Does Space Expand?

There seems to be something in the air these days that is making people speak out against the idea that space is expanding. For evidence, check out these two recent papers:

The kinematic origin of the cosmological redshift
Emory F. Bunn, David W. Hogg

A diatribe on expanding space
J.A. Peacock

Expanding Space: the Root of all Evil?
Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis

Admittedly, my first sentence is grossly unfair. The correct thing way to paraphrase the underlying argument here is to say that “space is expanding” is not the right way to think about certain observable properties of particles in general-relativistic cosmologies. These aren’t crackpots arguing against the Big Bang; these are real scientists attacking the Does the Earth move around the Sun? problem. I.e., they are asking whether these are the right words to be attaching to certain indisputable features of a particular theory.

Respectable scientific theories are phrased as formal systems, usually in terms of equations. But most of us don’t think in equations, we think in words and/or pictures. This is true not only for non-specialists interested in science, but for scientists themselves; we’re not happy to just write down the equations, we want sensible ways to think about them. Inevitably, we “translate” the equations into natural-language words. But these translations aren’t the original theory; they are more like an analogy. And analogies tend to break under pressure.

So the respectable cosmologists above are calling into question the invocation of expanding space in certain situations. Bunn and Hogg want to argue against a favorite cosmological talking point, that the cosmological redshift is not an old-fashioned Doppler shift, but a novel feature of general relativity due to the expansion of space. Peacock argues against the notion of expanding space more generally, admitting that while it is occasionally well-defined, it often can be exchanged for ordinary Newtonian kinematics by an appropriate choice of coordinates.

They each have a point. And there are equally valid points for the other side. But it’s not anything to get worked up about. These are not arguments about the theory — everyone agrees on what GR predicts for observables in cosmology. These are only arguments about an analogy, i.e. the translation into English words. For example, the motivation of B&H is to do away with confusions in students caused by the “rubber sheet” analogy for expanding space. Taken too seriously, thinking of space as an expanding rubber sheet convinces students that the galaxy should be expanding, or that Brooklyn should be expanding — and that’s not a prediction of GR, it’s just wrong. In fact, they argue, it is perfectly possible to think of the cosmological redshift as a Doppler shift, and that’s what we should do.

Well, maybe. On the other hand, there is another pernicious mistake that people tend to make: the tendency, quite understandable in Newtonian mechanics, to talk about the relative speed between two far-away objects. Subtracting vectors at distinct points, if you like. In general relativity, you just can’t do that. And realizing that you just can’t do that helps avoid confusions along the lines of “Don’t sufficiently distant galaxies travel faster than light?” And reifying a distinction between the Doppler shift and the cosmological redshift is a good first step toward appreciating that you can’t compare the velocities of two objects that are far away from each other.

The point is, arguments about analogies (and, by extension, the proper words in which to translate some well-accepted scientific phenomenon) are not “right” or “wrong.” The analogies are simply “useful” or “useless,” “helpful” or “misleading.” And which of these categories they fall into may depend on the context. Personally, I think “expanding space” is an extremely useful concept. My universe will keep expanding.

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181 Responses to Does Space Expand?

  1. Speedy Gonzalez says:

    With all due respect to all very intelligent theoretical physicists and mathematicians, it seems that we have a slight Blind Men and an Elephant problem here.

    I hope we all can agree that we are living is this real physical world, and not in an equation on a piece of paper, right? I can use my physical eyes to look at this fantastic and beautiful Hubble Ultra Deep Field Image, right? In this picture I can see about 100 small red galaxies, existing when the universe was just 800 million years old. The larger, brighter and well-defined galaxies thrived about 1 billion years ago, when the cosmos was 13 billion years old.

    Theoretical physicists have calculated (redshift) that some of these small red galaxies are at the mind-boggling distance of 27 billion light years away from the lens of the Hubble Space Telescope. Yes yes, I know the red galaxies aren’t in “this moment” 27 billion light years away, we only see the light that was emitted… wait!? 27 billion years ago!? That’s impossible!? The universe is only 14 billion years old!? Help!?

