# finite/infinite universe

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#### killium

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<p>just a wild running tought i wanted to put on paper, for&nbsp;"peer" review &nbsp;:</p><p>If the universe is finite, meaning that it has a size, and that all that exists is contained "inside", there would be a gravity gradiant everywhere.</p><p>&nbsp;</p><p>Ok, the explanation: Take our planet as an example. If you stand on it's surface, you feel a certain force of gravity (g). If you dig a hole and go to the center, you would then feel 0g. So the gravity field (the actual, localy measured, value of g) changes as you dig deeper. I would think it's the same thing with the universe. If it has a size, and all matter is contained inside it, you would feel more Gs if you get near the "surface" (if we agree that gravity's effect are unlimited in distance and additive, as it is considered the case for now).</p><p>&nbsp;</p><p>So, since we didn't see such a difference in locally measured values of g (remember i'm talking about the entire universe's scale), it implys that the universe is not finite. Unless those measures have been done and they show this and nobody knows why and i'm the one who found it LOL!! .... seriously, where is the flaw in my logic ?</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> </div>

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#### derekmcd

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>just a wild running tought i wanted to put on paper, for&nbsp;"peer" review &nbsp;:If the universe is finite, meaning that it has a size, and that all that exists is contained "inside", there would be a gravity gradiant everywhere.&nbsp;Ok, the explanation: Take our planet as an example. If you stand on it's surface, you feel a certain force of gravity (g). If you dig a hole and go to the center, you would then feel 0g. So the gravity field (the actual, localy measured, value of g) changes as you dig deeper. I would think it's the same thing with the universe. If it has a size, and all matter is contained inside it, you would feel more Gs if you get near the "surface" (if we agree that gravity's effect are unlimited in distance and additive, as it is considered the case for now).&nbsp;So, since we didn't see such a difference in locally measured values of g (remember i'm talking about the entire universe's scale), it implys that the universe is not finite. Unless those measures have been done and they show this and nobody knows why and i'm the one who found it LOL!! .... seriously, where is the flaw in my logic ?&nbsp;&nbsp;&nbsp;&nbsp; <br /> Posted by killium</DIV></p><p>General Relativity describes our universe as a 4 dimensional Lorentzian manifold for which we exist on the surface of this manifold.&nbsp; Much like our fabled ants, there is no center or edge.&nbsp;</p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

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#### why06

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<p>You might be interested in this. A space can be infinite and finite at the same time. Hyperbolic space is a kind of space derived by Poincare in which an inf. number of lines can go through a single point and never cross a line that goes through another point.</p><p>So essentially in this world Euclid's parrallel postulate no longer holds. The reason this is so is because in Hyperbolic space space actuality increases in density along the edges. <br /> <img src="http://sitelife.space.com/ver1.0/Content/images/store/3/11/43ab17f5-457e-44b1-abd6-12e10e36419d.Medium.png" alt="" /><br />Here is a 2-d example of hyperolic space. </p><p>However in are univers such a space would be three dimensional, and ofcourse in three spatial dimension one can have an inf # of lines go through a given point without the need for hyperbolic. </p><p>You might be wondering where Im going with this. I'll tell you that I'm merely giving place to further develop your idea, for as of this moment your logic is unfortunately wrong.</p><p>&nbsp;</p><p>You see even in the center of the earth gravity exists. Just because you might feel no gravity from earth ther is still gravity from mars, the sun, Jupiter, and trillions of other extra-terrestial objects. However the gravity of earth remains it is simply that earth pulls u equally in all directions at once. In other words while the net force of gravity may change the actually force of gravity on earth remains the same. As since this initial statement was ill-concieved u cannot apply it to the entire universe.</p><p>&nbsp;</p><p>It was an interesting idea, and ur logic is correct, but in science there is a term called "parsimony". Parsimony means taking the most economical of simplest way to a desired result. If ur realization can all ready be understood without implying that the universe is infinite then there is no reason to make such a claim. That being said the universe we live in is in a sense finite and inf. It appears most likely that our universe was created some time ago due to indications from the study of Cosmic Microwave Background Radiation in correspondance with the Big Bang Theory. Even so it appears that the galaxies are growing farther from each other. Not only that, but the speed of this seperation is accelerating Faster than the speed of light! So if one were to include the factor of time into this notion it would be impossible to reach some galaxies after a certain point because the Universe would be so far apart that even if one traveled at the fastest possible speed forever these galaxies could still not be reached. That being said I find the idea of a finite Universe much more pleasing than an infinite, but as the way things look we might soon get just what you asked for and the possibility of intergalactic travel would be virtually hopeless without some kind of quantum, tachyon, or hyperspacial drive.</p><p>&nbsp;</p><p>All that being said and you still think ur own to something read: "Euclid's Window" by:Leonard Mlodinow. Its insight on hyperspace might help u reach some sort of epiphany. Here's a question I've always wondered. </p><p><strong>"How can space be finite if that is all the space there is?"&nbsp;&nbsp; </strong></p><p>&nbsp;Maybe you could answer me that question one day. </p> <div class="Discussion_UserSignature"> <div>________________________________________ <br /></div><div><ul><li><font color="#008000"><em>your move...</em></font></li></ul></div> </div>

