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B What is empirically known about the shape and size of the un

  1. May 28, 2016 #1
    It may be that nothing is, or even can be empirically known about exactly how big our universe is, or the shape of its geometry (flat, round, etc.), but what are some basic, provable facts that can be used to work out a theory or to debunk one?

    I know this is a very broad question. I have come across a plethora of theories about the size and shape of the universe, but I can't seem to shake any solid facts out of them, being that I mainly read texts designed for a layperson.
     
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  3. May 28, 2016 #2

    Drakkith

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    Without a very in-depth knowledge of physics, especially the physics used in astronomy and astrophysics, I'm not sure you can "work out a theory". As for debunking them, there's little need. If it isn't a mainstream theory and isn't being proposed by an actual cosmologist or perhaps an astrophysicist (not an engineer, not a guy with a science degree, not even a "regular" physicist) then it's almost certainly nonsense. There are a number of signs to look for if you're trying to figure out whether something is nonsense or not and I can give you some links if you're interested.

    What do you mean? There is only one accepted, mainstream theory regarding the universe as a whole, the big bang theory, but there are still plenty of unknowns. Are you talking about these unknown possibilities?
     
  4. May 28, 2016 #3
    I'm talking specifically about whether the universe flat and infinite, or if it is curved, perhaps even closing in on itself like a sphere such that a long enough journey in any direction would end at its beginning. Or if it is finite, with an edge. I read somewhere that the matter in the universe may have an edge, bordered by dark matter. In trying to sort out all of these theories, I'm simply trying to understand what hard facts, empirically proven, could be utilized in forming an understanding. Or are all of these theories purely speculative, and based solely on what is mathematically possible, without any real evidence? In short, is anything actually known, and scientifically verifiable, about the shape and size of the universe as a whole?
     
  5. May 28, 2016 #4

    Drakkith

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    First a little terminology correction if you don't mind. These different possibilities aren't theories. They are more like properties of the universe that can exist within current theory, specifically the big bang theory.

    The possibilities themselves are based on a mixture of known physical and mathematical principles. The problem is that we lack the data to actually verify which one of the possibilities is the correct one. Unfortunately I cannot give you many specifics, as I'm not an expert in cosmology.

    Hmm... I've never read of this before and it doesn't sound like it could be a real possibility based on the little I know about dark matter and cosmology.

    Well, we know that the universe is very close to flat, and actually may be flat. Or its curvature could simply be too small to measure. We can also place a minimum size of the universe, which, right now, is around 96 billion light years in diameter if I remember correctly. If you're asking what the actual data and methods are that lets us figure this stuff out, I'm afraid I'll have to let someone else answer that.
     
  6. May 28, 2016 #5
    I've really been trying very hard to wrap my head around this lately, and i apologize if I seem to be!having difficulty asking the question in a way that makes sense, but if the universe has a measurable size (I did catch that "minimum size" detail, which I take to mean that it may not have a measurable size, but that it is at least that large), but if it does have a size, or ever did, but has always had its center everywhere at every moment, even as it's expanding, and if it doesn't have an edge, how can it be flat? I feel like in missing something really fundamental. Everyone has been very thoughtful in their responses (I posted another thread that sort of asked this question, but even more clumsily) but I can't shake out any "knowns" that can help me get it.

    The one "known" I can understand is that the universe is certainly expanding, whatever size and shape it might be. It was explained to me that just because it used to be more dense than it is, and is getting less dense, does not imply that the size of the universe is changing or that it was ever smaller than it is, but I still can't really comprehend it. I get that there is no outside space, empty until the universe expanded into it, but I constantly see references to the big bang as being an infinitesimal point of infinite density suddenly bursting into existence, creating space and time,where before, neither existed. But in the very first instants of the big bang, as it the universe sprang into existence, how could it already be infinite and flat? Wouldn't it have to be closed, or spherical?

    I'm told that no, it wouldn't. So what hard facts about this am I missing? What is the fundamental thing that my head just won't grasp?

    I understand these questions might be annoying, and i really appreciate anyone and everyone who has or might offer their knowledge and insight, but this is very difficult for me to understand. I'm not trolling anyone or trying to be difficult, it's just that, while I think I understand non-euclidean geometry, and general relativity, I just can't comprehend a flat universe. So I'm looking for a baseline of accepted, proven facts. It seems to fly in the face of logic, so must have some verifiable evidence to support it.
     
  7. May 28, 2016 #6

    Drakkith

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    Understandable. We aren't talking "normal" geometry that most people are used to. In addition, there's the problem that General Relativity itself is a theory of variable geometry, something most people have never even heard of. I'll try my best to explain what I know, but be warned that I may be mistaken.

