General Relativity.

Since so many topics have come up concerning the theory, perhaps a thread where people can ask questions and discuss the theory in its own right would be a decent addition.Anything from orbits to Wormholes, with actually decent, "non-pop science" answers.

In order to make this thread we need an opening question that touches a debatable point inside the theory. Try asking one of those "popular" questions and provide the answer. That will satisfy me to ge this thread going.Edited for grammarThis message has been edited by AdminJazzlover, 09-13-2005 08:24 PM

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"...science without religion is lame; religion without science is blind." Albert Einstein

What is General Relativity?
What did Einstein mean when he said spacetime is curved and how does this relate to gravity?
What is the Big Bang and what does it say of the origin of the universe?
How do Wormholes and Black holes work?Questions of this kind are often asked concerning Einstein's theory and answers in the media range from poor to nearly adequate.
Very often the subject is either dumbed down to a ludicrous degree or an off hand joke is made about how it is abstract and "detached from reality".How do you guys perceive the theory and does anybody have a question concerning its content and what it attempts to say about our universe?(I'm aiming for this to be a general "questions and criticisms" thread, so all comments concerning the theory are welcome.)

Thread moved here from the Proposed New Topics forum.

What is the exact relation between Special Relativity and General Relativity?Is it just that in SR spacetime isn't curved? As in, two straight lines through spacetime (constant speed and direction) view each other as inertial, yet in GR two inertial frames can be viewed as relatively accelerating from each others frames, which is a prediction of spacetime curvature?Also, does spacetime curvature just mean non-Euclidean geometry? In this way, it's not necessary to view spacetime curving into other dimensions as we see in the analogies involving two dimensions?

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Is it just that in SR spacetime isn't curved?

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In the context of Relativity that is exactly how they are related.

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Also, does spacetime curvature just mean non-Euclidean geometry? In this way, it's not necessary to view spacetime curving into other dimensions as we see in the analogies involving two dimensions?

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Yes, spacetime isn't "sitting" in something else.
The curvature refers to its own geometry without any reference to something external.

Here's another one I don't quite understand. How does time dilation, length contraction, and relativistic mass fit into general relativity?In other words, how does the time dilation that is caused by a gravitational field relate to time dilation between relative observers with different velocities?I can understand these phenomena based on Lorentz transformations and the fact that they are analogous to "rotations" in spacetime, so at different velocities observers are witnessing different "angles" of each other. But how do I interpret these effects caused by a gravitational field?

Great question Time to introduce the light-cone. I'm busy so read this very short overview: Light cone - WikipediaIn SR, you can change inertial frame and the insides of the cone will slew around, i.e. that vertical time-line will tilt anywhere within the cone. BUT, the cone remains fixed. There is a light-cone at every point in space-time an they are all perfectly aligned.In GR, curvature of space-time causes the light-cones to tilt, so that they are no longer aligned. Your world-line, if you do not accelerate, will simply follow a winding path of sequential light-cones, tracking their tilt as you move through time. So what we call gravitational attraction is simply following your light-cones... or more simply, just following time To not follow your light-cone, you must accelerate. But of course the best you can do is to accelerate towards c, i.e. the edge of your light-cone. You cannot tip beyond the edge of the cone...You are now effectively moving wrt your light-cone. You have also accelerated to get there, and if you think about this in SR-terms, you are going to experience a real time-dilation. It is quite possible that you are not now moving wrt a distance observer. But you are still moving wrt to your light-cone. E.g. stood on the earth, where you light-cone is pointing inwards towards the centre of the earth (actually, slighlty to the side becasue of the rotation) Thus you would expect to see a real time-dilation wrt someone who isn't fighting their light-cone so hard.Now imagine where your light-cone is tipped through 45 degrees, so that one edge is pointing in the time-direction. Unless you can move at c, you are going to be herded in the direction of the light-cone... no choice! The interior of the upper half of your light-cone is your future. If all of the light-cones on a sphere are tipped at 45 degrees inwards, you have a potential event horizon. This is what happens around a black-hole and is why you cannot escape. Your future lies within the event horizon. Inside the horizon, it gets worse. Now the light-cones are all pointing inwards towards the singularity. The singularity no longer exists in a spatial direction, but in your future!!! This is why you cannot avoid the singularity. Can you avoid tomorrow?Back to the event horizon. Remember I said that the light cones are tipped at 45 degrees. So their vertical edges make up the surface of the horizon. But the edge of a light-cone is a light-ray by definition. So the horizon is actually a surface of light rays, and therefore must be moving at the speed of light... wrt the light cone. We call it a null surface, in the same way we call a light-ray a null-path. If you hang just outside a black hole, you are effectively travelling at c. You would expect to see massive time dilation when you move back away from the black hole, and this is exactly what happens.Around a rotating object, the light cones don't just tip inwards, but sideways as well. This is what we call frame-dragging, but it is just your time-line being spiralled around the object (planet, star, black hole). Of course, your light-cone can tip so far sideways that you cannot prevent yourself from spinning without exceeding c. This generates a static-limit and marks the boundary of the ergosphere.How's that for now? Wish you hadn't asked?