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#### DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>just a wild running tought i wanted to put on paper, for&nbsp;"peer" review &nbsp;:If the universe is finite, meaning that it has a size, and that all that exists is contained "inside", there would be a gravity gradiant everywhere.&nbsp;Ok, the explanation: Take our planet as an example. If you stand on it's surface, you feel a certain force of gravity (g). If you dig a hole and go to the center, you would then feel 0g. So the gravity field (the actual, localy measured, value of g) changes as you dig deeper. I would think it's the same thing with the universe. If it has a size, and all matter is contained inside it, you would feel more Gs if you get near the "surface" (if we agree that gravity's effect are unlimited in distance and additive, as it is considered the case for now).&nbsp;So, since we didn't see such a difference in locally measured values of g (remember i'm talking about the entire universe's scale), it implys that the universe is not finite. Unless those measures have been done and they show this and nobody knows why and i'm the one who found it LOL!! .... seriously, where is the flaw in my logic ?&nbsp;&nbsp;&nbsp;&nbsp; <br />Posted by killium</DIV></p><p>&nbsp;</p><p>We don't really know if the universe is finite or infinite.&nbsp; But the general theory of relativity is based on the universe being a somewhat complicated object called a 4-dimensional manifold that includes both space and time, space-time.&nbsp; This structure is such that it has no inside and no outside, rather like dereckmd describes the surfact of a balloon, if you imagine that you live on the surface and that there is no inside and no outside.&nbsp; There is also no "center".&nbsp; But it is roughly true that it you were to get away from the immediate vicinity of the earth, the sun and in fact the galaxy and the&nbsp;local group that the universe would look about the same in all directions and as with the earth where at the center the gravity of the sphere "cancels" you would feel essentially no gravity.&nbsp; So your thoughts are not that far off, but the problem is that everywhere is the "center of the universe" so the cancellation takes place wherever you are away from a local concentration of matter.</p><p>The universe is also a manifold without boundary, so there is no "edge" or what you are calling the "surface" of the universe.&nbsp; That is again like the surface of a balloon, pretending that you live only on the surface and that the interior does not exist (we can't draw 4-dimensional manifolds very well so we use the surface of a balloon which is a 2-manifold to illustrate).</p><p>We don't know what that manifold actually looks like and there are several possibilities.&nbsp; Mathematicians are aware of several different types of 4-manifolds and they have different properties.&nbsp; One of those properties is curvature, and there are different types of curvature.&nbsp; Some of those manifolds are infinite in extent, called "open" in mathematical terminology.&nbsp; Some of them are finite, call "compact" and since there is no boundary they are also called "closed".&nbsp; If the curvature of space (Gaussian curvature) is positive then space will be finite.&nbsp; If it is zero it will be a flat Euclidean space in the large.&nbsp; If it is negative it will probably also be infinite, but there are closed manifolds of negative curvature.</p><p>So your thought is a good one, but the problem gets tangled up in some advanced mathematics that describes the potential geometry of the universe.&nbsp; It is not the same kind of geometry that you are used to and that you may have seen in high school or even in most university classes.&nbsp; It is a complicated non-Euclidean geometry that requires some very complicated mathematics to describe.</p><p>Many cosmologists would bet that you are correct and the universe is infinite.&nbsp; Most would bet that the curvature is zero.&nbsp; Some, Roger Penrose among them (and he an extremely bright expert in general relativity would bet that the universe has negative curvature and is infinite.&nbsp; But nobody really knows.</p><p>Here is some food for thought.&nbsp; If you run general relativity in reverse you predict that the universe started as a single point in the Big Bang.&nbsp; Now, this is really a breakdown in the ability of the theory to handle gravity and quantum&nbsp;effects at the same time and theorists will tell you that.&nbsp; But in any case the theory predicts that the universe began as a very very compact object.&nbsp; Now somehow that compact object&nbsp;has expanded to become the universe that we see today. And that universe may well be infinite in extent.&nbsp; But the theory says it was not that way at time 0.&nbsp; So in a finite amount of time the universe has gone from being finite in extent to infinite in extent.&nbsp; It is possible to describe this mathematically and in fact is not that hard to do.&nbsp;(For the mathematically inclined this is just exhibiting that Euclidean space is contractible in the sense of homotopy). &nbsp;I can do it, but it is really hard to get my head around that idea from a physical point of view, and I certainly don't know if that mathematics reflects what actually happened in any way.&nbsp; </p> <div class="Discussion_UserSignature"> </div>

