Yes, that is correct. Thank you for pointing that out.

[aib]

Sorry 'bout posting so many topics but there are too many things that are unclear to me.

CMBR measurements suggest the universe is pretty much FLAT, but I don't see it as flat, and forget our planet, all those vast spaces in every spatial dimension - all that is flat? It obviously has depth to it, that's observable, but measurements say otherwise.

Now we all know about cinema, and most of us have been to a 3D cinema, where a flat projection creates a 3D illusion. I know the "projection" universe has very few supporters in the scientific community and is mostly new age conspiracy theorists talk, but if the so called reality is really a projection, wouldn't it make sense for us to observe as a three dimensional and expanding universe, in the case it is not projected on a stationary screen, but more like a event horizon that travels at the speed of light?

 

[Wallace]

When we say 'the Universe is flat' this has a very specific meaning in relation to a particular solution to the equations of General Relativity that we use to describe the Universe. It doesn't mean that the Universe doesn't have depth, or that there is some kind of projection going on. It is confusing I guess because in science words get used with very specific meanings, that can get lost of confused when compared to everyday use.

So, when we say 'the Universe is flat' it means that if you took a 3D 'slice' of our 4D space-time (3 spatial dimension plus time) that this slice will have familiar 'Euclidean' geometry. That means triangles have all angles summing to 180 degrees, parrallel lines never meet etc. We know from measurements that the Universe is close to if not exactly flat by this definition. If it was not flat, then it would mean the geometry of the Universe was in fact different to this, such that is you made a large enough triangle, the angles don't add to 180 degrees (think about drawing a triangle on the curved surface of a ball for instance) and parrallel lines either converge or diverge.

The curvature of the Universe is in any case so slight that even if there was global curvature, you wouldn't notice it on Earth bound laboratories; think about the surface of the Earth, it is curved but so big compared to a Human than you can assume that it is flat and the assumption is good in any local region. Only by observing over vast distances and doing careful calculations can we measure the geometry of the Universe.

 

[sylas]

Sorry 'bout posting so many topics but there are too many things that are unclear to me.

One at a time would be much better. I think some of these should perhaps be locked. But they are common enough as the kinds of thing someone wants to know as they start to learn more about cosmology, so here goes.

CMBR measurements suggest the universe is pretty much FLAT, but I don't see it as flat, and forget our planet, all those vast spaces in every spatial dimension - all that is flat? It obviously has depth to it, that's observable, but measurements say otherwise.

I think the problem here is that you misunderstand what is meant by "flat". Flat means only that space fits a nice ordinary 3 dimensional grid in the way you expect.

A "curved" space is the alternative... and this doesn't mean what you think. In fact, it is hard to even imagine what it might mean. Roughly speaking, in a curved universe, if you make a really enormous triangle in space, connected with straight lines, the angles won't add up to 180 degrees. Seem strange to you? You would not be alone! So I suggest for now you simply stick with thinking "flat" means "just like I am always used to"... because it does.

Your question is not really coherent, because it seems to be based on a misunderstanding from the start. Let's leave it there, and stick to your OTHER questions, in other threads. Okay?

Cheers -- sylas

 

[Chalnoth]

Here is a short attempt an explanation of what is meant by flat. If we have a universe that is uniform on large scales, then its behavior can be described by the following equation:

$$H^2 = \frac{8 \pi G}{3} \rho - \frac{k}{a^2}$$

Here we have three parameters (the $$8 \pi G/3$$ is just a constant). The first parameter, H, is the rate of expansion, which changes with time. The second parameter, $$\rho_m$$, is the average energy density of the universe, which also changes with time. The third parameter, k, sets the spatial curvature. This parameter is a constant, independent of time.

One way we can perhaps more easily understand this equation is to take the case where a=1 (by convention, this is the current time), where we have:
$$H - \frac{8 \pi G}{3} \rho = -k$$

So here we have the current expansion rate, minus the current energy density (in some units) is equal to minus the spatial curvature. If the two are equal, then we get zero curvature, and the universe is flat. This is, in fact, what observations show, to within a precision of about 1% (so far).

 

[Skolon]

What do we know about topology of Universe? Do we have some estimations?

 

[Chalnoth]

What do we know about topology of Universe? Do we have some estimations?

Almost nothing at the present time. We do know that it doesn't wrap back on itself for at least a few Hubble volumes, but that's about it.

 

[Skolon]

Thank you for your answer.

So here we have the current expansion rate, minus the current energy density (in some units) is equal to minus the spatial curvature. If the two are equal, then we get zero curvature, and the universe is flat. This is, in fact, what observations show, to within a precision of about 1% (so far).

I suppose you want to to write "within an error of about 1%" or "a precision of about 99%", don't you?