Curvature of Space: Explaining Gravitational Forces

[Marcshall]

Hi!

A google search for my upcomming question lead me to this page, and I am delighted to find an online community of psysics who hopefully will answer my, maybe, very simpel question. In the study of Einstein's General Relativity theory, the picture of a sphere placed in a net representing spacetime is shown again and again (do a http://www.google.dk/images?q=curva...source=og&sa=N&hl=da&tab=wi&biw=1920&bih=965" of the titel of this post and you will see what I mean). While I do get the idea and think I've come to term and understand how this works and function, I just can't understand why the sphere's "bottom" is being pictured as the gravitational agent. Somehow my logic tells me that what should be "pulling down" the net should be the center of gravity inside the sphere, so that when picturing the curvature, the spacetime should penetrate the spheres. This actually also gives an illustration of how mutual gravity would work between two identical bodies, who would circle a gravital center in between the two.

Am I the one being far off or are the illustration just that, illustrations made to give an idea of the concept?

Thanks in advance and sorry for the possible inconvience of English not being my native language.

/Marc

 

[JesseM]

You're right that the illustration is a little misleading, although I don't know what you mean when you say the spacetime should "penetrate the spheres". The reason I'd say it's misleading is that we think that an object falls "down" into a well due to gravity but in fact the orientation is totally irrelevant, you could just as easily reorient the surface depicted in that diagram so that the gravity well became a bump pointing upwards in an otherwise flat surface--all the diagram is meant to do is show the geometry of space, meaning it correctly represents the lengths of different possible spacelikecurves at a single moment in time in some coordinate system (see [post=3143563]this post[/post] for more details on these 'embedding diagrams' which show the curvature of space at a single moment).

But to understand why objects move as they do in the presence of gravity, you really have to understand the curvature of spacetime, not just the curvature of space alone, since the general rule is that objects follow paths through spacetime (timelike curves, or lightlike curves in the case of massless particles--see the discussion here of timelike vs. lightlike vs. spacelike) which are geodesics in curved spacetime. On curved spatial surfaces, the notion of a "geodesic" is fairly intuitive, it just means the shortest path between two points on the surface, the closest thing to a "straight line" on that surface, like on a sphere the shortest distance between two points would be a segment of a great circle that crosses through both points. Geodesics in curved spacetime are harder to visualize, instead of minimizing the distance, timelike geodesics are instead local maxima of a quantity called proper time (time as measured by a clock which travels on that path through spacetime). For some attempt to visualize curved spacetime in diagrams, and show what geodesics on these diagrams look like, you could try these pages:

http://www.relativitet.se/spacetime1.html
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.adamtoons.de/physics/gravitation.swf

I found these posted by A.T. on this thread which has more discussion of the misleading aspects of the standard "rubber sheet" visualization of the effects of gravity which you discussed.