Cosmological Questions and Their Degenerate Answers

[cosmoboy]

I went to your site, and followed on to your notes. And as I suspected from your comment about any cosmology textbook, the relevant passage includes developing the restricted metrics for various cosmological cases by regarding spacetime as a three dimensional manifold M cross the real line for time : M \times R^1, and then embedding M in four dimensional euclidean space M \subset R^4. This is PURELY NOTATIONAL. You are not intended to conclude that Peebles or any other author is asserting that space is separated from time and embedded in a higher dimensional euclian space like that. The form M \times R^1 is already an idealization of full spacetime for the limited purposes of cosmology, and the rest is just a device for exploring the shape of space within this idealization.

I do not understand what do you mean. I am just saying that at some fixed time one needs a fourth spatial dimension to have (visulaize) the curvature of "space".
Note that time comes in picture when we talk about the dynamics. One can always study the universe at some fixed time.

Most of the people think that curvature "k" which comes in cosmology is the curvature of "space-time". However, this is not trure, this is the curvature of spatial section.

 

[selfAdjoint]

I do not understand what do you mean. I am just saying that at some fixed time one needs a fourth spatial dimension to have (visulaize) the curvature of "space".

For some of us, "have" doesn't equal "visualize". The curvature of spacetime, (yes it curves in the general theory, as shown by, e.g. the Schwartzschild metric where t is nonlinear along with the space coordinates) is no less visualizable than is curvature in R⁴. The GR pseudo-Riemannian curvature is intrinsic and doesn't need an enveloping space.

Note that time comes in picture when we talk about the dynamics. One can always study the universe at some fixed time.

Different observers will orient differently toward spacelike and timelike. There is no one favored way to dissect the local neighborhood into space and time, much less the whole universe. I repeat that the M X R¹ model is an idealization, which is not in any way the full correct state of GR but a useful false model for discussion of limited kinds of things - cosmological things.

Most of the people think that curvature "k" which comes in cosmology is the curvature of "space-time". However, this is not trure, this is the curvature of spatial section.

In this cosmological model, but not in general.

 

[pervect]

So if the fourth dimension isn't time in this case; what is it? I'm just breaking into GR so I haven't even hit special relativity yet.

Sidenote: someone please tell me what a tachyon is?

It may be a bit advanced, but tachons are discussed in the sci.physics.faq in a couple of places. The first is probably more readable, and is about FTL and relativity in general, the second is a little more advanced

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Basically tachyons are hypothetical particles that always travel faster than light. Some interesting mathematical gymnasitics is required to achieve this - tachyons wind up with real energies and momenta, but an imaginary rest mass.