Martin Posted January 11, 2010 Share Posted January 11, 2010 (edited) I agree with what Sisyphus says here. Folks remember that cosmology is a mathematical science meaning that it deals with equation models and fitting them to the data so that you get the best fit----which translates into being able to predict the next round of data. as the instruments constantly increase resolution and depth, more keeps coming in. Issues like how big is the universe are not what it's about. It is about a predictive theory that has to fit literally millions of data points. And agree with our well-tested theory of gravity (a theory of the universe's geometry.) In AstroCosmo forum our point of departure is current standard model (LCDM, for lambda cold dark matter). Understand that first then vary it all you like (if you too can fit the data and match the behavior of gravity/geometry as described by General Relativity.) The starting point is not philosophy. If you want to philosophize about the universe, try Spec forum. What we mean by the size of the universe is simply the size of the current model. And because the model has errorbars, ranges to its parameters, there will naturally be uncertainty about that. That is what I was saying, yes. Anyway, it definitely doesn't have a center. The way expansion behaves isn't consistent with expanding away from some central point, like a conventional explosion. That doesn't mean it must be infinite, though. A relatively simple alternative is that it folds back on itself. i.e., that a long enough straight line just points back at itself. Think of it like a computer game where going off one end of the map puts you on the opposite side, but 3D. So the volume is finite, but it has no center and no edges. I forget where I saw it, but I remember some physicist claiming that if the universe is finite, then the ratio of universe to observable universe would have to be at least that of the Earth to a 1 inch sphere. I have no idea if that's a consensus or current view. At present AFAIK the WMAP data that came out in 2008 contains the best, most widely accepted estimates of the LCDM parameters and about the size of the universe (which was certainly not the first thing they wanted) if it was finite, according to the S3 picture (the 3D spherical surface that gib is talking about), the circumference was at least 600 billion lightyears. I have to do something else, back in a while. Will try to same a bit more about this. Hmm... I have difficulty dissociating this scenario with the model of a 4D sphere on which our 3D universe is its surface. I guess I could chalk the 4D sphere up to a useful conceptual tool only and that the real nature of space - that is, how it wraps around like you say - to something beyond my ability to comprehend. But is there anything wrong with imagining an infinite amount of matter and energy filling the universe? It's no big deal, not to stress. I have a hunch you will without even trying get the concept of a closed 3D universe. What Sisyphus was describing was a toroidal 3D universe. Like PacMan 2D square with opposite edges identified but the whole 2D world jacked up one dimension. So a PacMan 3D cube with opposite faces identified. Try daydreaming that you live in such a thing. A room where you can pass out thru the east wall and the arm you stick thru the wall comes in from the west wall. In cosmology one doesn't hear very much about the toroidal 3D topology. But it is a workable example of closed 3D space, which is how S. used it in his post. It's the surface of a donut, jacked up one dimension. The more usual case is the socalled hypersphere or S3. This is the surface of a balloon, jacked up one dimension more. A balloon surface is S2 the socalled "two-sphere". It doesn't have to have a surrounding 3D space but can exist on its own as a closed 2D world. (That's important to realize.) The corresponding thing in one higher dimension also does not have to have a 4D surrounding---it can exist on its own. That's probably the most important thing to realize in all of differential geometry. Geometries can be experienced from within, curvature can be defined and measured from within---so they don't have to be embedded in higher dimensional surroundings. Use your imagination and try first to have the experience of a 2D creature living in the two-sphere. Slide around on the surface of a balloon. Go exploring. Then use your imaginatin and try to experience what it would be like to live in a reasonable size three-sphere. One not too large. So that you could circumnavigate. At this point we don't really have the right to believe finite, and reject infinite----or the right to believe infinite and reject finite. We don't know. It could be infinite. It could be finite three-sphere with circumference > 600 billion lightyears. There is virtually no difference numberwise. Both versions of the model give almost exactly as good fit to the data. So it's incumbent on us to get used to imagining it both ways. It could be either one. Future observations will probably decide the issue. Edited January 11, 2010 by Martin Link to comment Share on other sites More sharing options...

