Question: does the physical curvature of spacetime ever move ?

[Seminole Boy]

Question: does the physical curvature of spacetime ever "move"?

Something isn't adding up with Einstein's theory--or, more likely, I'm just not understanding it correctly!

How can we say that the curvatures of spacetime created by the presence of stress-energy is giving us a continuum? When I think of a continuum, I think of something like a tunnel. But it cannot be so! If all motion is relative, how can we have this tunnel?

Yeah, sure we live and die, so we like to think of the world in time-like ways, but if I'm reading Einstein's theory right, I don't see how we can look at spacetime curvature as anything more than a localized dent in space (that cannot be regarded as being bent in any kind of continued way, like a tunnel).

I'm really hoping the GREAT Peter Donis gets a hold of this question, because I know I'm not asking it perfectly but that he can probably figure out what I'm asking.

Edit: Wait a minute. Have I answered my own question? Is the passage of time the tunnel I'm trying to visualize? Ha! I think I figured it out! The tunnel--or the continuum--is time, right?

 

[Passionflower]

Every single point in spacetime has its own stress-energy or energy-momentum amount (usually expressed in the form of a tensor). With some proportionality constant that is equivalent with a certain amount of positive or negative curvature. There is no motion in spacetime. Motion you get when you take a certain 3D+1 slice of spacetime and all slices are equivalent in Einstein's theory.

 

[Seminole Boy]

PassionFlower:

Please explain your last sentence. What is a 3d+1 slice of spacetime?

 

[Passionflower]

PassionFlower:

Please explain your last sentence. What is a 3d+1 slice of spacetime?

3D+1 means take the three spatial dimensions (e.g. length, width and height) and plot the changes out against time.

 

[Dale]

When I think of a continuum, I think of something that is absolute

That is strange. I don't know where to go from there. I cannot even imaging why you might associate these two completely separate ideas in this way.

 

[Seminole Boy]

DaleSpam:

I wasn't using the right word. I corrected it--or changed it! Absolute was certainly not the right word.

 

[Dale]

When I think of a continuum, I think of something like a tunnel.

That is strange. I don't know where to go from there. I cannot even imaging why you might associate these two completely separate ideas in this way.

http://en.wikipedia.org/wiki/Continuum_(measurement)

A continuum is just something which is continuous rather than discrete. I.e. smooth and not quantized. There is nothing absolute nor tunnel-like implied.