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Expanding space

  1. Feb 26, 2004 #1


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    There is some discussion about the expansion "of space" in a thread that actually belongs to a different topic so I thought I'd start a thread about that with my input here. Consider the Robertson Walker metric in the following form
    [tex]ds^2 = dct^2 - \frac{R^2}{R_{0}^2}\frac{d\rho ^2 + \rho^2 (d\theta ^2 + sin^{2}\theta d\phi ^2)}{(1 + \frac{1}{4}k(\frac{\rho}{R_{0}})^2)^2}[/tex]
    Where R is a function of t. This metric represents the expanding universe and specifically what is expanding is the R term. If k = + 1 then the universe is positively closed curved and spacelike hypersurfaces can be taken from this spacetime that are conceivable as balloon like spheres embedded within a hyperspace where R would be the radius of the surface and would then have the interpretation of being the radius of the universe. So, when one talks of the radius of the universe or of the universe as expanding then it is this term changing in time that is being referred to. Some people more convinced that the universe is open curved don't like to think of the universe as having a radius and so call R by scale factor or whatever, but even then R still has the interpretation of the "radius of curvature" of the universe. It is still this radius of curvature that is actually expanding. Now the positions of comoving galaxies are constant with respect to the choice of coordinates expressed in this metric. Their coordinate velocities are zero. The fact that we observe them to be separating is because we are using a rigid ruler extension so to speed of local Cartesian coordinates to describe them instead of the choice of coordinates expressed in this metric. In a sufficiently local limit their rigid ruler velocities are related to the Doppler shift we see by the same formula that gives special relativistic Doppler shifts. So, in a sufficiently local limit saying the galaxies are stationary with respect to a coordinate frame according to which space itself is expanding is equivalent to saying that the galaxies are moving with respect to another coordinate frame according to which space is static. However when one considers the global behavior of the metric and the galaxies one can no longer use the special relativistic Doppler formula, nor the special relativistic metric. One instead finds that the metric in a global description is dynamic according to every frame and so globally speaking it is expanding space and not galaxies separating within space that is the accurate description.
    Last edited: Feb 26, 2004
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  3. Feb 26, 2004 #2
    Yes - that is the exact conclusion arrived at by Robertson - so what is the issue
  4. Feb 26, 2004 #3


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    In the abberation thread David was saying that no papers are saying that it is space expanding. I am pointing out that this is exactly what is being said.
  5. Feb 26, 2004 #4
    oh - ok DW - sorry - I didn't look into the history of the post - quite right
  6. Feb 27, 2004 #5
    Saying that the distant galaxies “aren’t really moving”, is like saying that the galaxies are “stationary” relative to themselves. Everybody already knows that. Just like parked cars in a parking lot are stationary relative to themselves, as the parking lot moves around the sun at 18.6 mps and around the center of our galaxy at 250 mps and through space at whatever.

    Now take a group of parked cars on a barge. The barge starts to move in the ocean, and so all of that “local group” of cars starts to move through space. That doesn’t mean “space is expanding”, it means all the cars are moving together. Their distances from the parked cars on land is growing, because the cars on the barge are moving through space.

    You seem to assume that our physical universe of galaxies has a boundary beyond which there is a big spherical brick wall, and behind that wall is “no-space”, and you assume that “expanding space” is pushing that brick wall further away from us and is inventing space as the universe expands.

    All you have in your growing radius is the expanding radius of a spherical 3-D universe of expanding matter, that is moving through space as it expands. This is the “big bang” theory.
  7. Feb 27, 2004 #6
    The Robertson-Walker metric describes the expansion of the physical matter in the universe, galaxies separating and moving apart, not the “expansion of space”. His so-called “radius of curvature of curved space” is the radius of the presumed spherical collection of galaxies that are moving apart. The universe of physical galaxies that we see is assumed to be spherical in shape, something like a spherical star-burst fireworks explosion. The galaxies are moving through space. We can say that “the space in between the galaxies is expanding”, but what that really means is the distance between the galaxies is expanding, because the galaxies are moving through greater space. Look at a spherical fireworks explosion. You can say that the “space” in between the glowing particles is “expanding”, but all you are really saying is the distance between the particles is expanding as the particle move through space. Thus, all of “space” is not just what we see in-between the galaxies, inside the spherical radius of the expanding collection of galaxies, but greater space, deeper space, more distant space, is also what the galaxies are moving into as they move apart.