beejewel Posted January 11, 2010 Share Posted January 11, 2010 Hi guys, I am sure this question has been asked many times and the standard answer is always "the standard model...bla bla bla, and only God knows the size of the U". Well I think it is time to change the way we think... To comply with your forum rules, I will take my ideas to the Spec forum, where I can hopefully get a good debate. I am going to propose that the size of the Universe does depend on the observers mass, and hopefully show you why and how we can work out the excact size. See you there Steven Link to comment Share on other sites More sharing options...

gib65 Posted January 11, 2010 Author Share Posted January 11, 2010 At present AFAIK the WMAP data that came out in 2008 contains the best, most widely accepted estimates of the LCDM parameters and about the size of the universe (which was certainly not the first thing they wanted) if it was finite, according to the S3 picture (the 3D spherical surface that gib is talking about), the circumference was at least 600 billion lightyears. WOW!!! That's an incredibly big universe. But isn't that still not big enough for a margin of error of 2% for measuring the universe to be flat? I can explain my reasoning if necessary. It's no big deal' date=' not to stress. I have a hunch you will without even trying get the concept of a closed 3D universe. What Sisyphus was describing was a [b']toroidal[/b] 3D universe. Like PacMan 2D square with opposite edges identified but the whole 2D world jacked up one dimension. So a PacMan 3D cube with opposite faces identified. Try daydreaming that you live in such a thing. A room where you can pass out thru the east wall and the arm you stick thru the wall comes in from the west wall. In cosmology one doesn't hear very much about the toroidal 3D topology. But it is a workable example of closed 3D space, which is how S. used it in his post. It's the surface of a donut, jacked up one dimension. The more usual case is the socalled hypersphere or S3. This is the surface of a balloon, jacked up one dimension more. A balloon surface is S2 the socalled "two-sphere". It doesn't have to have a surrounding 3D space but can exist on its own as a closed 2D world. (That's important to realize.) The corresponding thing in one higher dimension also does not have to have a 4D surrounding---it can exist on its own. That's probably the most important thing to realize in all of differential geometry. Geometries can be experienced from within, curvature can be defined and measured from within---so they don't have to be embedded in higher dimensional surroundings. Use your imagination and try first to have the experience of a 2D creature living in the two-sphere. Slide around on the surface of a balloon. Go exploring. Then use your imaginatin and try to experience what it would be like to live in a reasonable size three-sphere. One not too large. So that you could circumnavigate. Thanks Martin. I'm used to these thought experiments, so I don't really have much trouble with them or understanding what they signify. But what's new to me is how to imagine a finite flat universe. Whether it's a "three-sphere" or toroidal universe we're living in, those would be closed universes (right?) - and quite finite. But these models could only serve as useful guides for how to think of space travel in a finite flat universe. If the universe is flat, then we can't actually say we're living in a "three-sphere" or on the surface of a 4D torus - we can only say it is as if we were (and only in some respects). Link to comment Share on other sites More sharing options...

Martin Posted January 11, 2010 Share Posted January 11, 2010 WOW!!! That's an incredibly big universe. But isn't that still not big enough for a margin of error of 2% for measuring the universe to be flat? actually not! If you take the errorbar (the currently available 95% confidence interval) for the curvature, and take the upper limit, and calculate the radius of curvature from that, you get very close to 100 billion light years. An upperbound on curvature corresponds to a lower bound on the radius of curvature. With 95% certainty the radius of curvature (RoC) has to be at least that. So the circumference has to be at least TWO PI time that. Which is 628 billion light years. In what I wrote I rounded to 600 not to make it seem high precision. If it is at least 628 then obviously it is at least 600. My information on the RoC comes from table 2 on page 3 of the relevant WMAP report. As I recall the RoC is calculated using the formula Hubble distance/sqrt(|Omega_k|) Note that Omega_k = 1 - Omega_tot so it has the opposite sign from what you expect. The more positive the curvature the more negative Omega_k is. Just an accident of notation. If you are still getting numbers much bigger than 100 for the RoC, or much bigger than 628 for the circumference, let us know. Link to comment Share on other sites More sharing options...

