Okay, so people say the universe is expanding like a 3 dimensional balloon. Now in the 2 dimensional balloon representation, it is curved so you will eventually end up in the same spot if you went in a "straight line" across its surface, like a planet. People also say that the universe most likely isn't curved in on itself via the 4th dimension. Now i seriously doubt that our milky way just happens to be in the "middle" of the universe so when we see the Hubble deep field and all of those distant galaxies, I'm willing to bet that if we were in one of those distant galaxies, we too would see other galaxies all around us with a new cosmic horizon surpassing our current one in the milky way, right? Which means that the universe is either curved in on itself or infinite, right?
Imagination is a funny thing... If I imagine that I could "see" far enough through the universe that I could see myself (the back of my head), then I would be seeing the back of my head from a very long time ago that it took the photons to make one lap around the whole universe. And in any direction I chose to look, I would see the back of my head from a long time ago. So I would seem to be in the center of a large sphere whose inner surface was all the back of my head. If I could see further (as if my head was transparent), there would be another larger sphere of the back of my head corresponding to the light that had made two laps around the whole universe. This subsequent sphere or shell would be from a longer time ago. These shells continue indefinitely, but since the size of the universe is increasing in time, and since these further shells represent older views of the back of my head (and older shorter laps around the universe), the distance between the shell surfaces gets smaller as subsequent shells are further added. I suppose this would mean that as your view passed through more and more shells, the subsequent shell spacings decrease to a limit and ultimately you find a convergence on a very large shell limit boundary that corresponds to the time of the big bang. So, one will always be "in the middle" of the universe... :)
First, it is unknown whether or not the universe is curved or not. It may be infinite in size without curving back on itself or it may be closed and boundless, meaning it does curve back on itself. We simply don't know. Perhaps a better way to imagine it is if you imagine you are baking cookies or bread or muffines. As they bake and rise everything inside is expanding away from everything else. Just take this analogy to the next level and imagine the dough extends outward in all directions to infinity. As we bake we move away from everything else.
My imagination experiment only assumes the universe is expanding.... Doesn't the photon lap around the universe shell's eventual convergence to a limit suggest finite and bound?
It would if we had any observations that showed this was happening. We have never seen a photon lap around the universe. Current measurements of the CMB and other things suggest that the cuvature of the universe is VERY close to 1, but the error bar is still too high in both directions to know for sure.
In the past. I've had my fair share of misconception due to fact that i had insufficient understanding of the basic mechanics. And Often leads to added and future confusion. (Thanks to the members effort in providing us proper guides and reads). (Luckily i am exposed to working in 3d space manily effects on particle and dynamics (limitations of software program)). I had the advantage of imagining them in analogic 3D and the rest is just understanding the math and the mechanics. Anyways.. First. Its is important to understand the model and construct certain limitations and boundaries on your personal analogical components (closest comparative material/subject you can think of) in accordance to model's mechanics when doing such thought experiment. (Ex: Limitation/s of dough - representation of space Or restrictions and boundaries of the raisin - representation of galaxies and so on). Well, It can somehow avoid confusion and misconception as you go forward. http://www.astro.ucla.edu/~wright/Balloon2.html http://www.astro.ucla.edu/~wright/balloon0.html http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
The universe is a big place, so big it appears unlikely any photon has had time to complete one lap. Cosmologists have long searched for 'circles in the sky' as a clue to the size of the universe. The most well known of these studies is probably by Cornish, Spergel and Starkman in 1998, http://arxiv.org/abs/astro-ph/9801212 - Circles in the Sky: Finding Topology with the Microwave Background Radiation. The finite speed of light also plays tricks on you when you try to imagine how the universe looks to an observer in a far off galaxy. For a galaxy say 2 billion light years distant, their universe currently looks exactly like ours - about 13.7 billion years old and homogenously filled with galaxies. But, their universe, as viewed from that same galaxy as it was when the photons we presently observe were emitted, is only 11.7 billion years old and appears hotter and denser than it currently does to us. A galaxy 2 billion light years distant appears as it did 2 billion years ago. As a consequence, it is not currently where it appears to be in our present sky. Which raises another question: How would you know a photon has circumnavigated the universe? By the time it returned to its point of origin, nothing would be in the same place, nor look the same as it did when it departed on its epic voyage.