    To say that the space inside our universe is truly expanding, you’d have to show us the outermost galaxies of the expanding sphere, and you’d have to show us a big wall, beyond which there is nothing, not even space, and you’d have to show us that that wall is moving outward and away from us. Then you could say our “space is expanding” if you can prove that beyond the most distant galaxies there is some kind of solid wall and beyond it lies “no-space” at all.
  8. Feb 27, 2004 #7
    I said there are no papers that give us a physical mechanism and a physical description of how “space” itself can “expand”.

    When things move apart, the distance between them expands, but you can’t say the “space” in between them expands. They are merely moving into deeper space, and thus there is more space between us and them, but that doesn’t mean that its the space in between us that is expanding. The objects are just moving through space, that’s all. How complex is that to understand?
  9. Feb 27, 2004 #8
    David - your view is contrary to all interpretations of the metric - if you step down one dimension to a two sphere as the surface of an inflating balloon, dots placed on the balloon will recede from one another - all points on the surface can be described in terms of coordinates defined by the surface - or perhaps better said - the coordinates that define every point need not be related to the center of the balloon or any third dimension - you do not have to consider the balloon a two dimensional surface embedded in a three dimensional space - everything is contained in the metric that defines the surface - there is no volume to consider - the balloon surface is not expanding into something - it is all there is - there ain't no third dimension necessary to regard the expansion as "expanding into" Same is true for the 3d universe - there is no space into which expansion is progressing - it is the existing space that is strething just as the existing surface of the balloon stretches when it is inflated - that is the beauty of the metric description
  10. Feb 27, 2004 #9


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    David - I suppose you reject the idea that infinite (or at least boundless) space can expand. That is part of Big Bang Theory.

    Your idea would require that we see galaxies moving away from a central point. That is not the case.
  11. Feb 27, 2004 #10


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    Yeah, we discussed that in one of the other threads. David is not bothered by our lack of ability to see the edge (or in fact see any evidence that the universe isn't roughly homogeneous on the huge scale). Somehow he sees no problem with assuming the existence of something for which there is no evidence, simply because the alternative is in his words "silly."
  12. Feb 27, 2004 #11
    Hey, I’ve got Eddington’s original 1932 book in which he invents the “balloon” analogy. He says we live inside the rubber skin of the balloon! LOL! Some of you guys will fall for anything!

    Look, contrary to popular belief, we do not live on the “surface” of an “expanding balloon”. We live inside what appears to be an expanding Euclidean sphere galaxies. We do not live inside the rubber “skin” of a balloon. We do not live on the “surface” of our universe, we live inside it.
  13. Feb 27, 2004 #12


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    It's an analogy...a simple way to think about a complex idea. No one is saying that is how it actually is.

    No, that would imply a common origin point of the expansion. That does not appear to be the case.

    Again, it's just an analogy.
    There's also the "raison bread" analogy, but even that falls short of perfection because you can still see a center and edge, which is not what Big Bang Theory describes.
  14. Feb 27, 2004 #13
    In the 1960s, ‘70s, ‘80s, and ‘90s, the “big bang” theory discussed a specific “point of origin”. I talked to professional astronomers in the ‘90s who discussed a specific “point of origin”. When I interviewed Dr. Robert Jastrow, he specifically told me he thought the “point” was originally about the size of a “basketball”. Eddington in 1932 said he thought it was bigger than that, but something like a small sphere of galaxies. Lemaitre’s original 1927 paper had it as a “point”, what he called a “primordial atom” that sort of exploded outwards. So, all of that describes an expanding spherical universe of matter that is moving apart. When I’ve got professional astronomers from Mt. Wilson and Harvard and other places telling me in the ‘90s it was originally a “point” or a “basketball” sized thing, Ok, so I’ll accept that, as a tentative theory. I didn’t invent that idea, they did.

    If you want to call it an “expanding balloon surface” or a “loaf of raisin bread” or “not quite like that” or “something similar but not really like that” or “there is no way to explain it”, ok, then that’s your opinion. I express my opinion and you express yours.

    Is our universe really like any of that? I don’t know. You don’t know. Nobody knows. All of us are just speculating. Face it, human beings on earth today are free to speculate, muse, think, and express their own opinions in most countries. That’s all I am doing.

    Maybe the galaxies really aren’t moving. Maybe the redshifts are due to the Compton effect or something else. I don’t know, you don’t know, and nobody knows for sure.

