Some questions on the Cosmological Principle

[PeterDonis]

let's talk then about a finite thing growing to infinite.

That does not happen. Please, read more carefully. I explicitly said, several times now, that every spatial slice is infinite. Nothing grows from finite to infinite. It's always infinite.

 

[Buzz Bloom]

Sorry, my mind just doesn't grasp that! :) I can see how that works on the surface of a sphere, which is 2 dimensional, but we live in 3d space. So I can't see how there is another dimension 'expanding' which in turn causes our 3d 'space' to expand and the distance between galaxies grow.

Hi rede96:

I will try a different approach to explaining what I think you are not getting.

First consider the entire 3D universe at a fixed time, so its expansion is not relevant. Then think of a plane, say P, though the point where you are extending in all directions. In a flat infinite universe, P would be an infinite flat plane. If our 3D universe is finite, P really isn't a plane, but locally it almost is. As P extends from where you are as far as it can go, it will be a 2D curved surface of a sphere. Now this may be confusing because the center of this 2D sphere is not in the 3D universe at all. The math does not require that the center be discussed, because the equations related to the properties of the 2D P can be expressed without discussing where the center is. However, it may be conceptually helpful to think of the center of P as being in a direction from you that is outside of the 3D universe, and P is curved as the surface of a sphere in a 4th dimension. Of course, the particular plane P is not special. Any plane in any orientation at any point of the 3D universe would result in the same sized 2D spherical surface, with the same center point in the 4th dimension.

Using the analogy of the 3D curved universe to a 2D surface of a sphere like the (approximate) Earth's surface, if you are at the North pole, the analogy of plane P becomes a line through the North pole which when extended becomes a circle, that is, a circle of longitude. The center of all of these circles is the center of the Earth, which is not a point on the 2D surface.

I hope this is helpful.

Regards,
Buzz

 

[Torbjorn_L]

Thanks for the heads up, I was wondering why it was getting confusing. Found both now.

Been there, (unfortunately) done that. Wasted 30 minutes of productive study time.

Though I recouped it later by studying the differences too. There are some good material that is unique in both. (You don't need to watch both though, either one will do. The later is more up to date on the CMB results if I remember correctly, but that isn't too important.)

 

[Pizza]

That does not happen. Please, read more carefully. I explicitly said, several times now, that every spatial slice is infinite. Nothing grows from finite to infinite. It's always infinite.

Probably I didn't read it careful enough. But I do my best and read it again.

Lets say then there is no singularity (do not like it). Never was etc. That is, what I am talking about. I could imagine, that if something is zero and grows, would end in infinite. Just Imagination. Why should it end in finite? Why should zero should do anything else... (not mathematically of course, in a different manner, more physically)

So - and now - please be carefully - there was never any zero nor singularity, so the bing Bang happens from what? Not out of a singularity, not from zero. From Something. Not from nothing, right? I have some ideas about coming something out of nothing (without Religion), not kidding (discussed in Germany). But the case of the Big Bang, the standard, I've problems to understand? Why?

There is no evidence, that "nothing" "was" before. There is only something, coming out of something else, as I have to assume. According to the readings.Am sure.

 

[PeterDonis]

Lets say then there is no singularity (do not like it).

More precisely: in the idealized model we are talking about, there is no spatial slice labeled $t = 0$ that is of "zero size". All the spatial slices have infinite size. But there are spatial slices labeled by values of $t$ that are arbitrarily close to $0$.

I could imagine, that if something is zero and grows, would end in infinite. Just Imagination. Why should it end in finite?

I don't know what you are trying to say here, but once more: the spatial slices are always infinite. Nothing "grows" from zero to anything; nothing "ends in finite". Those things do not happen in the model.

there was never any zero nor singularity, so the bing Bang happens from what?

The idealized model we are talking about is not believed to apply to the very beginning of the universe; it only applies from the end of inflation forward. The end of inflation, where the universe was filled with matter and energy in a very hot, very dense, rapidly expanding state, is what is properly referred to as the "Big Bang", not the "initial singularity". Before that hot, dense, rapidly expanding state, we don't know for sure what existed; it depends on which version of inflation (or possibly some other model--the inflation models are currently thought to be the most likely, but they are not the only ones under consideration) ends up being confirmed by experiments.

 

[Pizza]

All the spatial slices have infinite size. But there are spatial slices labeled by values of t that are arbitrarily close to 0.

