Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How can empty space expand? (Reality behind the GR equations.)

  1. Jul 8, 2007 #1
    How can "empty space" expand? (Reality behind the GR equations.)

    I have a question - with some concerns over how it may be answered. On other websites, and in other print publications, I've seen Ph.D. physicists and cosmologists misunderstand the question: What does it mean when we say that empty "space" is expanding?

    Yes, I know that "space is expanding". We see this when we look at the motion of distant galaxies. We see this expansion modeled - predicted, even - in General Relativity (GR). Expansion of "empty space" is the basis of the Big Bang theory. GR mathematically models the expansion of empty space.

    Yes, I know that only the space between distance galaxies is expanding, not the size of the galaxies themselves. The size of stars and atoms is constant. The expansion of the universe only involves the space between very distant objects, and not the objects themselves.

    But what is the ontological reality that causes this to occur?

    Most books and websites dodge the issue. :grumpy: They simply state that space is described as a metric, and a metric can expand without objects in it. Yet that isn't an answer. The metric is not space itself! The metric is only a coordinate system that we use. The "metric" is no more real than "F = ma". It is a relationship and a mathematical tool.

    The question I'm after is this: What is the physical reality that causes this? :confused:

    Correct me if I am mistaken, but Einstein's theory of general relativity (hence, GR) doesn't address this issue. His equations predict the relationship between matter, energy and the path that matter will follow in a curved space. The equations create a coordinate system that is "stretchy". From a conceptual point of view, it is a tremendous advance over the Newtonian conception of space and gravity, and it actually answers the question "How does gravity work?" Wonderful! o:)

    But we now should be allowed to ask a deeper question: What is it about space that is expanding? How can empty space "expand", or have any properties at all? This isn't answered by GR; it only described.

    So what is the physical reality that lies behind the statement that the metric of space itself is expanding? I know that we don't have firm answers yet, but I'd like to know the current range of ideas. (If I understand correctly, the properties of space described by GR may actually be caused by various quantum effects, the foaming sea of virtual partices that exists even in empty space.)

    Any responses would be much appreciated! If this specific issue is addressed in some previous thread, then by all means please let me know the appropriate link.


  2. jcsd
  3. Jul 8, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It means that if we were to put a small cloud of noninteracting dust into that region of space-time, it would expand.
  4. Jul 8, 2007 #3

    Have a read of

    Expanding Space: the Root of all Evil?
    Authors: Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis
    (Submitted on 3 Jul 2007)

    Abstract: While it remains the staple of virtually all cosmological teaching, the concept of expanding space in explaining the increasing separation of galaxies has recently come under fire as a dangerous idea whose application leads to the development of confusion and the establishment of misconceptions. In this paper, we develop a notion of expanding space that is completely valid as a framework for the description of the evolution of the universe and whose application allows an intuitive understanding of the influence of universal expansion. We also demonstrate how arguments against the concept in general have failed thus far, as they imbue expanding space with physical properties not consistent with the expectations of general relativity.
  5. Jul 9, 2007 #4


    User Avatar
    Science Advisor
    Gold Member

    As discussed here.

    They are making a very subtle point, if we talk about something such as "expanding space" we have to be careful how we measure and test such a concept. The only way would be to fill space with non-interacting dust and watch how the dust particles move, as Hurkyl said above.

    Cosmology treats distant galaxies as 'non-interacting dust particles ' on the grandest scale.

    To demonstrate, others (Fred Hoyle, Jayant Narlikar) have suggested in a mass field theory that it might not be space that is expanding but rulers that shrink...

    That is why I say that you first have to define a steel ruler as your measure of distance (i.e. the diameter of an atom) and then you can say that the universe, as measured by the ruler, is expanding around it.

    Instead if you took the wavelength of a photon, sampled from the intensity peak of the CMB, as your length measure then the universe would be static and not expand, because a photon 'expands with the universe'.

    It depends on how you measure it.

    Last edited: Jul 9, 2007
  6. Jul 9, 2007 #5
    So far no one seems to have even understood my question. This is quite distressing, and unfortunately quite common. Please re-read my initial question; you are doing the same thing that other people do - you are answering a different question than the one being asked!

    Hurkyl writes "It means that if we were to put a small cloud of noninteracting dust into that region of space-time, it would expand." True, but WHY would it expand? What physical process is causing this to occur in the first place?!

