction to measurements). Furthermore I don't understand what you mean by saying "To be a tensor, you must have something to pull against". So please enlighten me! 


#17
Sep304, 09:40 AM

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John I'm not going to write out a long reply as I suspect that your posts will be deleted as they are inappropiate, anyway this is what a tensor actually is:
http://en.wikipedia.org/wiki/Tensor 


#18
Sep304, 11:56 AM

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