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. HoggA diatribe on expanding space

J.A. PeacockExpanding 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.

So can you explain *why* the GR space expansion point-of-view doesn’t apply to solar-system scale objects or galaxies? Every explanation I’ve heard throws around terms like “gravitationally bound”, but doesn’t say why that effects anything. So what if they’re gravitationally bound?

Is it just so long as the metric closely approximates, say, the Schwarzschild metric, that the deviations due to the large scale changes are small enough that they don’t matter, or are they even in principle not there? If the first, okay, but what’s so special about these cases that they should be called out that way, rather than any other case where the effects just happen to be too small? If the second, how does that come about that the local perturbation completely suppresses the large scale structure?

@aaron

If I’m not totally muddled, I think it’s because gravity and the other forces hold closely grouped objects such as the stars in galaxies (and of course anything smaller) together in clumps that don’t expand, even though the ‘fabric’ in which they exist is technically expanding. It would be like having some stones suspended in a gel that expands, carrying them further apart. Obviously the stones wouldn’t expand with the gel.

I understand all of this from a perspective that consists of nothing but analogy though, not knowing much of the underlying maths.

Paul: but what’s holding together the solar system, or a galaxy is just gravity — warped space-time — which is the gel in your analogy.

@Paul

I think that the point the physicists Sean has mentioned above are trying to get across is that such an analogy does not hold for localized clusters of matter. Unfortunately, I’m as muddled as you are. I don’t quite see why the analogy doesn’t hold locally. The only answer that has ever been offered to me by my teachers is that “gravity holds them together”, which never made sense to me.

I’m with Aaron. It would be absolutely great if someone could explain this better.

@(Aaron, Paul); There is an attempt at addressing this in Secs. 2.3-4 of the third paper to which Sean links. Section 2.3 is an extended mathematical argument using results from an earlier work, but it culminates in: “[o]bjects will not expand with the universe when there are su?cient internal forces to maintain the dimensions of the object;” while Section 2.4 is all prose and addresses the question of gravitationally-bound systems directly.

The section numbering in comment 5 is incorrect: I mean 2.6.2 and 2.6.3; please forgive my not double-checking! The reason an explanation such as “gravity holds them together” might be confusing is that it isn’t clear what is meant by ‘gravity’: the Newtonian picture of forces or the GR picture of an expanding space-time—it seems like these two must be competing for primacy. But there is only one gravity!

The gravitational motions here are the governed by solutions to the Einstein field equations, given a particular choice of ‘metric’ (a measure of distance between points). In the solution used for cosmology, the metric is changing with time (the distance between points is getting larger), and this is what is generally meant by ‘expanding space.’ But this says nothing of the galaxies themselves, which are usually put on the other side of the field equations to the metric. The Friedman equations, which are the stock and trade of theoretical cosmology, are a reduction of the field equations under the assumption of this expanding metric and a particular description of matter, both agreed not to be accurate on the scales of galaxy clusters or the Solar system. Instead, the metric on these scales must be some kind of strange admixture of the very-large scale cosmology form (expanding space) with the small-scale metric for isolated clumps of matter (like the Schwarzschild metric). But working that out has so far proved too difficult!

I hope that is some help; additionally, the passage I had in mind is: “Unsurprisingly then, the resulting picture the student comes away with is is somewhat murky and incoherent, with the expansion of the Universe having mystical properties. A clearer explanation is simply that on the scales of galaxies the cosmological principle does not hold, even approximately, and the FRW metric is not valid. The metric of space-time in the region of a galaxy (if it could be calculated) would look much more Schwarzchildian than FRW like, though the true metric would be some kind of chimera of both.”

Sorry again about the numbering; I feel like a dunce.

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I think it is very very important for Scientists to be concerned about producing useful analogies. They need to to do this to an even greater extent so that it reaches the general public. This needed communication of ideas and concepts to the general public is so very important, otherwise all this good science and information stays locked away in ivory towers and those of us in the unwashed and unlearned masses are left with nothing but the traditional analogies; myths and religions.

It would be great if everyone was able to think in terms of higher mathematics but that is not the reality. Today the entrenched ancient analogies are still influencing political debate with the potential to curb funding in some areas of study.