    In another discussion on this same topic, Garth writes: "The distance between a distant source and ourselves, as measured by metre steel rulers, increases with time, and the rate of increase of that distance may be described as a 'velocity'. However, as we agree, this velocity is due to the expansion of space itself, not to any proper motion within that space. So long that is clear all is well."

    But this is not clear! The question is this: *Why* does this phenomenon occur?

    I do appreciate their link to a relevant paper, "Expanding Space: The Root of All Evil", by Francis et al. These authors actually understand my question, and bravely confront the many physicists who use the phrase "Expanding space" without even taking the time to think about what this phrase really means.

    However, I am having some trouble understanding their paper. What do they mean by COSMOLOGICAL FLUIDS? I can't begin to understand what this means. Is this a poetic reference to the quantum virtual background of empty space (a background that is ignored by Einsteinian General Relativity)? Or do they mean something else by it? Without understanding their terminology I cannot follow their argument.

    Here is an example of the text I find incomprehensible (at least, without clarification of the phrase.)

    "...the continuity equation demonstrates that in other than finely-tuned or contrived examples, the density and pressures of COSMOLOGICAL FLUIDS must change over cosmic time, and it is this change that represents the basic property of an expanding (or contracting) universe. The general relativistic picture also allows the definition of privileged, co-moving observers...within the expanding universe, those at rest with respect to the COSMOLOGICAL FLUIDS; in our Universe, we know we are not one of these privileged observers as our measured CMB dipole reveals our peculiar motion with respect to the background photons. Being at rest with regards to the COSMIC FLUID...

    Additional responses to my questions are appreciated.

  7. Jul 9, 2007 #6
    How can "empty space" expand? Unfortunate choice of words leads to misconceptions

    Marcus, I found this quote of yours on the meaning of "expanding space". You recognize that this expression is a loose way of phrasing a change in distance. You write:

    "BTW Wallace does it help if one focuses on the idea of distances increasing rather than space expanding---to get people's minds away from the raisin-dough or stretchy-rubber idea? It could be that "space expands" is an unfortunate popularization choice of words because space is not a substance that can expand. Ontologically, all we have is the metric or an equivalence class thereof----namely the gravitational field itself---so we don't have some kind of material medium that can expand. All we have is distance and at least for now it happens to be increasing...."

    In my question here I try to make this same point. When Newton said that gravity is a "force", he also asked why this force exists. How is it that one object attracts another through space? Newton admitted that he had no answer, but his honesty lies in admitting that the question itself can be asked. When Einstein came up with General Relativity, he actually answered Newton's question: Einstein showed what gravity really was, how it worked. (And also showed that Newton's laws were an approximation to a much more sophisticated model.)

    GR shows us that "space expands", iow the distance between objects expands, and for far away objects this increase in distance can be superluminal. But, AFAIK, GR doesn't explain why occurs. Rather, it models this phenomenon.

    So why does space seem to expand? I know that we have no firm answers, but there must be a family of proposed ideas from mainstream physicists. Any thoughts, or references?


  8. Jul 9, 2007 #7


    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Hello Robert,

    my way out of the verbal jungle has always been to focus on the idea that THE DISTANCES EXPAND.

    try not to say "space expands" or "the universe expands" because then people get stuck wondering "what is space?" and "do the galaxies in the universe exand too"

    it says it just fine if you just say distances between objects at rest wrt CMB expand about one percent every 138 million years.

    That is the current rate, it used to be higher.
    another way to say the same rate is to say that the Hubble time is currently 13.8 billion years. (Hubble time is reciprocal of Hubble parameter H_0)

    the distances referred to are the large distances between objects which are not gravitationally bound so they are not hanging together or orbiting each other etc. the distance is estimated AT THE PRESENT MOMENT. it is not a light travel time or some other kind of distance schmeered out over past history.

    one shouldnt expect such distances NOT to change with time since geometry is dynamical--evolves according to the einst. eqns.---distances typically always doing something, growing shrinking whatever.


    that said, you have some deeper philosophical question in mind which I should perhaps address. or someone else may be able to address.