    To start, you need to know just a bit about General Relativity. The really short explanation is that GR is a geometric theory (a theory of geometry) that describes space and time. Unlike what you're used to here on earth, where the exact geometry never noticeably changes, GR states that the geometry of spacetime changes based on the presence of mass. The end-effect of this is to cause gravitation, time dilation between observers, and several other effects that I won't go into. In addition, cosmology itself uses GR as the fundamental theory from which to model the universe as a whole. So all of this geometry stuff is extremely important to cosmology.

    When we model the universe with GR, we run into the problem of having variable geometry. There are essentially three types of possible geometry: flat, open, and closed. Take, for example, the surface of a perfect sphere. The geometry on the surface of the sphere is not "flat". Lines that are initially parallel will end up crossing if drawn on the surface of the sphere. The angles of triangles do not add up to 180 degrees like they do on a flat piece of paper, instead equaling more than 180. A straight line drawn on the surface will come back around to its starting point. The geometry is closed.

    The geometry of a flat piece of paper is, well, flat. This is the geometry you learned in school. Parallel lines never intersect or get further away from one another. Triangle angles add up to 180 degrees. A straight line never intersects itself.

    An open geometry is like the surface of a saddle. Lines that are initially parallel will diverge. Angles of a triangle add up to less than 180 degrees.

    Now, a key thing to realize is that all of these descriptions have so far talked about 2-D surfaces within 3-D space. We can obviously see the different geometries with no problems, as we live in a 3-D universe. There is an "up" and a "down" side of a ball on the ground, and of a saddle and a piece of paper. We can put the coordinates of any point on any of the lines on these surfaces in a 3-D coordinate system as well as a 2-D. Since we can describe all of this curvature by referencing how it behaves within a higher-dimensional space, we call this way of measuring curvature "extrinsic".

    But this poses problems to measuring and describing the curvature of 3-dimensional space itself. We live in 3 dimensions and don't have the option of referencing a higher-dimensional space to describe any possible curvature. Fortunately, there is another way. By measuring things like angles and seeing how things that move in straight lines behave over very large distances, we can come up with a way of describing and modeling the curvature of our universe without referencing a higher dimensional coordinate system. Using a mathematical tool known as a "manifold", we can describe this curvature purely in terms of our own three dimensions. We call this curvature "intrinsic". This distinction between intrinsic and extrinsic is important because, at first, it seems like the universe must be embedded within 4-dimensional space in order to have a curvature. As far as we know, this is not true, and we have ways of measuring curvature that doesn't require us to reference 4-dimensional space. Whether there are other dimensions or not is not my point here, I merely want to explain that it is not required that there be other dimensions in order to have curvature.

    But, what does curvature of 3-D space mean? Put simply, it means something similar to what it meant when talking about 2-dimensional surfaces. The behavior of lines, shapes, and other things embedded within that space. In real life one obviously can't draw a line on empty space, so it makes measuring the properties of space a little more difficult. We have to look at what happens to objects as they move around though space. In the context of the universe as a whole, we typically look at how light behaves. At the very largest scales the universe is homogeneous and isotropic, meaning that if you zoom out REALLY far, the universe looks pretty dull. You wouldn't be able to see all the little clumps of matter and dark matter. Everything would look the same no matter what way you looked. Because the universe is homogeneous and isotropic at the largest scales, we can look at the behavior of light that has been traveling very long distances and, based on the behavior of that light, determine the overall shape of the universe. Thus, one of the things astronomers look at when determining the shape of the universe is at the CMB.

    Now, what do the different shapes mean for the universe? We still have our three types from earlier, flat, open, and closed. The different properties of each still apply. Parallel lines may converge, diverge, or remain parallel depending on whether the universe is closed, open, or flat respectively. The geometry of the universe does put constraints on its overall shape, but it does not determine whether the universe is finite or infinite except that a closed universe must be finite. A flat or open universe could still be either finite or infinite as far as I know.

    Note that all of this ignores expansion. Expansion itself doesn't change the geometry of the universe, but it does complicate its measurements. A closed, finite universe can still expand.

    Earlier I talked about variable geometry. This is important because by measuring the amount of matter and energy in the universe we can figure out whether our universe is closed, open, or flat. To quote wikipedia's article:

    General relativity explains that mass and energy bend the curvature of spacetime and is used to determine what curvature the universe has by using a value called the density parameter, represented with Omega (Ω). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way

    • If Ω = 1, the universe is flat
    • If Ω > 1, there is positive curvature
    • if Ω < 1 there is negative curvature
    Put simply, if there's enough matter and energy, the curvature should be positive. If there's too little then it will be negative. If there's just the right amount then the universe will be flat.