Albert Einstein made the effort to publish a book for the general population, “Relativity: The Special and the General Theory”.

Perhaps I have not searched hard enough but now that I am retired I am searching for reading that will bring me up to date on all the current research in Physics.

Great post as always Sean. Way off topic: As we all know tomorrow the Nobel prize in physics will be announced and there is not a single post in CV about predicting the winner. Come on people, what´s wrong with you? 😀

Berian: thanks. Of course I should have thought to *gasp* actually read the papers, and that they might discuss these points.

This description of the local metric as a mixture of FRW and Schwarzschild is exactly how I was trying to think of things.

Thanks.

Isn’t is true that for a wide range of cosmological models the total volume of space is finite and increasing with time, no matter how you slice it, right?

So how could anyone deny that space is expanding in this scenario?

To a first approximation, matter is uniformaly distributed in the universe. Precisely at that level of approximation, “space is expanding”. The “expansion” of the universe is really a statement about homogeneity, isotropy, etc. (of coarse-grained distributions of matter in the universe.)

Glaxies are test particles moving in the ambient spacetime curved by everything else in the Universe. When we look at local structure at the level of galaxies, we are already far from the regime of the original approximation.

There are two distinct issues here, and it’s very confusing to mix them.

Issue 1: The “rubber sheet” story is definitely an *analogy*. As Sean says, there is no right or wrong here, only misleading and not misleading. And this particular analogy really IS misleading, particularly when people are discussing Inflation. When you stretch a rubber sheet, you really do flatten out the inhomogeneities. Inflation is not like that: it just makes everything bigger, it doesn’t flatten anything out. Of course, to “small” beings like ourselves, making everything big makes it difficult for us to detect the inhomogeneities, but they are still there.

Issue 2: Is the universe “really” expanding? Is this too a matter of opinion, as some of the authors of these papers state or imply? Well, to say that the universe is expanding means that you have modified Pythagoras’s theorem to include an increasing function of time. Technically, the extrinsic curvature of the relevant spacetime foliation is non-zero. This is a question of fact, not opinion or convenience. So I think I have to part company with Sean here: several of these papers are either *wrong* or so close to it that it makes no difference. Certainly any idea that GR can be understood in terms of Newtonian mechanics is quite nonsensical. The essence of FRW cosmology is isotropy, and a vector cannot be isotropic unless it vanishes. So you will never understand cosmology if you insist on thinking in Newtonian terms. [In particular, thinking of cosmic acceleration in terms of “gravitational repulsion” is a terrible mistake — vacuum energy cannot point in any direction, it is intrinsically isotropic.] Similarly, thinking of cosmological redshift in terms of Doppler effects…..well, if you *really* want to get your students badly confused about proper motions etc, go ahead, and if you *really* want to complete their utter confusion you will talk about that stupid Milne cosmology; but those of us who prefer clarity will avoid this idea like the plague.

What I find strange about this Doppler business is this. The “correct” explanation of cosmic redshift, in terms of the extrinsic curvature, is really beautiful and, as students say, “cool”. You are directly observing the curvature of spacetime every time you measure a redshift. The alternative “explanation” in terms of the Doppler effect is contrived, clunky, and boring. Why do these people prefer boring to cool?

> Why do these people prefer boring to cool?

We don’t – we prefer accurate to cool. Breaking redshifts into three “different” kinds actually confuses the beautiful E=-p.u underpinning all redshifts, and as we know, we can play around with the metric to do the dot product and so your “interpretation” will be different.

>Similarly, thinking of cosmological redshift in terms of Doppler effects…..well, if you *really* want to get your students badly confused about proper motions etc, go ahead, and if you *really* want to complete their utter confusion you will talk about that stupid Milne cosmology; but those of us who prefer clarity will avoid this idea like the plague.

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 and point you towards discussions in

Coordinate Confusion in Conformal Cosmology

Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, J. Berian James

http://arxiv.org/abs/0707.2106

and

Cosmological Radar Ranging in an Expanding Universe

Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, Juliana Kwan, J. Berian James

http://arxiv.org/abs/0805.2197

There is more than one way to skin a cat (luckily).