gib65 Posted January 11, 2010 Author Share Posted January 11, 2010 actually not! If you take the errorbar (the currently available 95% confidence interval) for the curvature, and take the upper limit, and calculate the radius of curvature from that, you get very close to 100 billion light years. An upperbound on curvature corresponds to a lower bound on the radius of curvature. With 95% certainty the radius of curvature (RoC) has to be at least that. So the circumference has to be at least TWO PI time that. Which is 628 billion light years. In what I wrote I rounded to 600 not to make it seem high precision. If it is at least 628 then obviously it is at least 600. My information on the RoC comes from table 2 on page 3 of the relevant WMAP report. As I recall the RoC is calculated using the formula Hubble distance/sqrt(|Omega_k|) Note that Omega_k = 1 - Omega_tot so it has the opposite sign from what you expect. The more positive the curvature the more negative Omega_k is. Just an accident of notation. If you are still getting numbers much bigger than 100 for the RoC, or much bigger than 628 for the circumference, let us know. I'm not getting any numbers. That might be the problem. I'm not thinking of this mathematically, but visually. I'm trying to visualize the size of the visible universe in comparison to one whose circumpherence is 628 billion lightyears. I'm assuming the visible universe has radius 13.7 billion lightyears (it's 13.7 billion years old, and so the farthest light could have traveled is 13.7 billion lightyears, and so the farthest we can see is 13.7 billion lightyears away, and that defines the "visible universe"). If the minimum radius of the universe is roughly 100 billion lightyears as you say, that's a ratio of 13.7:100 or 13.7% the size of the total universe. At this point, I'm just using some layman's reasoning and my visualization to figure that taking a portion of 13.7% of the total universe and trying to measure some curviture therein should give you something, shouldn't it? It ain't like the surface of a penny compared to the surface of the Earth - it's more like the UK compared to the surface of the Earth. The surface area of the UK should have some noticeable curvature. No? This all probably sounds like silly reasoning to an expert like you, Martin, but it's the best reasoning I can figure out Link to comment Share on other sites More sharing options...

Martin Posted January 12, 2010 Share Posted January 12, 2010 I'm assuming the visible universe has radius 13.7 billion lightyears (it's 13.7 billion years old, and so the farthest light could have traveled is 13.7 billion lightyears, and so the farthest we can see is 13.7 billion lightyears away, and that defines the "visible universe"). The farthest stuff we can see is what emitted the CMB light. The microwave background. The current distance to that stuff is 45 billion light years. Think of freezing expansion and then timing a radar signal. It would take 45 to reach that matter (which we see as it was over 13 billion years ago) and 45 to get back. A round trip time of 90. Don't think of it as 13.7 billion lightyears away. In terms of today's distance it is much more because of expansion. 45 billion lightyears is what astronomers call the particle horizon. The present distance of the most distant particles which we can see (from the light they emitted in the past). If the minimum radius of the universe is roughly 100 billion lightyears as you say... I said the radius of curvature was estimated at least that. RoC is a technical mathematical concept. It is used as a measure of curvature. The RoC doesn't correspond to any actual distance in our space. If you imagine embedding our space as a hypersphere in a space of higher dimension, then it would have a center and every point of our space would be the same distance (100) from that imagined center. I thought you were calculating the circumference and got the wrong numbers, so that all this would be familiar to you. You would understand what the radius of curvature means. Sorry I mentioned it, if it caused you confusion. Think of it this way. In the smallest finite case, the circumference is 628. And the farthest distance we can see is 45, in all directions. That 45 is along the curved hypersphere surface. So the farthest distance we can see is 45/628 of the circumference. Light follows the curvature of space, so it travels along the "balloon surface". So distances we measure are like great circle airplane routes, and should be compared with the circumference, not the imagined radius (which if it existed would be outside our 3D world.) And the 628 is a lower bound. Could be much more. Link to comment Share on other sites More sharing options...

liarliarpof Posted January 12, 2010 Share Posted January 12, 2010 This is reminiscent of Galileo's 'result', after his attempts to measure the speed of light using men with lanterns on distant mountaintops: "Extraordinarily fast, if not instantaneous." Link to comment Share on other sites More sharing options...