    And now there’s an academic discussion on highest level on which proper words should be used to get around this “problem”.

    Sean claims that this is a “well-accepted scientific phenomenon” and that “you can’t compare the velocities of two objects that are far away from each other”. Okay, it would be more than bold to question this, but I still can NOT get this in to my simple little hillbilly brain, and I still have simple unanswered questions that wouldn’t be that hard to answer if what you are saying is correct:

    1) Exactly at what precise distance are the normal human thoughts about measuring velocities breaking down; on one tenth of a light year, or 800 million light years, or 13 billion light years, or what?

    2) Are Michael S. Turner/Judy Jackson right when claiming; “There is no speed limit on the universe.“, or is Sean right when claiming; “There is no such thing as expanding faster than the speed of light.“?

    (I sure hope that everybody agrees that No. 2 is perfectly contradictory?)

    Please, can anybody explain this in plain English!?

  2. jpd says:

    you make approximations like that all the time.
    the distance from me to the door is a strait line
    measuring about 3 meters. (i can neglect the
    curvature of the earth)
    the distance from me to a door in the southern hemisphere
    would need to take the curvature of the earth into account.

    things measured on large scales have to take cosmological
    curvature into account

  3. John Peacock says:

    I wrote my “diatribe” on expanding space to address many of the confusions and disagreements aired in these comments – which are arguments I’ve heard so often. I encourage people who still think expanding space is trying to rip the Earth away from the Sun to read my note.

    The only other thing I would add is that the virtue of GR is that you can calculate things from any point of view and still explain what you see. So there is no unique right viewpoint – but if a viewpoint leads you to get the wrong answers unless you are very very careful, then its use should be discouraged. I’d say it’s clear that the idea of *locally* expanding space falls into this category. Experts can use it correctly, but we should certainly ban it from public talks, since it so easily leads people to incorrect conclusions.

  4. Chris W. says:

    Doctor in Brooklyn: Why are you depressed, Alvy?

    Alvy’s Mom: Tell Dr. Flicker.
    [Young Alvy sits, his head down – his mother answers for him]

    Alvy’s Mom: It’s something he read.
    Doctor in Brooklyn: Something he read, huh?

    Alvy at 9: [his head still down] The universe is expanding.
    Doctor in Brooklyn: The universe is expanding?

    Alvy at 9: Well, the universe is everything, and if it’s expanding, someday it will break apart and that would be the end of everything!

    Alvy’s Mom: What is that your business?
    [She turns back to the doctor.]
    Alvy’s Mom: He stopped doing his homework!

    Alvy at 9: What’s the point?

    Alvy’s Mom: What has the universe got to do with it? You’re here in Brooklyn! Brooklyn is not expanding!

    Doctor in Brooklyn: It won’t be expanding for billions of years yet, Alvy. And we’ve gotta try to enjoy ourselves while we’re here!

    (— from Annie Hall)

  5. Speedy Gonzalez says:

    jpd, even I can use elementary math to calculate the circumference for a trip to the southern hemisphere (c=pi*d) but it doesn’t change the speed of my car anyhow.

    There seems to be some mix-up in using plain English.

    My (stupid) understanding of physicists saying “well guys here is a supernova 27 billion light years away” was that this is not where the object is “now”, but how far the light has traveled. But after reading this Understanding the expansion of space, this seems to be totally wrong!?

    Oh man! Take me back to earth. This picture of embedded Lambda-CDM geometry explains it all. It’s not complicated and you don’t have to grasp miles of mathematical hieroglyphs to understand what’s going on. It’s just a woolly use of plain English that lead to this confusion.

    The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.

    It’s perfectly clear and as easy as taking your car to the southern hemisphere. Sure, the supernova is 28 billion light years away. But we are never going to see any emitting light at this point in worldline! It’s forever beyond our reach and Einstein can rest in peace, as always.

    Why are physicists creating this kind of “pseudo confusion”? Or is it me?