You are right, of course; imagining things needs to avoid taking too many liberties with the time and space mechanics. I sympathize with the op. When I first tried to combine the concept of an expanding universe with the common statement that the universe "looks the same everywhere" it seemed impossible. If what we see now further and further away is from progressively older times from the past, and if the universe is expanding, then it seems that those older parts should be from a "smaller" or denser period of the universe. If these older parts "look the same" now as the present local parts around us, this would lead to thinking that in order for those older distant parts to look "the same" to us now as the local present region, then those parts must have been much bigger back then (and bigger "now" than we are "now" locally). In other words, the "looks the same" observation would imply that the distant older parts must have had to "look the same" back when they emitted the light, so that compared to what we observe locally it would match... but that makes it seem like the universe must be contracting! So basically, the "looks the same" observation does not seem to work in an expanding universe with a finite light speed. If all present regions of the universe are "really the same", then each should be observing distant parts as being more dense; likewise, in order for all parts to observe a uniformity, then taking the finite speed of light as delaying these observations would mean that the uniformity is an illusion and the delay just happens to match the difference in density change. This bothered me no end because every reading mentions this observed uniformity, and mentions the delayed nature of the observation, but I never found where these two concepts were put together to show a conflict, nor any attempts to resolve it. I was able to satisfy myself with a "solution" by drawing a series of 2-d "movie frames" of an expanding universe and plotting the course of two light rays from two proximate points converging on a distant third point. My interpretation is that the light rays are traveling through expanding space so that their paths curve away from each other as they progress. It appears to me that things balance out so that the observed uniformity must always be the case, even if the universe was contracting, the effect would work as the rays curved in toward each other, maintaining the observation of uniformity. It looks like the paths of light rays changing their relative angle as they move through an expanding space will always meet the observer so as to make the distant part of space "look the same" as that of the local observer. Another way of looking at the rays is that the rays that "originally" pointed geometrically to the target are not the ones that make it to the target. The expansion of space makes it so the rays that ultimately find their way to the target were directed "inside" at an angle that would converge far too close before reaching the target, like a short focal length. But the subsequent expansion of space places the target at that focal length so that the angle "opens" to match the observation of uniformity... The expansion of space makes the apparent path of the rays as inferred from the target not correspond to the actual rays' curved paths geometrically through the expanding space... If someone knows the name of this idea (aberration?), I'd like to know that. If I have convinced myself of a wrong idea, I'd like to know that, too; and what the correct account might be. :)
So going along with the cookie analogy, i get that everything is expanding away from everything else, but what about the part of the cookie on the very edge. Like the galaxy on the very edge of our horizon. If i were in one of those, i would see other galaxies all around me (as we established). But will that distant galaxy's visible universe consist if the same galaxies that make up our visible universe in the milky way?
No, because if you were instantaneously transported to a distant galaxy, it will have aged by the light travel time between that galaxy and our galaxy. And the milky way would appear younger by the same amount as viewed from that galaxy.
If you assume that the universe is homogeneous and isotropic, this puts a big constraint on the shape of the universe. In this case, the universe with positive curvature (like a balloon) is finite, and a flat or negatively curved (like a kale leaf) universe is infinite. If you don't assume those things, you can have finite flat space such as a 3 torus or a finite volume hyperbolic space (Picard horn) or all sorts of wacky shapes. The popular balloon picture for the universe is bad because we don't have any evidence that the universe is finite or ball shaped.
I think you are right. People often say the universe is nearly flat or approximately flat. They shouldn't say "exactly" because we don't know that. Space could be very slightly positive curved and finite---or it could be perfectly flat and infinite (and there are other possibilities). We don't know. The key thing is the measurements people have been making of the "mean curvature". I'll fetch the most recent data I've seen. That's kind of a flat statement we don't have any? There is evidence concerning the mean curvature. It is not conclusive, but to me it suggests the possibility of a very slight positive mean curvature. recent cosmology parameters: http://arxiv.org/abs/1212.5226 Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, J. Dunkley, M. R. Nolta, M. Halpern, R. S. Hill, N. Odegard, L. Page, K. M. Smith, J. L. Weiland, B. Gold, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, G. S. Tucker, E. Wollack, E. L. Wright (see table 9, page 19---from WMAP+eCMB+BAO+H_{0}) Ω_{k} = −0.0027^{+0.0039}_{−0.0038} Ω_{tot} = 1.0027^{+0.0038}_{−0.0039} http://arxiv.org/abs/1210.7231 A Measurement of the Cosmic Microwave Background Damping Tail from the 2500-square-degree SPT-SZ survey K. T. Story et al. (see equation 21, page 14) '' The tightest constraint on the mean curvature that we consider comes from combining the CMB, H_{0} , and BAO datasets: Ω_{k} = −0.0059±0.0040. " The SPT (South Pole Telescope) survey, combined with the other datasets, gives this range: Ω_{tot} = 1.0059±0.0040 That's a 95% confidence interval that is all on the positive curvature side. So the balloon analogy, although it is just an analogy, is not ALL that bad
If you want to calculate the circumference based on a curvature number like 0.0059, you take the current Hubble radius 14 billion ly, multiply by 2π, to get 88 billion ly, and divide by the square root of that curvature number. The smaller the curvature number you take, the smaller the square root will be, and the LARGER the circumference estimate will be, that you get when you divide. In the case of the SPT data (combined with the other datasets) the SMALLEST curvature number in their 95% confidence range is 0.0059 - 0.0040 = 0.0019 and the square root of that is 0.0436. So when you divide 88 billion ly by that you get 2018 billion ly That is the largest circumference based on their confidence interval. I'm not offering this as a serious estimate, just showing a sample calculation. If you want you can see what their central value 0.0059 or their highest value 0.0099 translate into as circumferences. The highest curvature number 0.0099 translates into about 880 billion ly in circumference terms. That is how far you'd have to travel in a straight line in order to get back to where you started (if you could stop the expansion process long enough to make such a "circumnavigation")