Can someone please explain to me what a friggin geodesic is, in the context of space time structures/diagrams and null-geodesics?
A geodesic is the shortest path between 2 points in spacetime. Here’s a nice link about it. I don’t know what a null geodesic is. Maybe somebody can fill us in on that.
Thanks, I have a partial understanding of what one is.....the shortest distance thing, My problem is when arises when the book i'm trying to read: the nature of space & time, makes reference to maximimum length geodesics and minimum length geodesics between conjugate points in space-time. Hawking is prooving "that the assumption of geodesic completeness, which can be taken as a definition of a non singular spacetime" is false by contradiction. by showing that conjugate points occur in globally hyperbolic spacetime. wouldn't a geodesic be both the minimum AND maximum distance between 2 points in space. maybe i'm on the wrong track I KNOW some of you astro grads know and are just not telling me
I would assume that a null geodesic is a geodesic where the two endpoints are in the same place, or more to the point where there is no distance between them. With respect to bjnorman's minimum/maximum conjecture - there is more than one path between two points. One of them (or possibly a group of them, since space isn't necessarily flat) should be the shortest path, but there are still an infinite set of other paths between two points which are longer than the geodesic. I am also assuming that "the assumption of geodesic completeness" is the assumption that there is a shortest path from any point to any other point in the universe. This may refer to the topology of space/time, that is, whether spacetime is a solid like a sphere, or whether it has a more complex shape like a doughtnut, swiss cheese, or something like that. Even with a doughnut-shaped space/time, you can see how some points would have more than one geodesic (shortest path) between them if they were in the right place. (Of course, this is true of the sphere as well, but with the sphere the only such pairs are those on opposite sides of the sphere, whereas with the doughnut each point has an infinite number of points that have at least two shortest paths to them through the universe.) Please bear in mind that I am shaky in this field; in any case my 2D metaphors for the 3D universe are probably a bit uninformed.
A geodesic is the path which links the shortest spacetime interval for for an object travelling between two points in spacetime. A null geodesic is one for which the interval is zero. Light follows null geodesics. Zero spacetime interval does not mean no distance between the two points, of course, since you also have to take the time difference into account.
Ya, like I said, I'm hardly an expert. I have a question though... How does one seperate "time" (the sequence of events that are a function of the propagation of light) from "time" (the time against which the speed of light is measured)? I've wondered about this for quite a while... how is it that there are two different times? For that matter, if events propagate at the speed of light, how can the speed of light be measured?
Thanks James R & Big Blue, I'll follow those leads.... BigBlue: How does one seperate "time" (the sequence of events that are a function of the propagation of light) from "time" (the time against which the speed of light is measured)? I think the direct answer to your question lies deep in GR somewhere. This may help you though: As far I understand it, if you velocity = C, time is actually measured as a 'distance' not an interval of time as were use to. correct me if i'm wrong though
<i>How does one seperate "time" (the sequence of events that are a function of the propagation of light) from "time" (the time against which the speed of light is measured)?</i> I don't know if I understand your question. I'd say that there is only one kind of time. Events don't propagate, by the way. An event is something which happens at some point in space at some particular time. For example, you sneezing is an event in spacetime. That event doesn't propagate at the speed of light, or at any speed for that matter.
Yeah, but you only witness events once their signature has propagated over to you at the speed of light - if something happens a light year away, it'll take a year for the information to get to you. (Unless you believe in action at a distance, but I didn't think that was proven yet.) As I'd understood it, the reason for time distortion in GR was due to the fact that when you are in a different inertial frame from another person, the path that light takes for you is different from the path it takes for the other person - longer, usually. But light always travels at the same speed for your frame, even though the propagation of events through space happens at the speed of light. How then can the speed of light be measured when speed is a function of time and time is a function of the propagation of light?
what I get from GR is that the time distortion thing is for conserving the universal speed of light thing ex) the difference in the speed of light for different reference frames is explained by changing the rate of change or rate of time for one of the frames to make the speed of light consistent in both.
Yes, that's what I mean by time being a function of the propagation of light. But isn't it just as true in your inertial frame? And if so, then isn't there some uber-time governing the propagation of light, since it's always the same? Even if light merely coincides with the propagation of events, that propagation is still governed by some other time than our regular time, since regular time only exists relative to the propagation of the event. (Or effect or whatever, I'm not sure of the terminology for the effect of an event.)
i dont know, your over my head Please Register or Log in to view the hidden image! I get what your asking i've just never heard anyone ask about the distinction between the propagation of events and C. One interesting thing that comes to my mind about propagation of the effects of an event is...'Wheelers' delayed choice experiment' which is basically a 2-slit experiment on a cosmic scale...He set up 2 telescopes to observe 2 different paths that photons take to get to earth from a distant quasar many light years away. The end result was that the experimental setup on earth decided which path, or both, the photons took to get to earth (eg: interference or no interference) even though the photons were emitted from the quasar years before wheeler decided to do his experiment. I don't know if you'd call this action at a distance but it surely puts a spin on causality as we may imagine it. here's a link http://www.discover.com/june_02/featuniverse.html later
I just saw this thread and would like to continue it unless all bigj's questions have been satisfactorily answered and there's no more interest. the "shortest distance" definition doesnt seem quite adequate at least for a simpleminded example of a 2D surface like surface of the earth---where "geodesic" IIRC just means great circle route then there are two geodesic paths between london and singapore, but only one is the shortest (the other is great circle starting off the wrong way so going the long way round) do we call the one that goes the long way round a geodesic? and if so there must be some way to improve the definition while keeping it intuitive and not overly technical like saying that the other geodesic, even though it is not actually the shortest, is always following the shortest path between two points along the way if they are close enough so that at least locally it is as straight as possible given the circumstances I was just thinking of stretching string around a cylinder and pulling it tight (to have a kind of shortest-distance path and it seems that one can have a fair number of geodesic paths between two points on that 2D surface was also thinking about geodesics on a 2D donut surface it seems like an interesting business to understand (in 4D too!)
