Is it true that gravitating bodies actually warp the fabric of space towards them like in this picture? http://www.astronomynotes.com/evolutn/grwarp.gif
That's a nice analogy, but personally I'd be careful with words like "the fabric of space". It is true, that light is bent in the direction of gravitational masses. In fact, if the mass is large enough (or more strictly speaking, the mass density) light can be bent so strongly that its orbit is bent into a circle or even more. In that case you have black hole. Usually, however, the effects are visible near stars. In that case, an object can lie behind a star, like in the lower picture you linked. However, for an observer at the tip of the arrow, the light seems to have originated from somewhere like the far upper corner of the sheet (just draw a tangent line to the last part of the light orbit). This effect has been measured for the sun, as one of the first experimental tests of GR (actually, this effect also exists in Newtonian gravity, but its a factor off which GR gets right) and since it has been seen in action numerous times in so called gravitational lensing, mostly with large clusters and gas clouds.
Thanks but my question is still unanswered. Is space bent towards a gravitating mass? Or does no one know? What did Einstein think? Thanks, Jake
I suggest you take a look at the gravitomagnetic field equations, which are a first-order approximation to GR but good enough to give you an idea of what is going on. The effect is similar to the effect due to a magnetic field caused by a moving charge. "Is space bent towards a mass?" is, I think, a strange question to ask. To properly examine the curvature, you have to take time into account as well. The result of the curvature is that straight lines in space-time appear to be curved toward masses in space.
I appreciate your post. It sounds like I don't need to understand gravitomagnetic field equations. "...straight lines in space-time appear to be curved toward masses..." So the answer to my question seems to be a simple "yes." Right? Thanks, Jake
"...straight lines in space-time appear to be curved toward masses...when isolated in space". You have to take time into account. The fact that space in curved toward something makes little sense to me. The only way to get it right, as far as I know, is to include all four dimensions of space-time.
Ok, gravitating bodies warp spacetime toward them. Is that correct then? What do you mean by "when isolated in space"? Thanks, Jake
well I think 'isolated in space' is means that body of certain mass is alone to be observe or in other words it is alone. You can imagine that it is easy to observe the effect when it is only one who shows some deformation in light's straight line path. prakash0
What I meant is that geodesics, which are the straightest possible paths in space-time, sppear curved in space (i.e. not straight lines in space). What does it mean that something warps spacetime towards it?
If you think about space time as a baloon where the stretchiness of the ballon at a spot on its surface is determined by its mass/energy density, then the surface of the ballon will be dimpled. The rate of time and the spacial dimensions are all determined by the radius of the dimple. Motion across the surface of the baloon means that you will be moving through dimples in space time as well as causing a dimple to propagate over the surface.
Thank your for that idea. It sparked some of my own. I guess it works as a 2D analogy of a closed universe, but it doesn't help jaketodd, since inhabitants on the baloon surface cannot experimentally determine the direction of the curvature (positive if on the outside, negative if on the inside, but this is impossible for the 2-dimensional inhabitants to determine). Nevertheless, the baloon analogy is exellent for demonstrating that asking in what direction spacetime curves is nonsense. We can see that on the balloon, spacetime is embedded in 4 dimensional space (2 spatial dimensions, 1 temporal dimension and a fourth dimension into which spacetime also curves). By analogy we can see that we would need a 5-dimensional space in which to embed our 4-dimensional spacetime for us to be able to ask in which direction spacetime curves, and even then it would be a question of definiton.
I like the ballon analogy because it allows me to visulaize masss/energy density as the thickness of the rubber and also that we are part of space time, were part of the fabric that holds the universe together.
You don't necessarily need a 5th dimension. Imagine, instead of a dimple, spacetime stretched toward a massive object without curving into a 5th dimension. However, the question remains: What force or tendency makes objects go into regions of stretched spacetime?
Objects are like wave packets in space time, where the the medium of oscillation is the energy density. Greater energy density changes the elasticity and causes time to slow down. When the localized energy in a wave packet enters a high energy density region, the rate of energy transmission through space slows down. Accordingly, the wave energy is trapped in the slowed down area of space and since the location of the object is based upon the location of the energetic portion of its wave function, the object goes into the higher energy region of space time.
It is the tendency to move on straight lines in spacetime: http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
That explains why something in motion would follow stretched spacetime or a dimple in spacetime, but it doesn't explain why something starting from rest, relative to a massive object, starts falling toward the massive object.
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html Yes it does: The "falling object" here is initially at rest in space : it advances initially only along the (proper)time dimension. But It starts moving in space towards the massive object ("more stretched spacetime"), just by advancing locally straight in spacetime.
If the "falling object" mirrored the path of the proper time in the graphic, then it would stay at the top of the house.