    Yea yea, I know you all Gurus out there is laughing you pants of right now! 🙂

  6. jpd says:

    i wasn’t saying anything about your abilities, i was
    addressing your comment:
    “Exactly at what precise distance are the normal human thoughts about measuring velocities breaking down; on one tenth of a light year, or 800 million light years, or 13 billion light years, or what?”

    we (you and me) make adjustments depending on scale all the time,
    my example was distance on the earths surface.

  7. Geraint says:

    One minor point – Sean says

    > For evidence, check out these two recent papers:

    but lists three. Should we read anything into this (considering ours is number 3)?

  8. Speedy Gonzalez says:

    jpd, it’s all okay and forgot to say, thanks man!

    My “exasperation” falls back on my own stupidity and fixation with the fact that there was something weird going on with the speed of light. Your thoughts about curvature, took me back to earth for some “reconciliation”.

    And I must apologize to both Sean and Michael S. Turner, it was all perfectly correct, if I just had examined all text carefully. My only excuse is that this is not my native language and I’m a complete “Swedish Chef” in physics. 🙂

    Well, nice to be back on track again with the universe and the speed of light. It took me four (light) years, but it was worth every second! 😉

    Oh, and by the way, I have no problems what so ever that Brooklyn Is Not Expanding, i.e. Steady State Brooklyn. 🙂

  9. JP says:

    Hi John,

    Your analysis seems a bit fishy. You say Birkhoff’s theorem implies that a test particle at distance r0 from us at time t0 in an isotropic universe should fall towards us. If the universe is isotropic, why does it choose to fall towards us?

    I don’t intuitively understand the idea that local stuff doesn’t respond to the expansion. If it’s purely kinematic and driven by initial conditions, why do peculiar velocities of galaxies damp out over time? Why wouldn’t the same damping of peculiar velocities occur on the small scale, does the analysis leading to that damping formula depend on scale?

  10. JP says:

    [ Of course I understand the effect on the scale of the solar system is totally negligible/unmeasurable and swamped by local gravitational fields, but still finite ]

  11. Neil B. ? says:

    My understanding of “space expanding” is, that in such a case particles have rates of separation based on successive distances in a way that resembles classical kinematics. IOW, it’s not like special relativity, and we can actually assign rates of recession to extremely distant objects in principle, and those rates of recession can be indeed greater than c. Space could be huge, even infinite, and if the galaxy at distance X goes 0.1c then the one at 10X goes c, and the one at 100X goes 10c.

    Here is how it could be rightly defined: increase in “distance” means what it intuitively suggests, defined in terms of successive adjacent increments. So, I see a galaxy 100 MLY from me, critters there see another one 100 MLY from them, opposite me; and so on and so on. This works because those distances can be all defined and calibrated in terms of “cosmic time” – how long since your own proper clock ticked from the big bang, the time when things started receding. Everyone notes local distances at such and such moment of CT. No, it doesn’t matter whether they can get together to compare notes since we consider an objectively realist view of the universe. The very large distances are simply what the increments all add up to at successive moments of CT whether anyone is around to understand or deal with it or not. Isn’t this the basic concept you can tease out of the Robertson-Walker metric? The only problem I see is, space is not perfectly uniform and things are moving a bit to and fro, ruining the perfection of cosmic time and the regimentation of the progression of increments and local relative recessions.

    As for red shift, this is usually put as: the ratio of wavelength equals the ratio of the “size of space” (benchmarks like two galaxies each “at rest” relative to CMB) between reception and emission.

    One issue though, is that apparently one can pretend that SRT still applies. Imagine that the receding material is ever-more Lorentz contracted with distance and speed, relative to any self-appointed “central observer.” Supposedly the results are the same as “expanding space” only if the rate of recession stays the same, and there’s no way to slow things down and run them back together. This is what Milne tried in his off-beat cosmology. It’s fun to play with, and imagine what happens if one properly “infinite” but limit-Lorentz-contracted edge bashes into another …

    Since the properties of “space” depend on material relations and the existence of gravity, I can get the idea of “space expanding” because there is a difference in effect as I said (the unbound extent possible for collections of mutually receding or approaching vantage points.) However, what bothers me instead is how to demarcate a given “space” from another “space” in which it supposedly can be embedded, like a soap bubble in the air – but what keeps it constrained as a separate thing? See my comment, at Backreaction thread “100 Years of Space-Time” at No one gave me an answer. Better luck here?