    Ignore those references. Realize that in order to model the history of the universe we can only do so by basing our theories off of observations. Because the speed of light is finite, we can see further back into the past as we look further away. But the problem here is that we can only see so far, both in distance and in time, so we can't actually see what things were like at the very beginning. What we do know is that in the past the universe was more dense than it is now. If we construct a model and look at the density of the universe over time, we see that it approaches infinite density as we go further back in time. If we let it reach infinity we have a singularity, which is just what happens when our math stops working. I get a singularity when I try to divide by zero, so this isn't something that just popped up in cosmology. Now, if the entire universe, all of it according to the model, gets denser as we go back in time, then when the density is infinity and we get our "singularity" then this singularity is everywhere. So any references you see that claim the big bang started at a single point in space is simply wrong.

    As for the creation/beginning of the universe, we don't actually know anything about that. It's possible that the universe came into existence already infinite and flat. I mean, if we want to talk about things popping into existence from utterly nothing prior, then why would a finite universe popping into existence from a single point be any more plausible than an infinite universe? Either way you still have the building blocks of everything that will ever exist suddenly coming existence.
     
    Last edited: May 29, 2016
  8. May 28, 2016 #7
    Wow, that was awesome. I didn't mind at all hearing you explain some of the things I basically already understood, because you explained them very concisely and elegantly. I feel I understand them better now than I did before.

    General relativity explains that mass and energy bend the curvature of spacetime and is used to determine what curvature the universe has by using a value called the density parameter, represented with Omega (Ω). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way If Ω = 1, the universe is flat If Ω > 1, there is positive curvature if Ω < 1 there is negative curvature

    Reference https://www.physicsforums.com/threa...shape-and-size-of-the-un.873529/#post-5485412

    For some reason I couldn't get that to quote right, but this was the real jewel for me. Thank you a thousand times, Drakkith.

    For what is worth, I think it's been a real disservice to science for so many popular texts to take the singularity so literally. I know that singularities and infinities generally indicate a breakdown of mathematics and basically tell us that the way we are asking the question is flawed, but having seen this universe as a singularity concept so many times, sometimes rendered in CGI as a glowing sphere rapidly growing in size, I assumed that there was a scientific consensus that the singularity in this case was real, and have focused a lot of time and energy imagining an infinite universe confined in a finite space. Teaching people things that are patently untrue, in my pinion, is more of a travesty than teaching no one anything.
     
  9. May 28, 2016 #8

    Chronos

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    You apparently are stumbling over some of the most profound aspects of GR. In GR the concepts of time and distance have no absolute meaning. Einstein concluded that "in the general theory of relativity, space and time cannot be defined in such a way that differences of the spatial coordinates can be directly measured by the unit measuring rod, or differences in the time coordinate by a standard clock...this requirement ... takes away from space and time the last remnant of physical objectivity". Given the arbitrary nature of space and time in GR, the task of even defining space and time reduces to an exercise in futility. Since all observable quantities of time and space become self referential under this constraint, we are strictly limited to comparing their local properties If all this seems pardoxical and defies sensibility, you are making progress. For further entertainment, the ugly details are summarized here http://mathpages.com/rr/s5-08/5-08.htm. Even the most brilliant minds of the early 20th century had difficulty reconciling these ideas with the brilliant mathematical tour de force that lays them bare, so, you are in good company if the discussion is less revelatory than hoped. Even now researchers, are still uncovering the ramifications of GR.
     
  10. May 28, 2016 #9

    PAllen

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    Just a small comment: the flat, positive and negative curvature possibilities Drakkith refers to are the curvature of 'standard spatial slices', which I will try to explain. The contrasting point is that the universe as a whole 4-dimensional spacetime is curved (unless it is completely empty, which we assume to be false :wink:). To get at this by analogy, the space around you that you are familiar with is (exceedingly close to) flat 3-d space. However, you can have e.g. a tennis ball within this space. This is a 2-sphere slice of the 3-space; it has positive curvature. Of course you can also embed a plane in this space, which is a flat 2-d slice of the 3-space. Similarly, within a 4-d spacetime, there are many types of spatial slice that can be taken (each with different 3-d geometry).

    However, for cosmology, we are talking about space-times with a very special property: there exists a unique family of slices such that each slice looks identical in all places and all directions (homogeneity and isotropy). These are what I have called 'standard slices'. It is these standard 3-d spatial slices of 4-d spacetime (which is always curved) that may be flat, positive or negatively curved depending on the matter/energy density of the universe.
     
    Last edited: May 28, 2016
  11. May 28, 2016 #10
    Yes, this is the context in which I was trying to imagine an infinite universe in a finite space. I had a pretty hard time with it. However, that's not to say that I came to believe that it was impossible, I just couldn't wrap my head around it completely. I still have a lot to comprehend, even if I may have been going down a dead end road on that one.
     