    Here are some questions about distance and geometry (where your question fits in). WHY? why is space 3D? (this is an intelligent question and a fundamental theory of quantum geometry should answer it)

    what are the fundamental degrees of freedom at microscopic scale-----what are the elements of the quantum state which, at macroscopic scale, gives rise to the illusion of space, and time, and matter?

    how do the fundamental d.o.f. underlying matter INTERACT with the fundamental d.o.f. underlying geometry, so that matter can bend geometry, and are they the SAME basic d.o.f.?

    is matter or what underlies it merely an ASPECT of geometry or what underlies it? are particles just kinks or tangles in the web of geometrical relationships?

    what is going on with the fundamental d.o.f. when distances expand?

    these all seem to me to be interesting questions which an successful theory of quantum geometry/quantum gravity (QGQG) should answer

    There will be an international QGQG conference at nottingham UK in July 2008, John Barrett is an organizer, he thinks about these questions as do a bunch of other non-string QG people.

    a book is scheduled to come out sometime this year, from Cambridge U. Press, called *approaches to QG, towards a new understanding of space, time, and matter*, I fear it will be somewhat dated already when it appears! but it should give some idea of the current state of the field. a bunch of essays by around 20 authors, edited by Dan Oriti, who is at Utrecht.

    there is no one perfect source of information about the state of research, maybe the program of next years QGQG conference could serve as a kind of "table of contents", when it comes out online.

    here is a link to the QGQG school they had earlier this year
    it has this link to John Barrett's website that gives info about other related events:
    here is about the conference, not much detail as yet of course!
    http://www.maths.nottingham.ac.uk/conferences/qgsquared-2008/ [Broken]

    this year the international conference most relevant to these questions has just taken place (at Morelia, Mexico). check out the talks. they have slides and audio online for most of them

    on any blade there is only a small section that is the cutting edge and it is not always easy to find
    you have to learn to inspect the whole blade and find for yourself what is/are the edge(s)
    for me, right now, Bojowald's cosmology work seems right at the edge----also what Carlo Rovelli is doing with spinfoam---but it's better
    if you find it for yourself, so I don't stress what I personally think is where progress is happening and it changes from year to year also
    Last edited by a moderator: May 3, 2017
  9. Jul 9, 2007 #8


    User Avatar
    Science Advisor
    Gold Member

    Rather than "ontological reality" start with the operational meaning of "space is expanding". Then go deeper and ask "what is the operational meaning of space (and time)".

    Is space a "thing" in and of itself or does it derive from "properties of things"?
    I believe it is better to think of space as derivative and not fundamental. This is counter to the usual methods of Field Theories but this aspect of the methodology can be seen as a model and not given special ontological status.

    Operationally speaking we say "space is expanding" because we observe Hubble's distance correlated red-shifts and we formulate Einstein's GR using a geometric model of a spatial membrane being dynamically acted upon and acting upon massive objects.

    Most especially in most cosmological models the spatial universe has finite volume which is increasing over time. As to cause for this expansion it is the inertia of the massive objects which perpetuates the expansion minus the gravitational attraction which is trying to slow it down (plus speculations about additional factors accelerating the expansion). This reduces it down to initial conditions (first causes) which are not well addressed. We simply refer to it as "the Big Bang".

    One can argue that we cannot well extrapolate back beyond these first causes within a scientific framework since we cannot pragmatically reproduce --even in part-- these initial conditions to a degree which will allow this. One can only hope that a suitable deeper theory say of quantum gravitation will allow extrapolation beyond "the Big Bang".

    However we should also allow for the possibility that future theories may provide explanations which in fact negate the "Big Bang" as well. I refer to "tired light" theories which would allow that the red shifts are not Doppler in nature but rather an effect of light's propagation over large distances. (That is badly stated. I have played with a model where it is indeed a "Doppler" shift, where objects do indeed move away from one another and yet the spatial extent of the universe as a whole is fixed.)

    Back to your question of ontological reality, that is a question we cannot answer in science except to eliminate certain ontological realities. What is left may be several different "realities" which yet yield the same empirical phenomena and so we either define a relativity principle where the different versions of "reality" are combined as different perspectives or we ignore the "reality" questions and stick to an operational language of "what happens".
    (These are actually two aspects of the same thing... a meta-relativity principle if you will).

    As I see it space-time is a conceptual scaffolding we construct around the universe of physical phenomena. It is a meaningful construct but not a fundamental physical object in and of itself. Saying "it expands" is thus meaningful not as a statement of reality but rather as a description of the behavior of those objects from which its meaning derives.
  10. Jul 9, 2007 #9


    User Avatar
    Gold Member

    Einstein was unhappy with GR because he viewed it as incomplete. It is a mathematical model that accurately predicts the behavior of massive bodies (at least within some limits - it may not be adequately predictive on galactic and cluster scales), but it does not address the mechanics of gravitation. In other words, GR is a better model than Newton's, but there is still no explanation for how and why massive bodies attract one another.