  12. Neil B. ? says:

    In case it wasn’t clear, we concatenate successive separations and relative velocities all together, calibrated under “cosmic time” (I didn’t make up that term, it’s out there.) Then we can get a “cosmic” definition of both separations and recession velocities over boundless extents of space. So add up the little distances to get the big distances, and add up the little relative velocities to get the big velocities at big distances (and other derivatives by extension – so for example, acceleration should be a = -(4/3)pi*rho*R relative to a given observer. It doesn’t make direct physical sense anymore as the gravity from the sphere “under” the shell of matter beyond the point you’re looking at, but it has to be consistent with the kinematics all the way out (well, not counting overall curvature.))

    BTW this is an over-simplification since it only makes good sense over the region space is reasonably flat, but if expansion is about the right rate then that is the case – well, dark energy has made this all a mess, so I’m not sure anymore.

  13. Geraint said “Hmm – it seems we do disagree – are you arguing that the standard FRW metric is the “correct” metric for the universe? If so, then I disagree”

    Surely not? Perhaps you really meant to say that you don’t believe that the usual coordinates used to *describe* the FRW metric are “correct”.

    If that’s what you meant, consider the following. An FRW spacetime has the property that it can be sliced up into spacelike pieces which are isotropic about each point. This statement has nothing to do with any choice of coordinates. Now it turns out that in GR a set of timelike geodesics perpendicular to these distinguished slices necessarily have non-zero geodesic deviation if the stress tensor is not zero. [I’m including the cosmological constant in the stress tensor.] This geodesic deviation is what we call, very naturally [look at any textbook picture of geodesic deviation] “the expansion of the universe”. Again, no coordinates. So yes, space is expanding. An observation of cosmic redshift is a direct observation of geodesic deviation. Nothing to do with Doppler effects of course, though the random motions of galaxies does give rise to an ordinary Doppler effect which is superimposed on and should not be confused with geodesic deviation.

  14. Geraint says:

    > Surely not? Perhaps you really meant to say that you don’t believe that the usual coordinates used to *describe* the FRW metric are “correct”.

    No – I don’t think that the FRW coordinates are the unique way to cover the underlying geometry, and that any other slicing is equally valid way of doing so. If this means homogeneity is lost, then so be it, homoegenity was special to the FRW slicing anyway.

    The point is that the observable, the observed redshifts at a particular time for a particular observer are the same, irrespective of how we chose to slice and dice spacetime in terms of coordinates.

    I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!

  15. neophyte says:

    Geraint: “I note that several posts in this thread are on the verge of declaring space as a “thing” that can bend and expand. This is where the problems begin!”

    What?! Are you saying space is not some thing?

    In fact, I emphatically declare that space is some thing! I would go further to state that space is essentially every thing! (at least in our observable patch of reality)

    So, what are you saying space is, if it is not some thing?

  16. Geraint says:

    > So, what are you saying space is, if it is not some thing?


  17. “No – I don’t think that the FRW coordinates are the unique way to cover the underlying geometry, and that any other slicing is equally valid way of doing so. If this means homogeneity is lost, then so be it, homoegenity was special to the FRW slicing anyway. ”

    But you do believe in the approximate validity of the FRW *metric*, right? The point being that the metric doesn’t care about coordinates.

    I think you are missing the point, which is that FRW spacetimes have a very special property which corresponds precisely to [the rate of] “the expansion of space”, AND this property has nothing to do with how you choose your coordinates, or indeed whether you choose any particular coordinates at all. Again, whether one thinks of space as a “thing” [whatever that is] is completely beside the point, though I agree with an earlier commenter that the rubber sheet business is really horribly misleading. Still, it is not a good idea to replace one horribly misleading statement [“galaxies are like bumps on a rubber sheet”] with another [“the universe is not *really* expanding — it depends on how you look at it.”]