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#### killium

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<p>"You see even in the center of the earth gravity exists. Just because you might feel no gravity from earth ther is still gravity from mars, the sun, Jupiter, and trillions of other extra-terrestial objects. However the gravity of earth remains it is simply that earth pulls u equally in all directions at once. In other words while the net force of gravity may change the actually force of gravity on earth remains the same. As since this initial statement was ill-concieved u cannot apply it to the entire universe."</p><p>&nbsp;</p><p>I used the earth's center gravity as an example for the whole universe. In my example, the earth represents the whole universe so there is nothing outside of earth, no mars, no sun, no jupiter etc.... If earth was all that there is and you&nbsp;were "living" inside it, by measuring the relative values of g at different places, you would be able to mathematically deduced the earth's shape (oh!, i'm inside a sphere ....). (and a by-effect would be that the more you near the edge, the more it would be difficult to go farther...).</p> <div class="Discussion_UserSignature"> </div>

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#### bzannone

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>You might be interested in this. A space can be infinite and finite at the same time. Hyperbolic space is a kind of space derived by Poincare in which an inf. number of lines can go through a single point and never cross a line that goes through another point.So essentially in this world Euclid's parrallel postulate no longer holds. The reason this is so is because in Hyperbolic space space actuality increases in density along the edges. Here is a 2-d example of hyperolic space. However in are univers such a space would be three dimensional, and ofcourse in three spatial dimension one can have an inf # of lines go through a given point without the need for hyperbolic. You might be wondering where Im going with this. I'll tell you that I'm merely giving place to further develop your idea, for as of this moment your logic is unfortunately wrong.&nbsp;You see even in the center of the earth gravity exists. Just because you might feel no gravity from earth ther is still gravity from mars, the sun, Jupiter, and trillions of other extra-terrestial objects. However the gravity of earth remains it is simply that earth pulls u equally in all directions at once. In other words while the net force of gravity may change the actually force of gravity on earth remains the same. As since this initial statement was ill-concieved u cannot apply it to the entire universe.&nbsp;It was an interesting idea, and ur logic is correct, but in science there is a term called "parsimony". Parsimony means taking the most economical of simplest way to a desired result. If ur realization can all ready be understood without implying that the universe is infinite then there is no reason to make such a claim. That being said the universe we live in is in a sense finite and inf. It appears most likely that our universe was created some time ago due to indications from the study of Cosmic Microwave Background Radiation in correspondance with the Big Bang Theory. Even so it appears that the galaxies are growing farther from each other. Not only that, but the speed of this seperation is accelerating Faster than the speed of light! So if one were to include the factor of time into this notion it would be impossible to reach some galaxies after a certain point because the Universe would be so far apart that even if one traveled at the fastest possible speed forever these galaxies could still not be reached. That being said I find the idea of a finite Universe much more pleasing than an infinite, but as the way things look we might soon get just what you asked for and the possibility of intergalactic travel would be virtually hopeless without some kind of quantum, tachyon, or hyperspacial drive.&nbsp;All that being said and you still think ur own to something read: "Euclid's Window" by:Leonard Mlodinow. Its insight on hyperspace might help u reach some sort of epiphany. Here's a question I've always wondered. "How can space be finite if that is all the space there is?"&nbsp;&nbsp; &nbsp;Maybe you could answer me that question one day. <br />Posted by why06</DIV><br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A couple of questions arising from the above post. Forgive my ignorance as I am only semi educated. The Big Bang, CMB and uniform expansion of the cosmos are ideas I am familiar with, and are all straightforward enough to grasp. However, if the universe is expanding radially from a central event with the same initial force in all directions (ala "big bang") and there is evidence of expansion via the observation that distances between galaxies is increasing ( a concept I thought was accepted as fact long ago) then how is it possible that galaxies are colliding every where we look? Furthermore, if what was stated above is correct, that the rate of expansion is greater than the speed of light, isn't it possible we&nbsp;are observing our own galaxy at different points along its route within this expansion? Any reply is appreciated. Thank you.</p>