  12. May 28, 2016 #11
    Is the CMB radiation left over energy from the battle between matter and anti-matter?
     
  13. May 28, 2016 #12

    anorlunda

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    I prefer to focus on the phrase "nearly flat" If the universe is nearly flat, then there is no practical difference between slightly positive, zero, or slightly negative curvature. Sure, you can imagine a philosophical difference but not a practical one.

    My favorite professor, Leonard Susskind, likes to say, "Physicists are not concerned with what is true, but rather what is useful." [my paraphrase]

    @Drakkith, you put a lot of effort into very good answers in post #6, but you know this question will occur again and again in other threads. Might I suggest an Insights article?
     
  14. May 28, 2016 #13

    1oldman2

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    Most definitely ! an article of that quality would be very welcome. While reading #6 I was able to make connections that have eluded me for years. Thanks and "likes" for everyone involved in this thread. :thumbup:
     
  15. May 28, 2016 #14

    Drakkith

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    Maybe. @Greg Bernhardt I'll try to put more together on this if that's alright.
     
  16. May 28, 2016 #15

    Drakkith

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    Kind of. Its a direct result of the temperature of the plasma filling the universe about 380,000 years after the big bang. This plasma is itself a remnant of earlier state in which matter and antimatter were both present. If you'd like to know more, please make a new thread, as this is off topic for this thread.
     
  17. May 28, 2016 #16

    ogg

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    I note some errors in various posts in this thread:
    1. The Universe is not 3 dimensional; it is (at least) 4 dimensional - or 3-1 dimensional. Anyone speaking of it as a sphere is just not getting it. The Universe is, provably and observationally 4 dimensional (although we can't see "forward" in time).
    2. The word "Universe" is being used here in (at least) two very different ways: a) as the entirety of space-time and b) as the Observable Universe (the part of the Universe which has been or is causally connected to us.) By definition, the parts of space-time that are NOT part of our Observable Universe can not offer any "empirical evidence" to us, ever. The meaning of the term "Observable Universe" is tied into the Inflationary Big Bang model, and needs to be understood in that context.
    3. I've read a couple of journal articles placing lower limits on the size of the Universe, they are out there and are based on OBSERVATIONAL evidence.
    4. Great care must be exercised when thinking about the Universe. The shape of the Observable Universe is generally understood to mean the geometry of space-time in the limit as x(i)→0, that is, crudely, microscopic structure, not macroscopic (over-all) shape. Many discussions of the "shape" ignore gravity on local scales. Each and every black hole (and we know there are billions of them (at least)) IS an edge of our Observable Universe. As well, the continuing expansion of space-time places a limit on the distance from us which a photon can travel to (or from). The distance at which a photon can not reach us (assuming expansion continues to accelerate) is roughly 16 billion light years. You'll note that this distance is much smaller than the diameter of the Observable Universe which is estimated to be 92 billion light years. And yes, this implies the (Observable) Universe was much more "connected" in the past. It's not really correct to say that there was a time = 0 (the instant of the Big Bang, or more accurately, the instant of the beginning of the Big Bang - "Big Bang" might include the inflationary period or might include everything from the "beginning" to now (uncommon) or might include a certain time period. Times before ~~1E-44 seconds are NOT accessible to our analysis - our Physics is inadequate to handle times less than this. This time can be considered another "edge", but an open edge, like the event horizons of Black Holes. There IS observational evidence that the (Observable) Universe is isotropic and homogeneous. This implies that the entire Universe is infinite and unbounded (otherwise an observer closer to the "end" wouldn't see the same things we do). There is consensus that the (Observable) Universe has an infinite future in time. This can't be proven. If you're familiar with sets, the number line, and line segments, you may understand the difference between the interval (0,1) and the interval [0,1]. One is open and one is closed. But what about [0,1)? Is it open or closed? The answer is, of course, it is both.
     
  18. May 28, 2016 #17

    Drakkith

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    I can't speak for anyone but myself, but I've been talking almost purely about spatial dimensions.

    In general, the shape of the universe should be thought of as the shape of the universe as a whole, not just the observable part.

    Did someone claim otherwise?
     
  19. May 28, 2016 #18
    Great job, Drakkith. If I were you I'd at least copy and paste that 'epic' reply of yours into a text file so you can just paste it the next time this question is asked (which seems to be at least once a week - or more). Wouldn't want you to get writer's cramp.
    And since we should post some evidence to go along with our 'opinions': Drakkith's reply was almost perfect in the way it could be understood by a layman as dense as I am or by a professional as educated and opinionated as Ogg. Again, great job...
     
  20. May 28, 2016 #19
    I posted about CMB, because you mentioned it in your post as a reason for the shape and size of the universe.
     
  21. May 28, 2016 #20
    I've been lurking on this forum for quite some time, and I registered just now for the sole purpose of explicitly thanking you, Drakkith. Your reply is enormously helpful.

    Best regards,

    jb
     
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