    Einstein tried to address this by discarding the Machian notion of gravity and inertia as action-at-a-distance and treating them as purely local phenomena that arise from matter's interaction with the space in which it is embedded. This "etheric" model of space (with variable properties) never caught on, but it might possibly make a resurgence. I am encouraged by the LQG notion that space may have a fine-scale structure, and hope that someone can vindicate Einstein by demonstrating that this property (coarseness of the fine-scale structure) can be varied by the presence of embedded matter. This would open the door to a dynamic, variable G. The MOND folk have already quantified the required corrections on galactic scales, but theirs also is a purely ad-hoc model with no mechanics. When Roger Penrose lectures on unification, he always says that both quantum theory and GR will have to be modified. I think that GR will take the brunt of the modification. In Einstein's essay "On the Ether" he speculated that GR might eventually be overthrown by quantum theory, and he may well have been right. Certainly he was troubled by the fact that GR provided no mechanism for gravitation, inertial effects, and the propagation of light through space, including gravitational lensing, which he considered to be refraction (as in classical optics).
  11. Jul 9, 2007 #10
  12. Jul 9, 2007 #11


    User Avatar
    Staff Emeritus
    Science Advisor

    I like it, particularly the following quote, talking about experimental tests of whether a FRW universe is expanding or not:

    If I'm understanding the question correctly, it is basically about philosophy (which cannot be tested, even in principle ) rather than about science (which can be tested by experiment).

    If I'm not understanding the question correctly, please describe a thought experiment that would resolve the issue one way or the other. :-)

    What I don't want to see get lost in the shuffle is the notion that there are statements being made by General Relativity which are ultimately testable by observation, because while philosophy isn't testable (and as a consequence, philosphical arguments tend to go on until one side or the other gets tired of talking or typing), science is testable.
  13. Jul 9, 2007 #12
    :rofl: We've all been there in science politics and philosophy and many other areas of discussion, it's not a preserve only of philosophers. Philosophers, at least those with any competence, tend to talk until one side is more logically stated: a non empirical but conceptual victory, or until they agree to disagree, or they agree. In science, there is a slight difference, when the subject your talking about is not clearly verifiable then it can devolve into philosophy, at which point the thread will either get moved, or warnings will be issued thankfully:smile:

    I actually thought I clearly understand the concept of expanding space, thanks a lot all for pointing out that I clearly don't. :smile:
    Last edited: Jul 9, 2007
  14. Jul 9, 2007 #13
    Read the paper again - the point is that "expanding space" means that in the Friedmann-Robertson-Walker metric (where "cosmological fluids" - matter, photons etc are smoothly distributed) means that the distance between the particles of the fluids increases with time (i.e. the density of matter decreases with time).

    The important point is that "expanding space" does not cause this - the density is decreasing because of the initial conditions at the big bang (i.e. things were moving apart then, and are so are moving apart now).

    The situation is a little more complicated than that as the rate of expansion changes with time, and the dynamics of the expansion depends upon the densities of the cosmic fluids (i.e. in our best cosmology with dark energy, the expansion rate will accelerate).

    So - the point is - the expansion of space is "not a thing" - it is not a rubbery material that stretches - it is an interpretation of the FRW metric. Exactly how mass moves in the universe depends upon the matter distribution in the universe.

    Cusp (an author on the Root of All Evil paper)
  15. Jul 9, 2007 #14
    There is no coordinate independent definition of 'expansion of space' in GR. The 'expansion' in the usual FRW comoving coordinates signifies expansion of distance between closeby comoving observers. Those observers define a preffered coordinate system in which the cosmological fluid appears frozen in place.

    If you think that is coordinate independent think of the so called Milne universe. This is a part of flat Minkowsky spacetime coordinatized with expanding FRW coordinates. In those coordinates, you have nonzero 'Hubble parameter' unlike the usual inertial coordinates for Minkowski. What is 'expanding' in Milne universe except the coordinates?

    The bottom line is, expansion of distances for a family of observers is well defined (but observer dependent) quantity. On the other hand, 'expansion of space' is not defined in GR at all so don't ask GR to explain it just because some cosmologists try to create a vusual for the laymen public using that term.
    Last edited: Jul 9, 2007
  16. Jul 9, 2007 #15
    Are you simply asking, WHY does empty space expand? If it is truly empty, ie. NOTHING, then how can it expand?
  17. Jul 9, 2007 #16


    User Avatar
    Science Advisor

    Joza, one could ask a similar question of the curvature of space. For instance, the Schwarzchild solution for a Black Hole is a vacuum solution, the space around the Black Hole is empty, yet we describe this space as being curved. You could then ask 'how can nothing be curved?'.

