Chalky
Jan2-09, 06:00 AM
On Jan 1, 12:05 pm, Igor Khavkine <igor...@gmail.com> wrote:
> Before your question can be answered, you have to first fix what you
> mean by "3D space", as different ways to slice 4D space-time into 3D
> space-like surfaces give different notions of "3D space" even for the
> same 4D space-time.
>
> In cosmology, there is a specific way to slice space-time that is
> commonly used. That is, 3D space is defined as slices of of constant
> cosmological time, which measures the proper time counted from the Big
> Bang along world-lines of observers stationary with respect to the
> homogeneous matter-energy background. It is the curvature of these
> spatial slices that is observed to be approximately zero (on scales
> where the homogeneity assumption is warranted).
>
> Now, what you said about "inclusion of time" and "such manifolds",
> does not make a whole lot of sense to me. So, I'll go ahead and guess
> that you are wondering about models that are alternative to standard
> general relativity that still fit cosmological observations. Sound
> about right?
Yes.
> Well, it's never possible to exclude all alternatives,
> but to date general relativity and homogeneous cosmological models fit
> observations better than other proposals, which do not include either
> relativity or homogeneity as assumptions.
This approach is relativistic, but pregeometric, and not published (to
date), being developed from ch.44 of MTW.
As for homogeneity, yes, this seems to be a vital assumption on the
large scale.
On the smaller scale, this could be debatable.
> Unfortunately, it's not
> clear what specific kinds of alternatives you are interested in.
> Perhaps you can be more specific.
Bit tricky, as unpublished, but hopefully the above will suffice for
now.
> Then you might get a more specific
> answer then.
This discussion is already progressing fruitfully, afaiac, helping me
to clarify a few things at the interface between geometry and (my
> Before your question can be answered, you have to first fix what you
> mean by "3D space", as different ways to slice 4D space-time into 3D
> space-like surfaces give different notions of "3D space" even for the
> same 4D space-time.
>
> In cosmology, there is a specific way to slice space-time that is
> commonly used. That is, 3D space is defined as slices of of constant
> cosmological time, which measures the proper time counted from the Big
> Bang along world-lines of observers stationary with respect to the
> homogeneous matter-energy background. It is the curvature of these
> spatial slices that is observed to be approximately zero (on scales
> where the homogeneity assumption is warranted).
>
> Now, what you said about "inclusion of time" and "such manifolds",
> does not make a whole lot of sense to me. So, I'll go ahead and guess
> that you are wondering about models that are alternative to standard
> general relativity that still fit cosmological observations. Sound
> about right?
Yes.
> Well, it's never possible to exclude all alternatives,
> but to date general relativity and homogeneous cosmological models fit
> observations better than other proposals, which do not include either
> relativity or homogeneity as assumptions.
This approach is relativistic, but pregeometric, and not published (to
date), being developed from ch.44 of MTW.
As for homogeneity, yes, this seems to be a vital assumption on the
large scale.
On the smaller scale, this could be debatable.
> Unfortunately, it's not
> clear what specific kinds of alternatives you are interested in.
> Perhaps you can be more specific.
Bit tricky, as unpublished, but hopefully the above will suffice for
now.
> Then you might get a more specific
> answer then.
This discussion is already progressing fruitfully, afaiac, helping me
to clarify a few things at the interface between geometry and (my