    Again: the key point here is geodesic deviation of geodesics corresponding to galaxies. Maybe you can twist words in some ingenious way so that geodesic deviation is not describable in terms of “expansion” [which by the way has a technical definition], but what you hope to gain from such a strange exercise escapes me. Whatever it is, “clarity” is in a different world.

    The problem with all of these papers seems to be an obsession with the freedom to choose different coordinates. It would be better to just ignore coordinates altogether, neither they nor the freedom to choose them are of any importance fundamentally.

  18. Geraint says:

    > But you do believe in the approximate validity of the FRW *metric*, right? The point being that the metric doesn’t care about coordinates.

    I am not talking about any approximations anywhere – when you say “metric” do you mean geometry? the FRW “metric” is a coordinate system on the underlying geometry. But it is not special in anyway and there are may ways you can cover the same geometry with different “metrics” (same geometry). The important thing is the observables are the same.

    I do understand the FRW metric – have a read of the papers above.

  19. Rob Knop says:

    Heh… I just came down strongly on the side of expanding space here:

    Hogg once took me to task for using the “space expanding” picture, even warning me that he was afraid people were going to think me ill-informed for speaking out against the “galaxies flying apart” picture…. But, to my mind, the “galaxies flying apart” picture introduces *more* confusions and problems and misconceptions than the “space expanding” picture. That’s part of what my blog post is all about.

    Another important point about the “space expanding” picture… if you live in a Universe that has vacuum energy… and, there is some reason to suspect that just perhaps our Universe is like that… saying that there is “more space” between galaxies, as opposed to thinking about the galaxies as moving apart from each other, conceptually fits closer to the mathematics of what’s going on in GR when you have something whose density is constant. Dark Energy is becoming an ever more important dynamical contributor all the time. Really, there is something *physical* between the galaxies that there is more and more of as the Universe expands. Saying there is more “space itself” is perhaps a nebulous concept… but there is most definitely more Dark Energy between the galaxies as the Universe expands.

  20. Rob Knop says:

    There’s an incorrect statement in the Burns & Hogg paper:

    that “hydrogen atoms, the solar system, and the Milky Way Galaxy must all constantly “ressit the temptation” to expand along with the Unvierse. … is an erroneous consequence of the reaification of the rubber sheet: there is no such temptation, because there is no expanding rubber sheet.

    First, to be fair to them, there is no such temptation for a matter dominated Univesre; there, the expansion is the left over coasting from the Big Bang, and there’s no ongoing “force” driving the expansion any more than a golf ball flying through the air continues to feel the force of “the hit”.

    However, in our Unvierse, there is a temptation, and that is Dark Energy. I don’t want to comment on the scale of the hydrogen atom, since that would probably involve quantum gravity, but on the scale of the Solar System and the Galaxy, without the gravitational forces that hold those systems together, test particles placed initially at rest with respect to each other on those spatial scales would begin to move apart from each other due to the negative gravity effects of Dark Energy. Those effects are tiny compared to the gravitational binding of the systems, but the temptation exists.

    My problem with viewing cosmological redshifts as an infinite number of infinitesimal Doppler shifts is that it’s *more* confusing than the other picture. You have to implicitly consider the infinite (or at least one over epsilon) of reference frames between source and observer in that picture… whereas the “space itself has expanded” picture doesn’t require implicit consideration of all of that. E=-p.u at the beginning and the end does it– yes, for Doppler and Gravitational redshifts. But in each case you need consider only the event of emission and the event of detection. If you only consider those two events, then it becomes very tempting to take u as a relative velocity between the source and observer… but, as even Burns and Hogg agree, that relative “velocity” is ill defined if there’s no single special relativistic frame that is valid at both events.