Martin Posted January 12, 2010 Share Posted January 12, 2010 (edited) This is reminiscent of Galileo's 'result', after his attempts to measure the speed of light using men with lanterns on distant mountaintops: "Extraordinarily fast, if not instantaneous." To have had the balls to try to experimentally determine the speed of light in william shakespearse's day or 1620 or whenever. the guy was awesome! And within 50-60 years from Galileo's experiment a young Dane in Paris actually measured it! inspired by Galileo. He got within about 10 percent of the right answer by timing the eclipses of one of Jupiter's moons. Galileo put the idea out there, that it could have a finite speed and you could measure it. And Olaus Roemer followed up within 50-60 years. Edited January 12, 2010 by Martin Link to comment Share on other sites More sharing options...

gib65 Posted January 12, 2010 Author Share Posted January 12, 2010 The farthest stuff we can see is what emitted the CMB light. The microwave background. The current distance to that stuff is 45 billion light years. Think of freezing expansion and then timing a radar signal. It would take 45 to reach that matter (which we see as it was over 13 billion years ago) and 45 to get back. A round trip time of 90. Don't think of it as 13.7 billion lightyears away. In terms of today's distance it is much more because of expansion. 45 billion lightyears is what astronomers call the particle horizon. The present distance of the most distant particles which we can see (from the light they emitted in the past). Oh, I think I understand. So while the light was traveling its 13.7 billion lightyear journey, the light source was on a journey of its own in the other direction (because of expansion), and the total distance between the source and us now is 45 billion lightyears... right? So the farthest distance we can see is 45/628 of the circumference. Light follows the curvature of space' date=' so it travels along the "balloon surface". So distances we measure are like great circle airplane routes, and should be compared with the circumference, not the imagined radius (which if it existed would be outside our 3D world.) [/quote'] Sure, but they are proportional. A ratio of 45:628 gives us something which seems to me more reasonable (roughly 7% - half of the UK). Is 7% of a circumpherence too little to discern any curvature given the means by which we measure it (and the 2% margin of error)? Link to comment Share on other sites More sharing options...

Martin Posted January 12, 2010 Share Posted January 12, 2010 Yes I reckon so. Must be, because the best they have done so far with 95% confidence is say the circumference has to be at least 628. (you know the units I mean). Compliments on getting an understanding of it with the help of visual intuition. Good intuition---I mean about the 7% horizon and the 2% error margin. Link to comment Share on other sites More sharing options...

MM6 Posted January 12, 2010 Share Posted January 12, 2010 See, the problem I have with an infinite space is that it conflicts with my understanding of the Big Bang Theory. According to what I understand, the Big Bang began as a singularity (or something close to one) and this included space itself - that is to say, space itself began to expand with everything else. To my mind, the only model that fits this is the one of a 4D sphere where our 3D universe is its surface. If the universe is flat or open, that means either space has expanded to infinity already (which is untenable) or there is some kind of limit to space - a "wall" so to speak - that is a finite distance away and can supposedly be encountered if one traveled far enough (which seems absurd to me). An alternative is that space is infinite to begin with and the Big Bang occured at some local region in space. Space could still be said to be expanding according to this model, but not all of it starting from a singularity. The problem with this is that, from what I understand, the contents of the early universe (particles, gas, photons, etc.) are said to have filled all space and so they can't be limited to a local region. I agree, if the universe came from a point source (or even something smaller than it is now), then it cannot be infinite in size, ever, unless you remember to consider time as a variable--at some potential infinite point in time the universe could be infinite in size. For the universe to be infinite now that would require the possibility of forward and backward space-time travel in infinite quantities at any point and at any time. But the physical concept of infinity is no more satisfying than a mathematical point, so I'm not sure where that gets us. I think somebody has since addressed this, but the Big Bang didn't occur somewhere in space and expand into it. It created space as it expanded. Link to comment Share on other sites More sharing options...