    Look, only in Fascist and Communist countries (and a few others) are people required to all think alike and all support exactly the same science theories that are approved by their dictators or their governments. We don’t live in that kind of country. So ease up.
  15. Feb 27, 2004 #14
    There is no requirement that everyone think alike - what the members of PF are doing is attempting to convey a concept - we use the 2 sphere analogy because it is something we can all visualize. But we cannot visualize a three sphere embedded in a forth spatial dimension - but we can extrapolate from two dimensions to what three dimensional expansion involves mathematically.

    PS ... I have some of Eddington's original publications also - you have misinterpreted what is being said by the authorities - I do not believe that any of the authorities you mentioned would ratify the interpretation you have put upon their statements.

    That is ok - again, you are free to misinterpret things in the light of your own convictions - God knows we have all been guilty of that. I suggest, however, that if you really think about the issue objectively rather than defensively, much will be revealed.

    Its ok to be wrong sometimes - Once when Lincoln was accused of doing an about face he commented: "I don't think much of a man who isn't smatter today than he was yesterday."
  16. Feb 27, 2004 #15
    Where is the observational evidence that the universe has 4 dimensions of space?

    What the observational evidence reveals is us inside a 3 dimensional universe in which the distant galaxies are moving apart with time. What does a 4th spatial dimension have to do with this?

    Why are you trying to convey a certain “concept” about the universe, and exactly what is that concept?
  17. Feb 28, 2004 #16
    There is no evidence of a forth dimension per se - but if you ask questions like what exists beyond the 3 dimensional expanding universe - or alternatively, what is our three dimensional sphere expanding into - you imply the existence of a 4th dimension in which the bounded three sphere is embedded. But if you say the three dimensional Hubble sphere is all there is, then the RW metric totally describes the universe as a three dimensional surface without reference to anything beyond.

    Think about how a two dimensional being on the balloon would describe his universe - there is no center to the 2 sphere - no volume - no interior and nothing exterior ... the surface is all there is - and it can grow larger unto itself - one can always argue that a two sphere requires a three dimensional embedding-space - and that is of course the real world because we don't have a two dimensional laboratory in which to construct two dimensional cosmological models. Every real two sphere can only exist in three dimensions, but the address of any point on the sphere relative to any other only requires a 2 dimensional coordinate groundform.
  18. Feb 28, 2004 #17

    Whatever is “beyond” our own outer-most galaxies (assuming there are outer-most galaxies in our system) could very well be more “empty space”. In fact, for all we know, there could be dozens of other physical universes also expanding spherically into greater “empty space”. There is no need to evoke a 4th dimension of space.

    Of course we can not see beyond the radius of our own current sphere of observation, but anyone at all should be free to speculate about what is out beyond what we can now see. I don’t understand why there must be some kind of formal “official” view about what might be out there. If science adopts a rigid “official view” about anything, that discourages speculation and creative thinking. It discourages imagination and discovery. It discourages new ideas in science. It makes everyone have to conform to an “official” point of view, just as people in Europe had to conform to the church’s “official” point of view back in the middle-ages.

    Geez! We are not two dimensional beings living on the surface of a sphere!
  19. Feb 28, 2004 #18
    I fully agree with your philosophy about conformity - a bit of a rebel myself - but there are some interesting differences that arise between the notion of an exterior space into which the galaxies are moving, and a finite space that is swelling - one concerns how or why the totality of cosmic energy can be zero, another concerns the notion of whether the properties of the vacuum can be explained by expansion, another involves how matter might be created from the notion of an expanding false vacuum (inflation either previously or contiuing) ...or why the velocity of light has the value it does, or how a transverse wave can exist in medium (this can happen if the medium is under tension i.e., a false vacuum). In other words, if space is just a static nothing that has existed eternally, we forfeit perhaps some opportunity of relating certain cosmological mysteries to known physics. In my opinion, physics has already boxed itself in with ideas like "Planck units" and other common assertions expressly or impliedly endorsed by all present writers - the notion of a dynamic expanding medium leads to a lot of answers as to why things have the value they do. Interestingly, the notion of expansion does not necessarily imply a finite age for the universe.

    As for the two dimensional sphere to which I referred - it is only metaphorical - but if a two dimensional universe can be finite, so also can a three dimension universe - we can't visulaise it any more than the two dimensional being can comprehend up or down on this balloon universe - but he could write an equation that would be descriptive of its finite-ness ....as we can with the RW metric
  20. Feb 28, 2004 #19
    Tell me a little more about this “expanding medium” and the “tension” in it. Lorentz wrote something about “tensions” in the medium in his 1895 book. He called it “Spannungen im Aether”.
  21. Feb 28, 2004 #20
    Back to you David: There are a number of ways of modeling a medium in tension - one simple picture is to consider space as a plenum of three dimensional vortices - for an example of something we already know of, consider the neutrino - nearly massless, yet it carries an angular momentum h bar/2 (same as proton, electon etc) - so the angular momentum cannot be tied to any particular mass, but rather to a spatial vortex ... now vorticies exist because the pressure is less in the center - so space might be considered a sea of quasi-static neutrinos - each having a center of negative pressure - ergo there is a tension between adjacent vortices - when space expands the tension is increased.. if you consider a filament of space under tension, and you know the average cosmic density per unit length (consider the universe as having a critical mass), you can apply the classical formula for the velocity of a wave in a stretched string under tension. Using Newton's formula for the reactionary force developed by the expansion of a uniform sphere, and a gausses law, you have all that is needed to calculate the free space velocity of a wave - not surprisingly it is c
  22. Feb 28, 2004 #21
    Ok, very good. Excellent. I’ve copied that, and I’ll go over it and study it. This is some of the best information I’ve gotten in the past few years. Thanks.

    Now, tell me, how does a gravity field fit into this? A field near the surface of an astronomical body, field areas of deep space in-between bodies within galaxies, and field areas in-between the galaxies? I haven’t been able to find out much information about this. How do these gravity fields fit into the “medium in tension” idea?
  23. Feb 28, 2004 #22
    One of the interesting aspects of expansion is that it can be related to the magnitude of the gravitatinal field. o- take the Hubble radius as R and assume it is distending at the rate c - now the volume V of this sphere is (4/3)(pi)(R^3), and this volume is changing at the rate of dV/dt = (4)(pi)R^2)dR/dt but dR/dt = c so the rate of volumetric growth is [4(pi)R^2]c and if you differentiate one more time the rate of volumetric acceleration is 8(pi)Rc^2 if the radial expansion remains constant. Now for a critical density universe, the rate of expansion should slow (ignoring the interpretation put upon the 1a supernova data). So there is a variable "c" term where c here represents the expansion rate which incidentally is the same as the velocity of light in a vacuum. When you factor in the slowing for a critical density universe (q = 1/2), the volumetric acceleration is reduced. Without going throuth all the math, what is sometimes overlooked is that the volume of the Hubble sphere is accelerating when the the radial rate of grown is constant. Now I don't know where you math level is, but there is theorem do to Gauss call the divergence theorem - and it allows you to transform the total volumetic acceleration to a surface integral - it basically says if you sum the total volumetric acceleration it will be equal to the integral of the normal component over the surface - but for a sphere the surface area is 4(pi)R^2 --- so the normal component is obtained by dividing the volume integral by the surface area. What results after you factor in in the slowing is value for G.
  24. Feb 28, 2004 #23
    Opps - somehow hit the post key by mistake and before finishing and reviewing - anyway, note the units of G (vol acceleration per unit mass) .. what is accelerating is the rate at which volume is created by expansion - a constant Hubble rate c gives rise to a value that corresponds to G if H is 42 ... but a critical density universe leads to a correlation that corresponds to H = 57. Since we do not have a perfect model for the universe, we cannot say whether the theory is worth while - but it leads to numbers that are within the limits of the excepted value for H
  25. Feb 29, 2004 #24
    I’ll accept that statement about the “volume” 100%. That is quite different from saying, “space is expanding”. I have no problem with an expanding “volume” because that is what we actually observe.

    The big question is, where is the “space” of that increasing “volume” coming from? Seems to me that the way you’ve explained it and your own point of view is that this “volume” is just sort of somehow being “created” within our physical universe, as the universe expands. My point of view is that the “volume” could already be out there in deep space, it could exist outside our known physical universe, assuming there is an ultimate spherical “boundary” of “most distant galaxies” out in deep space, beyond which there are no more of our own galaxies, and it seems to me that some of the “greater volume”, ie the “space” beyond that “boundary” (if there is one) gradually becomes part of our own physical universe as the distant galaxies move deeper and deeper into it, and as the “spatial volume” inside our own physical universe increases.