In my effort to understand general relativity, I have pondered the attributes of space as is required. I have tried to build a model of understanding that is consistent with what I understand regarding other things, and I am sure this is how most understanding comes about. Most analogies of this curvature are done so as a two dimensional representation as opposed to a three dimensional one due to the difficulty in visualizing a 3-D model. This bothers me to the point at which I feel that since the space we are familiar with is three dimensional, then we should be able to visualize this three dimensional curvature. The only analogy that I can use to make sense of this is to ascribe a “density” to space, and therefore an increase or decrease in “density” for space that is curved. This leaves me wondering with respect to what is this “density” increasing or decreasing?I come about with this idea because one idea calculus reveals to me is that the slope, or curvature, of one “thing” is dependent upon the instantaneous value of another, wholly independent, absolute “thing”. The curvature of space depends upon your location in space relative to a gravitational field. I see the curvature of three dimensional space as being the increased or decreased density of volumes of conventional spatial units (call them Planck lengths) per “something”. Is the “something” I am referring to a gravitational field itself (I wouldn’t think so considering the magnitude of a gravitational field varies according to your location in space and not absolute as my definition requires)? Is matter compressing “empty space” as it occupies this region of “something” and therefore “compressing” “empty space” relative to this “something”? If not, then where is matter located? Does it make sense to ask what is inside an electron or a quark, and if there isn’t anything (or if there is no "inside"), then where is the space that it “occupies”, or does the space simply become part of the matter? Is this “something” an entity separate from space and subsequently an absolute property of the universe with respect to which all things can be considered?Is this a correct line of thinking considering, as I understand it, there really is no sense in ascribing density to something such as space since it is merely a void? After all, how do you have more of a void in one location? How do you have more units of “space” per unit space, hence my calling the latter “something” instead of space? Perhaps I have completely missed something in my attempt to understand these things, thus the immense confusion, or perhaps this is why a three dimensional model is never used as an aide in understanding.

Nothing feeble here. Some very astute points and some very deep questions. Good stuff! I will get back to this as time allows... or maybe SG will show up and actually put some work in

That was actually kindof illuminating. Through I'm having a trouble seeing how you are moving wrt your light cone when you accelerate. Do you mean that you are moving with regard to the axis of your light cone?This message has been edited by JustinC, 09-16-2005 06:55 PM

Exactly. The axis of the light cone is the path you will follow as long as you don't accelerate. By accelerating, you can move your path so that it points anywhere within the forward cone.

One last question that may clear things up for me. In GR, is there a distinction between "real" acceleration and apparent acceleration. Because I know that if two observers are following intertial trajectories in curvered spacetime they will view each other as relatively accelerating, but is this relative acceleration different than the acceleration in the light cone you are referring to?

Yes there is a distinction, otherwise all of this would be meaningless. But all you ever know is what you are doing, not what someone else is doing. You know if you are experiencing force, or if you are "weight-less". If you are weight-less, you are following your light-cone, following your geodesic through space-time. If you feel a force, you are accelerating, fighting your light-cone, deviating from your geodesic.It is as simple as that. This is what gave rise to GR in the first place. Einstein considered a person in an elevator. He asked if the preson could tell the difference between the elevator being sat on the ground, or it being accelerated at 1g through free-space. He realised that in both cases, you are simply accalerating against your light-cone.

Phew, that's a lot of thoughts Rather than talk to your points, which can get confusing, I will give a brief overview to explain both your ideas and your confusion.There is no gravitational field... there is no gravity. To simplify things, I will take your view and talk about space rather than space-time.Objects move along straight lines in space, just like good old Newton I: an object will remain in a state of constant velocity unless acted upon by an external force.If space is curved, objects will appear to be deflected from straight lines, but in reality they are just following the "straighest" line on a curved surface, like a plane following a "great circle" as it transits the world. An orbit is actually a straight line!For space to be curved, there must be something that describes how curved it is at each point in space. We call this the "metric" or metric-field. The metric is sometime described as the gravitational field, but this is confusing and incorrect. It is best not to think of gravity at all when looking at this. You are bang-on when you talk about a density of space, becasue this is what the metric measures. It gives the distance between two infinitesimally close points, and from this distance-element, you can construct a volume-element which is your density.Considering the distance-element to be based on the planck length is racing beyond General Relativity into Qunatum Gravity, so I will simply ask you to slow down a bit! But you are talking about precisely the right things if you wish to pursue that avenue once you have mastered your GR...Mass curves space. Matter has mass, so matter curves space. Curved space itself has mass. So curved space can curve space... how cool is that! But what is matter? Well, the clue is in this paragraph. What do we know that already curves space? Curved space! So matter is actually curved space... very tightly woven, highly curved space!I wish it were that simple, but this cannot be true in basic General Relatvity. However, when we expand to something like supergravity or string theory, we regain this wonderful picture that space and matter are the same thing.Now, we have been talking about all of this while ignoing time. Just add time back in to your space, so you now have space-time. It's exactly the same, only now your density is a 4d density.Digest the above and come back with your next set of musings and questions