adam SA Posted February 6, 2010 Share Posted February 6, 2010 (edited) I just always though that like in a vaccuum (if one really exists) that positive and negative matter can appear and dissapear (positive and negative energy), in that you can "borrow" energy from the universe as long as you pay the energy back quik enough. In this, from nothing (singularity, "before" the big bang) why cant you borrow "near infinite" positive and negative energy (mass), and as we know mass creates a "time warp" (like a black hole). So in an essence the universe only existed for an instant, yet because of its immense gravity (like a black hole) it bends wat we perceive as space time enough for us to perceive it as near infinity (near infinity, wasnt that dumb). (if you put an object next to a object with immense gravitational field it would age relatively lower than everything observing it that is not near a large gravitational field)? (I have trouble differentiating zero from infinity, in the same way i have trouble seperating the speed of light from a physical distance. It is hard to express zero without infinity and infinity without zero. We apparently know 1-1 =0 , also f(x) = x-x = 0, whether x be infinity or zero, and infinity is best expressed as f(x) = x/0, in that x can be any number positive or negative) just one of my theories atm, I will soon come up with a better one when i learn more Edited February 6, 2010 by adam SA mispellings, was drunk :D Link to comment Share on other sites More sharing options...

purintjp Posted February 8, 2010 Share Posted February 8, 2010 I just always though that like in a vaccuum (if one really exists) that positive and negative matter can appear and dissapear (positive and negative energy), in that you can "borrow" energy from the universe as long as you pay the energy back quik enough. In this, from nothing (singularity, "before" the big bang) why cant you borrow "near infinite" positive and negative energy (mass), and as we know mass creates a "time warp" (like a black hole). So in an essence the universe only existed for an instant, yet because of its immense gravity (like a black hole) it bends wat we perceive as space time enough for us to perceive it as near infinity (near infinity, wasnt that dumb).(if you put an object next to a object with immense gravitational field it would age relatively lower than everything observing it that is not near a large gravitational field)? (I have trouble differentiating zero from infinity, in the same way i have trouble seperating the speed of light from a physical distance. It is hard to express zero without infinity and infinity without zero. We apparently know 1-1 =0 , also f(x) = x-x = 0, whether x be infinity or zero, and infinity is best expressed as f(x) = x/0, in that x can be any number positive or negative) just one of my theories atm, I will soon come up with a better one when i learn more Adam, you are not the only one who thinks about this kind of stuff. I posted the following some time back. Just how empty is space, really. There are all the various radiation spectra and things like neutrinos and other exotic particles rushing through space pretty much everywhere. Not to mention stuff we probably can't even detect. Maybe the idea of 'nothing' does not even exist. I think that the proof of nothing is tied to the proof of infinity. Is not the best definition of infinity as 'something' divided by 'nothing' ? They both could be just pure mathematical concepts. I know scientists are dead set on using mathematics to describe everything but I doubt they will. I often wonder if mathematics is not a victim of it's own precision. Everything seems to break down around 0 and infinity. What is it that is exactly equal that is larger than quantum level ? Are we 100% sure that even quantum level stuff is equal down to the most infinite detail ? Link to comment Share on other sites More sharing options...

adam SA Posted February 9, 2010 Share Posted February 9, 2010 Yeh Plancks constants are amazing, He has got to be one of my favorite scientists, with Shrodinger, Copernicus and Michio Kaku. Link to comment Share on other sites More sharing options...

Chriton Posted February 10, 2010 Share Posted February 10, 2010 Adam Just how empty is space, really. There are all the various radiation spectra and things like neutrinos and other exotic particles rushing through space pretty much everywhere. Not to mention stuff we probably can't even detect. Maybe the idea of 'nothing' does not even exist. I think that the proof of nothing is tied to the proof of infinity. Is not the best definition of infinity as 'something' divided by 'nothing' ? They both could be just pure mathematical concepts. I know scientists are dead set on using mathematics to describe everything but I doubt they will. I often wonder if mathematics is not a victim of it's own precision. Everything seems to break down around 0 and infinity. What is it that is exactly equal that is larger than quantum level ? Are we 100% sure that even quantum level stuff is equal down to the most infinite detail ? Lets face it people we are limited in what we understand about the universe. As single cell creatures we had to survive knowing what was good or bad for us. Our evolution was just knowing enough to survive so how do we know that what we know or observe is the true picture... we measure things according to our limited knowledge of what we are limited to understand. There could be particles faster than light, and the universe could be something we dont understand...we all want to get a picture in our heads of what and why...but with our limited evolutionary knowledge can we ever truly know? But please strive to have theories and enlighten us, not just Math, as we all want to know. Link to comment Share on other sites More sharing options...

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