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#### DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A couple of questions arising from the above post. Forgive my ignorance as I am only semi educated. The Big Bang, CMB and uniform expansion of the cosmos are ideas I am familiar with, and are all straightforward enough to grasp. However, if the universe is expanding radially from a central event with the same initial force in all directions (ala "big bang") and there is evidence of expansion via the observation that distances between galaxies is increasing ( a concept I thought was accepted as fact long ago) then how is it possible that galaxies are colliding every where we look? Furthermore, if what was stated above is correct, that the rate of expansion is greater than the speed of light, isn't it possible we&nbsp;are observing our own galaxy at different points along its route within this expansion? Any reply is appreciated. Thank you. <br />Posted by bzannone</DIV></p><p>The universe is not expanding radially froma central point.&nbsp; What is occurring is an expansion of space itself, and there is no central point.&nbsp;&nbsp; </p><p>Back to the balloon analogy.&nbsp; Imagine two things:&nbsp; 1) most importantly imagine that the <strong>surface</strong> of the bqlloon is the universe.&nbsp; The universe is all that there is and in&nbsp;this analogy the surface of the balloon is also all that there is.&nbsp; You are a 2-dimensinal being in this analogy and the "interior" of the balloon does not exist, only the surface.&nbsp; The balloon surface is meant to represent the full 4-dimensional space-time.&nbsp; 2)&nbsp; Now imagine that the balloon is being inflated and expanding.&nbsp; On the surface of the balloon all points move away from one another, and the rate at which they recede is proportional to the distance separating them,&nbsp; There is no central point (on the balloon) from which everything is radially expanding.&nbsp; In fact, there is no radial direction at all on the surface of the balloon.</p><p><br /><br />&nbsp;</p> <div class="Discussion_UserSignature"> </div>

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#### weeman

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>just a wild running tought i wanted to put on paper, for&nbsp;"peer" review &nbsp;:If the universe is finite, meaning that it has a size, and that all that exists is contained "inside", there would be a gravity gradiant everywhere.&nbsp;Ok, the explanation: Take our planet as an example. If you stand on it's surface, you feel a certain force of gravity (g). If you dig a hole and go to the center, you would then feel 0g. So the gravity field (the actual, localy measured, value of g) changes as you dig deeper. I would think it's the same thing with the universe. If it has a size, and all matter is contained inside it, you would feel more Gs if you get near the "surface" (if we agree that gravity's effect are unlimited in distance and additive, as it is considered the case for now).&nbsp;So, since we didn't see such a difference in locally measured values of g (remember i'm talking about the entire universe's scale), it implys that the universe is not finite. Unless those measures have been done and they show this and nobody knows why and i'm the one who found it LOL!! .... seriously, where is the flaw in my logic ?&nbsp;&nbsp;&nbsp;&nbsp; <br />Posted by killium</DIV><br /><br />The flaw in your logic is that you are using the dynamics of Earth's gravitational field to help visualize an otherwise finite universe. Remember, Einstein once stated that, "the universe is finite, but unbounded." What he was saying is that the universe is finite in age and matter, yet it has no boundries and it has no edge. Furthermore, the way I take it,&nbsp;is if you could hypothetically fly around the universe and count every single galaxy,&nbsp;you would find that you would start counting galaxies that you've already counted, coming to the conclusion that you've circumnavigated the entire universe without hitting any kind of physical/imaginary barrier.&nbsp;</p><p>So, you would then realize that the universe has no center. From there,&nbsp;you could further calculate that trying to find a suitable gravitational gradient would be impossible, since there is no single point to start from. &nbsp;</p><p>Many astrophysicists will argue that the universe doesn't expand into anything other than itself. There is nothing that it is expanding into, it's simply just expanding. </p><p>So, IMO, using Earth's gravitational field, and trying to apply it to the bigger picture, is where you're hitting a road block in your logic </p> <div class="Discussion_UserSignature"> <p> </p><p><strong><font color="#ff0000">Techies: We do it in the dark. </font></strong></p><p><font color="#0000ff"><strong>"Put your hand on a stove for a minute and it seems like an hour. Sit with that special girl for an hour and it seems like a minute. That's relativity.</strong><strong>" -Albert Einstein </strong></font></p> </div>

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