  21. Luke Barnes says:

    Mentioned in CV – that’s probably as close to immortality as I’ll ever get …

    One of the main points of our paper was that even though the “expanding space” analogy is open to misinterpretation and can be pushed too far, it is still the most useful way of thinking about the RW metric. John Peacock is right to point out its flaws, especially in the local universe, but I don’t think a “global vs. local” dichotomy is perfect either, even though it is rigorous (the RW metric can be approximated locally by Minkowski spacetime).

    To JP: John’s analysis is correct. From the standpoint of “space is not expanding locally”, the particle falls toward us because a particle that is not moving away with the exansion will be pulled back toward the origin by gravity – what’s not going up will start coming down. From an exanding space perspective the expanation is slightly more subtle. We have to analyse the situation from the perspective of Bob, who is in the hubble flow, but wayy out there next to the particle. From Bob’s perspective, the particle is being shot out into the universe, in our direction. It will approach us because, even though the particle’s peculiar velocity and our expansion velocity are initially equal, the expansion of the universe is decelerating in this scenario, and so the particle starts to catch up with us as we both race away from Bob.

    Also, the issue of dampening peculiar velocities and joining the hubble flow isn’t as straightforward as you might think. I’ll refer you to one of our earlier papers:

    Joining the Hubble Flow: Implications for Expanding Space
    Authors: Luke A. Barnes, Matthew J. Francis, J. Berian James, Geraint F. Lewis

  22. Geraint says:

    > E=-p.u at the beginning and the end does it– yes, for Doppler and Gravitational redshifts. But in each case you need consider only the event of emission and the event of detection. If you only consider those two events, then it becomes very tempting to take u as a relative velocity between the source and observer…

    Tempting, but clearly wrong 🙂 Just thinking of two observers who are spatially at rest at two different radii in the schwarzschild metric shows this.

    Personally, I feel the problem lies with the with to label redshifts as being “different” – gravitational, cosmological, doppler – when in reality E=-p.u is it and the components of g, p and u depend on which coordinate system you choose –

    i.e. in the FRW u has zero spatial components (for a comoving observer) and so people say the redshift is “cosmological”, where as the conformal representation of the same spacetime has non-zero spatial component for the same observer and now there is a doppler component to the redshift – but it’s exactly the same situation, with exactly the same observable – the only thing that changed was the coordinate system you threw down.

  23. Speedy Gonzalez says:

    Rob Knop, I’m going to be a little bit rough here because I have been going through a sort of intellectual core meltdown in this post here, here and here, but it’s nothing personal, just physics.

    Before I start, I must proudly announce the birth of a new acronym; Hazy English Language of Physicists – HELP

    I have also formulated a pseudoscientific law saying: HELP = HELP, and I urge everyone to shout for HELP when physicists talks woolly in the hazy smog. 🙂

    Okay Rob, there seems to be a clear case of HELP in your post about Randall Munroe and the Size of the Observable Universe.

    Why then isn’t the observable Universe at most 28 billion light-years? If something emitted light and it took 14 billion years to reach us, and it was moving the other way as fast as it could, it would only be 28 billion light-years away right now. What’s with the 46?

    For physicists it’s probably clear what the observable Universe represents mathematically, for all others observable correspond to a visual object that you can see with your eyes.

    I hope that you are not saying that we can receive photons here on earth that has been travelling for 46 billion years? Alternative; that you are not saying that we can receive photons here on earth that has been travelling for 14 billion years at 3.28 times the speed of light in vacuum?

    A picture is worth a thousand words and this one is the best I’ve seen explaining the observable universe and Understanding the expansion of space.

    It’s high time to demystify our universe and use a proper language for everyone!

  24. Geraint says:

    Actually – I find Tamara Davis’s conformal representation as the best for explaining why the observable universe is 46 billion LY in radius.

    As for use of proper language, we do already.

  25. Speedy Gonzalez says:

    Geraint, when saying “observable universe”, are you saying that we can see (receive photons) from an object that is 46 billion years away?