    In both cases (the expansion and the curvature of space or space-time) what we really have is a mathematical framework, the Einstein Tensor, that tells us what will happen. We can however talk about this in terms of the curvature or expansion of space as long as we are careful about not taking these concepts too literally.

    For some reason people are generally happy that the nothingness of space can be curved but are often worried that it might expand. I'm not quite sure why!
    Last edited: Jul 9, 2007
  18. Jul 9, 2007 #17


    User Avatar
    Science Advisor

    This has been largely addressed above, but to make it clear, this is in fact not a test of the expansion of space. Again, see the 'Root of all Evil' paper for the full details. The cloud of dust will only expand if it is given a correct set of initially expanding velocities. If you put a cloud in which the particles were initially at rest with respect to one another into an expanding but decelerating universe for instance, it would in fact collapse. That's before you even consider the self gravitational effect of the cloud itself!

    This is really at the heart of the misconceptions about expanding space. It does not 'cause' anything to happen at all! It is the description of an effect, the increase in distance between things, rather than the cause of the increase in said distance. This may seem a pedantic difference but in the above case we can see that they give different results.
  19. Jul 10, 2007 #18
    How can "empty space" expand? What are these cosmologists thinking?

    Ok, this makes sense to me. Moreover, that seems to be what most people here believe, and it is the point of the "Root of all evil paper", which I have found useful to study.

    My initial question comes about because many cosmologists explicitly say otherwise. I've come across many who say that objects in space do not move, and that it is empty space that is somehow (mystically!?) expanding. (How this empty space can expand is simply glossed over.)

    Even the Harvard-Smithsonian Center for Astrophysics makes this claim. In their FAQ they state:

    When they say "the universe is expanding," what exactly is expanding? As bizarre as it may seem, space itself is expanding — specifically, the vast regions of space between galaxies.

    Are the galaxies in the universe moving through space? No, the galaxies sit more or less passively in the space around them. As the space between galaxies expands, it carries the galaxies further apart — like raisins in an expanding dough.


    And this kind of answer is the most common one out there, from Ph.D.s in physics. I am beginning to suspect that many people literally don't understand the physical meaning of their calculations. Have you all seen such statements? What do you make of this? Why is it so common to give an explanation that seems to make no physical sense?

    I take it that this rate has been more or less constant (only slowly changing) over the last 10 billion years, but was wildly higher in the first nanosecond.

    Also, if I understand correctly, we seem to be living in an era when it has begun to increase again, due to (poorly understood) dark energy.

    Thanks for all of your replies!

  20. Jul 10, 2007 #19
    Thanks to everyone!

    This is not an easy subject to understand on a qualitative level, given the fact that commonsense notions of time and space don't work well in studying the universe as a whole.

    Thus, I want to thank Hurkyl, Marcus, Garth, Cusp (thanks for the link to the paper!), jambaugh, turbo-1, voltage, prevect, Schrodinger's Dog, smallphi and Wallace (thanks for the explanations and clarifications!), and anyone else I may have missed, for the time you took to give your thoughtful responses. You really made a difference.

  21. Jul 10, 2007 #20


    User Avatar
    Science Advisor

    I have a quick question about an example in this paper which is used to illustrate a problem with the "expanding balloon" analogy. In section 2.5 on p. 4 it says:
    But is it true that the analogue of this situation on an expanding balloon would give a different result? Suppose we have a bunch of marbles sitting on the surface of an expanding balloon in zero gravity, being carried in a radial direction by the outward movement of the balloon's surface. Now, I apply a force to some marble A in order to keep it a constant distance from some other marble B. By doing this, I am giving marble A some angular momentum in the direction of marble B, since it is no longer moving in a purely radial direction. I haven't done any calculations so I'm not sure this is right, but I think if the expansion rate were decelerating, then after giving A its initial angular momentum, I would actually have to apply a changing force in the opposite direction as its angular momentum, so marble A would have an ever-decreasing angular momentum in the direction of marble B, in order to keep the distance between them constant. If that's the case, then it seems that if I stop applying the force, marble A will then move towards marble B despite the stretching of the balloon, just as with the galaxies in the GR situation above. Is there an error in my reasoning here?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook