
#19
Feb913, 11:38 AM

P: 207

Still, even being exactly flat leaves the global structure of the universe, it's topology, open. In case the universe has a compact topology, e.g. a 3torus which is flat locally, then it's size is finite. Some date indicate this possibility. If it's nearly flat, we know less. 



#20
Feb913, 11:56 AM

Astronomy
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Hi John, I'm more of a cosmologywatcher than a participant. I follow developments as best I can, and love the subject. This is my personal perspective. To answer the part I highlighted in blue I would say that cosmology is a mathematical science i.e. it aims at the simplest bestfit mathematical model. And GR is our law of gravity and our law of geometry (why triangles add up to approximately but not exactly 180 and how matter affects this) that we base the cosmic model on.
Someday GR will be improved but for now it is the accepted dynamics of geometry that has been tested repeatedly in many ways and passed all the tests and has proven remarkably accurate. So the key thing to realize is that cosmology is an APPLICATION of the accepted law of gravity/geometry. The aim is not merely an ad hoc model that fits the observational data it is to find the simplest bestfit model which is a solution of the GR equation. The simplest bestfit model which accords with the currently accepted dynamics of geometry and matter. But I don't think that one can MODEL that situation with a SOLUTION OF THE GR equation. A region of nonexistence is not a feature of our currently accepted dynamics of geometry and matter, which we are pretty much stuck on using as the best available so far. Now to respond to the blue highlight paragraph. I think the assumption of approximate uniformity is a reasonable working assumption because 1) it is simple 2) so far no evidence to the contrary has withstood scrutiny People regularly review this assumption to see how it is holding up, and people challenge it now and then. It is a serviceable working assumption, I would not think of it as an article of faith. As long as the model continues to fit the data people will keep on using ituntil something better shows up. 



#21
Feb913, 11:59 AM

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Hi Naty, in post #18 it sounded as if you were quoting me but I think you were actually quoting John, so i was a bit confused and didn't see how to respond.




#22
Feb913, 04:21 PM

P: 96

However, in the part of your reply quoted above, you are being too generous towards my logic! My thought experiment of sending a rocket in the opposite direction to all of the known universe does not involve going through a boundary into nothingness. That's impossible. The rocket is part of the universe and is enlarging it. This is my way of illustrating how the universe could have a boundary. The universe does not need any space to expand into, it creates its own space by expanding. This is what you told me already, so I am sure you agree. With my thought experiment I am merely wanting to show that it's possible to be at the boundary of the universe without implying that there is anything beyond. So far I have read everywhere that the universe does not have a boundary. So if my experiment is possible, then it can have a boundary. . 



#23
Feb1013, 08:44 AM

P: 5,634

Marcus:
Relax and enjoy; Bask in the glory!! [LOL] 



#24
Feb1013, 12:00 PM

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Thanks for the compliment, Naty! What puzzled me in your post #18 was that it looked like you were quoting me, saying "it seems speculative" when the words in quotes were actually from somebody else. I knew I had not said what you had me down as saying, so I went back looking for those words and found they were from Johninch.
======= Johninch: ...... I am not so sure as Johninch about the last sentence... ======= What you were saying made a lot of sense, you just had the people's names confused. I see now how I should have responded. 



#25
Feb1013, 12:19 PM

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I wouldn't call the cosmological principle (the basic uniformity assumption) speculation, exactly. It think it comes under the heading of Occam's Razorthe idea is that in a mathematical science you should use the SIMPLEST model that fits.
You keep the model simple until you actually get evidence that you need to make it more complicated. And you keep watching out for such evidence! I would call it speculative to start imagining some boundary off somewhere too far away for us to see, when we have no indication of a boundary. Some day we might, but we haven't yet seen any suggestion of one that withstood scrutiny. I would likewise call it speculative to start assuming there is a center of the universe far away in some direction (but we just don't know in what direction to point in :) Those would be unnecessary complications for which there is no justification. But we should always keep an eye out for any asymmetries in the statistics that might suggest NONuniformity. And people do watch for that, and periodically sound the alert. What I've seen happen is that the alleged evidence is carefully examinedand so far has been found wanting, and dismissed. 



#26
Feb1013, 01:41 PM

P: 5,634

Marcus
Just be glad I threw the compliment at the correct person!! 



#27
Feb1613, 08:34 AM

P: 96

Thanks everybody for your help on my questions. In the meantime I have been reading more about the cosmological principle, which doesn’t allow a boundary to the universe. Therefore my example of half the sky not containing anything is simply false. Why this cosmological principle has to be true, I don’t understand yet, but I accept it as current theory.
To conclude, could somebody give me definitive answers to the following questions (please note that I am talking about the total universe and not just the observable universe): 1) Does the cosmological principle imply that the universe is infinite? This seems to follow from it not having any boundary. Why then do I read about the universe having dimensions like radius and a certain number of galaxies outside of the observable portion? 2) How do I get from the finite BB event to an infinite universe? How can the universe expand when it is already infinite and boundless? I already know that expansion means distances increasing. Perhaps it has to be explained to me what infinite means. Please note too, that a) I never suggested that the universe had or has a center, b) I never suggested that my imagined boundary could be crossed and c) I always understood that the universe could double back on itself, so that there would be no boundary in certain directions. I am really not wanting to challenge the cosmological principle, I just want to understand what current theory is saying. . 



#28
Feb1613, 08:49 AM

P: 5,634

Best bet is to read here about the cosmological principle: This might be a good time to reread the posts above as Chronos,for one, already answered the question about the 'size of the universe': It does take a while to absorb such information and to then try to put the pieces together..... 



#29
Feb1613, 10:00 AM

P: 96

My question: Does the cosmological principle imply that the universe is infinite?
Your answer: Well then, in whichever direction and however far I travel, I will see more of the same. What’s the difference between that and infinity? My question: How do I get from the finite BB event to an infinite universe? Your answer: Basically we are stuck on the point, whether BBT is compatible with an infinite universe. My reading is that it is not. If I am right that the universe must be finite, I want to understand why it is not possible to stand somewhere and look in some direction and see few or no galaxies. We don’t have to call it a boundary or edge if that jars. . 



#30
Feb1613, 10:45 AM

P: 5,634





#31
Feb1613, 10:56 AM

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It is the easiest thing in the world for a spatially finite universe to satisfy homogeneity. To make it simple imagine that space is onedimensional, with one dimensional galaxies, and the 1D creatures find that if they travel long enough and far enough in one of the two possible directions they find themselves back where they started. (They discover they live in a finite 1D space with "ring" geometry.) And then think of the analogous thing in 2D. Space is 2D with 2D galaxies scattered about, and the 2D creatures discover (by exploring and measuring triangles and stuff) that they live in a finite "balloon surface" geometry. You can't take geometry for granted, you can't assume it is standard Greek Euclidean, you have to find out empirically, by measuring, what the geometry you live in really is. Cosmology is the business of finding out the largescale geometry. Just like the 1D and 2D creatures had to do in the examples. Now think of the analogous thing in 3D. Imagine space is 3D with 3D galaxies scattered about more or less homogeneously. And suppose we 3D creatures start measuring very large scale triangles to find if there is a very slight deviation from 180 degrees. If there is a consistent pattern of getting very slightly MORE than 180, this will indicate that we live in a finite 3D analog of the "balloon surface" geometry. So far the measurements have not been conclusive but there are some recent measurements that lean in the direction of that kind of spatial finiteness. Maybe you should click on the "balloon" link I keep in my signature, and watch the movie a few times. Think about the experience of being in one of those 2D galaxies you see in the movie, with the other galaxies receding from it. finite volume, but no boundary anywhere. 



#32
Feb1813, 10:06 AM

P: 96

You have to see that these pictorial illustrations are doomed to failure, because you can't draw a finite universe without boundaries. It's impossible  you may come to the edge of the paper or let the ink fade out, or draw anykind of complex geometrical shape but you can't demonstrate absence of a boundary with an illustration. And if it can't be shown on paper, this is an indication of the problem. The oft repeated analogy of the balloon's surface is not translatable to 3D in my mind. I also want to emphasize that I came off the idea of a crossable boundary some time back. I hope I made it clear that I am only imagining lack of galaxies and other observables from a vantage point within the universe. The problem of the word boundary is that it implies something on the other side and that is not what I mean. In the meantime I have done more searching and have found a couple of very interesting threads in this forum on this very subject in 2006 and 2007. I have the impression that several posters treating the subject of BBT, expansion, finite/infinite universe, boundary, and so on from a logical point of view were not satisfied before those threads were locked. I thank everybody for their efforts and I will for sure keep my eyes open for further insights into BBT. As far as I am concerned, the thread can be closed. "Locked" is so agressive! . 



#33
Feb1813, 10:54 AM

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There is no "inside" or "outside" to the sphere. You have to concentrate in order to get the help from the analogy. You as a 3D creature cannot point your finger in a 4th spatial direction. In fact we may live in a 3D analog of the 2D sphere. But so far we have no evidence of any "inside" or "outside" or any boundary. No more would 2D creatures living in a universe in which all of existence was concentrated on that animated sphere. About locking this thread, I am not a moderator or mentor, so I don't decide about those things. Personally I see no reason to lock. If you are dissatisfied or bored you can always drop out. But at this point it's possible someone else might be reading and have questions or comments they want to make. I'm happy with the thread so I think I will hang around a while longer, and see. Plus you might conceivably change your mind and want to discuss some more. Who knows? 



#34
Feb1813, 11:52 AM

P: 5,634

Johnich
I think I already posted about the fact that each day we receive new CMBR...and it's like yesterdays. No surprises there. Each additional bit looks like the prior homogeneity with small fluctuations.... There may in fact be a 'lack of galaxies' out, say 100 times or 1,000 or 10,000 times further than we can observe today. Nobody can prove that one way or another. But then you should have some reason for such a hypothesis. I can't think of any, we have no such model, but such things don't make it impossible. It's fun to speculate, to do thought experiments, and then see if they 'pan out' or not. Or whether you can even justify a thought one way or another. The great Richard Feynman noted something to the effect that 'a successful physicist succeeds by making just about every imaginable mistake before arriving at a correct solution.' [I don't mind being shown to be wrong here; I am used to it because my wife does it every day!!] 



#35
Feb1813, 12:13 PM

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I don't think anyone has a wife that doesn'l lol. Trying to describe outside the universe is like trying to describe non existence. As many are pointing out.




#36
Feb1813, 02:52 PM

P: 5,634

In my next life I'd like to be right all the time...like my wife in this life!!



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