    I think probably that we would both be speculating as to whether or not their might be a “boundary”, so I think we’ll just have to guess about that. My opinion that there might be a boundary (an outer limit to the physical galaxies), comes from what I’ve been told by astronomers about the universe being less than about 15 billion years old and originally, perhaps, starting out from a “point”, and then expanding from that. Unless the outermost galaxies are traveling at an infinite speed, then it seems there must be a boundary out there somewhere, even though we can’t see it yet. In fact, there were some articles written in the early 1990s, and some mentions made in astronomy textbooks, that astronomers had already seen “95% of the time and distance back to the big bang,”(looking from the inside out, of course), so in my mind, that left only 5% more distance to the outer “boundary”, the outermost galaxies. This would have given our physical universe a total visual radius of about 15 billion light years, with us being able to see out to a distance of about 13-14 billion light years distance in the early 1990s.

    But after the Hubble telescope went up and was fixed, all it could photograph was more galaxies in the distance, but no boundary. So I don’t know if there is one or not.

    And I’m not interested in the “center” of the universe issue, so I’m not trying to prove that we are in the center. I don’t care where we are within our universe. But it does seem to me that this “visual center” problem does worry some astronomers, since, based on the laws of chance, we shouldn’t be anywhere near a physical “center”. So let’s just not worry about the “center” problem. If we are inside a spherical expanding physical universe, let’s just say we are not anywhere near a possible “center” of it.

    Maybe you can explain to me why such a condition as a boundary and “empty space” beyond the boundary could not, or “should not”, exist, and why our most distant galaxies could not be moving into that “empty” space, thereby increasing the “volume” of space that is contained within our own universe of galaxies.

    The reason I’m asking you so many questions is because I can not find your kind of straightforward answers in books or on websites, and I can’t get them from professors on the internet. All I get are the standard clichés and the same repeated phrases over and over again, with no detailed explanations or personal opinions. This is what makes me so angry when I just keep hearing the phrases “space is expanding” and “think of two-dimensional creatures on the surface of a balloon.” Those phrases tell me nothing at all that I can’t get out of Eddington’s 1933 book.

    I have consistently asked different professors for years why our most distant galaxies (the ones we can not yet see) could not be moving into deeper space that lies beyond them, and I’ve gotten no real answers at all, just a bunch of double-talk. It’s as if they have never even thought of that idea before and they don’t know how to answer it. So maybe you can answer the question for me, and if so I will accept it as your own personal opinion. Even if you have to guess at an answer, that’s ok, because I’m guessing that there is a “boundary” of “most distant galaxies” out there somewhere. I do appreciate your answers very much. And thanks for leaving out the math equations. I don’t need them. All I need are the results. I’ll trust your proficiency at working out the equations accurately.
  26. Feb 29, 2004 #25
    Hi David

    I can totally relate to your frustration - seems that most of the so called experts are of the same mold - and I certainly cannot fault you for asking the same questions I myself have struggled with. If I am correct, I think the first attitutude's on expansion were essentially those you have expressed - galaxies moving through an unlimited space with the limit of observeability bing the 15 billion light year of the Hubble sphere. I do not know of any experimental proof that invalidates your ideas - and it is natural to rationalize that there must be something beyond - the reason for the ballon analogy is that it makes it possible to visualize the topology that results if you take a two dimensional flat sheet and bent it into a sphere - it can still be described topologically with only two dimensions - a two dimensional metric so to speak - and you will say - but what about the space encompassed and that outside the surface - and the answer you get is it doesn't have any mathematical necessity or significance - everything is contained in the surface!

    Now the interesting thing about this is that the two sphere surface is finite but unbounded (you have heard that before I am sure) - if this surface is all there is, the dots on the surface cannot be moving away from each other in every direction because they will crowd up somwhere assuming they were uniformly distributed at some point - so the only way they can spread out is if the two dimensional surface dilates - it is this idea of cosmological uniformity (isotropic and homogenous) that is foundational to modern ideas - otherwise we would have to postulate an infinite space into which the galaxies are drifting or a concentration of galaxies within the Hubble sphere and none beyond - all of which implies some center. So to avoid these consequences, we consider the universe as a three dimensional surface (cannot be visualilized but easily treatable mathematically) that contains all there is - and in order for the nebula to be separating - this three dimensional surface must be enlarging,

    One book that deals fairly and with almost a complete absense of dogma regarding the various models of the universe is Ed Harrison's book "Cosmology" The science of the universe. It is a little out of date (pub about 1990) as to some of what we think we know now? but in terms of explanation and fair treatment, it is the best book that can be bought, borrowed or stolen on the subjects that are frequently discussed on these forums. Also see http://cosmicgravity.com
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