Thank you for your explanations. [Sorry for replying a little late - I had been overwhelmed by the latest events here in Europe eventually. My latest post here more or less a try to come back to everyday life - trying it again now]
I have probably too many difficulties to grasp the concept of the model, which - to make it even worse - starts just after the lynchpin, excluding it.
An infinite slice is no problem for my imagination, because every slice of the Euklidean space is infinite by default. This does not imply that "content" is infinite as well. Like a white paper without any border, hard to draw something "inflation-or-not" literally everywhere...

I have less difficulties with t the time. Time is when something is existent, consequently it can only start with the existence of "content", no matter what before. But how can something (content) grow to infinite isn't answered, in my eyes.

 

[PeterDonis]

This does not imply that "content" is infinite as well.

It does in the case of the universe--there must be, on average, the same density of matter everywhere in the infinite space. A finite region of matter surrounded by emptiness would not look the way our universe looks.

Time is when something is existent, consequently it can only start with the existence of "content", no matter what before.

In terms of models in the context of GR, this is not true; it is perfectly possible, theoretically, to have a universe with a meaningful "time" but empty of "content". Such a model does not match our actual universe, but it is still a consistent model.

how can something (content) grow to infinte

You still don't understand: it was always infinite. Nothing ever "grew" from finite to infinite. That includes "content" as well as "space"; in every infinite spatial slice, there is, on average, the same density of matter everywhere. (The density varies from one spatial slice to another, but it is the same everywhere in each slice.)

 

[Pizza]

Hmm, ok. But still difficult, emptiness with time, by the GR?

A finite region of matter surrounded by emptiness would not look the way our universe looks.

And why not? The principles would maybe allow that observation, or the observations, leading to these principles are maybe still consistent, if the border is, let's say, 100 times farther than the observable universe!?

 

[PeterDonis]

The principles would maybe allow that observation, or the observations, leading to these principles are maybe still consistent, if the border is, let's say, 100 times farther than the observable universe!?

No, they wouldn't. It's not enough to say "maybe"; you have to actually look at the math. In this case, the math is the Einstein Field Equation. A solution of the Einstein Field Equation describing a finite region of matter surrounded by emptiness would not look the way our universe looks, even if the finite region were much larger than our observable universe. That's why we don't use such solutions in cosmology; we use the FRW solutions, because they match observations.

 

[Pizza]

Allright then, will have to have a look on the math. I was not aware of that, that it would look differnt. Have to believe you. Are you sure? Even if it is 10000 times larger, we not sitting in the middle but somewhere far enough from any border?

 

[PeterDonis]

Even if it is 10000 times larger, we not sitting in the middle but somewhere far enough from any border?

Yes. Remember that we can see back 13.7 billion years or so, so we have an entire history of development that any model has to match. It's not just a matter of "well, we can't see an edge".

 

[Pizza]

Remember that we can see back 13.7 billion years or so, so we have an entire history of development that any model has to match.

But this is exactly what did not imply - in my thoughts - that edges are impossible, so may exist. Looking back in time would have the same appearance I imagined.

 

[PeterDonis]

But this is exactly what did not imply - in my thoughts - that edges are impossible, so may exist. Looking back in time would have the same appearance I imagined.

You may have "imagined" it that way, but that is not what the math actually says. "Imagining" is not a good strategy when dealing with this subject area; even cosmologists can have trouble "imagining" the things that the models tell us must be the case in order to match observations.

 

[Pizza]

Lets have a look then, if there are no loopholes in this math in question. For me actually "just" a matter of some (many) years or never. I like math, but am far beyond the necessary skills.
Ahm, I mean for the math itself, to find loopholes probably likely never of course.

Thanks for your patience with a layman.

 

[PeterDonis]

Lets have a look then

Are you familiar with the math of the FRW models? As discussed, for example, in these two Wikipedia articles?

https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric

https://en.wikipedia.org/wiki/Friedmann_equations

And are you familiar with the general class of asymptotically flat solutions to the Einstein Field Equation? ("Asymptotically flat" is GR-speak for "a finite region of matter surrounded by empty space".) See, for example, here:

https://en.wikipedia.org/wiki/Asymptotically_flat_spacetime

 

[Pizza]

No, I just remember that the LCDM model ist the present favorite one. But please, do not ask me what exactly these letters are representing, even if read about it. I even discussed something in German already, but still have problems. You said it: look on the math. That is what I should do, you are right. And your explanations and answers were a good lesson for me today, not kidding, think I understood a little better already, without math. But math is the key, am convinced now.