Thanks Sean! This is my absolute favorite question! And I crave for answers! 😉

On Science Saturday: Cosmic Bull Session, John Horgan asks you to explain how the universe can expand faster than the speed of light, and you answer:

There is no such thing as expanding faster than the speed of light.http://bloggingheads.tv/diavlogs/9433?in=11:09&out=12:43

At my very basic non-mathematical-amateur-level we seem to have a “problem” here, or maybe two:

1) The universe is about 14 billion years old, and we observer objects that is 27 billion light years away. How on earth can that ever be possible?

2) If you are right Sean (

and Mr Einstein of course!), what will happen with the expansion speed in the future? We know today at that the expansion of the universe is actually accelerating (measuring quasars)? Will the “mass” of the universe increase due to acceleration, and slowing down the speed, or what? Otherwise, we will eventually expand at the speed of light (or more!), right?Okay, I trust you Sean as a serious scientist. I also trust this guy, Michael S. Turner and you are on a sort of “supernova collision course”, as far as I can see.

Michael S. Turner writes; How Can an object we see today be 27 billion light years away if the universe is only 14 billion years old? And the answer is:

According to Einstein’s general theory of relativity, the expansion of the universe is actually an expansion of space itself, and galaxies are moving away from each other because they are “being carried along by space.” The theory does NOT limit the speed at which space expands, only the motion through space. Thus, the distance to this quasar can be greater than 13 billion light years. In fact, if we ask the question, “How fast is the distance between us and this quasar increasing?” we get the seemingly amazing answer of 540,000 km/sec or about 1.8 times the velocity of light. This number is ultimately not very interesting, both because this is not the best way to think about distant objects, and because there are objects farther away whose distance is growing even faster. To quote Fermilab’s Judy Jackson, “There is no speed limit on the universe.”So what is actually going on here, what is the right way to tackle this question?Points of space and spacetime slide around. J. A Wheeler called general relativity geometrodynamics to bring this point out. The FRW metric

ds^2 = -dt^2 + R(t)(dr^2 + r^2 d(Omega)^2)

has the radius R(t) changing with time and curvatures determined by derivatives of it. We all know or have seen these. As way of analogy it is the old picture of points on a balloon being blown up.

However, how points move is given by a gauge condition. How one shoves points on a spatial manifold is entirely given by the coordinate gauge-like choice one imposes on the problem. For a given point p one can define one spatial surface (a surface where one has set all clocks to synchronicity) and how this point along with others are lapsed into the future. Similarly one can chose another surface and push the same point into a completely different point by this change of coordinate condition on the second spatial surface of choice. So the points on a “rubber sheet” moving apart really only makes sense when one is talking about the relative deviation between two points — the geodesic deviation equation.

We can well enough say that space expands in a cosmology, or that galaxies are on comoving frames with this expansion and the rest. However, I do think this is in some ways a model construction. General relativity as a theory of general covariance only makes reference to moving points or coordinate systems when one imposes a gauge-like coordinate condition on a problem. Of course this condition is freely chosen by the analyst.

Lawrence B. Crowell

I think analogies are very useful. More useful than simply a means of communication with non-scientists. Analogies also can lead to the construction of actual experiments that can tie mathematics to the physical.

Unless I’m wildly mistaken, being directly tied to the physical is still something important to physics.

This was a wonderful post. I’m very happy seeing things that shine a light upon orthodoxy. It needs to be lit up.

Well, the nice thing about the “expansion of space” description, for physics students at least, is that it translates extremely well to the mathematics.

As for why the local universe isn’t expanding, another way to look at it is this. First, remember that the force that is driving this expansion is gravity. The universe as a whole is expanding on average because the initial conditions combine with gravity to make this occur. But the action of gravity depends upon the distribution of matter, and this expansion depends upon an approximately homogeneous distribution of matter.

Here near the Earth, we don’t have anywhere close to a homogeneous distribution of matter. So gravity acts differently, and doesn’t drive any expansion. On the contrary, gravity supports a nearly steady state set up due to the fact that matter near us isn’t distributed uniformly.

As is alluded to above, one could examine this explicitly by embedding a Schwarzschild metric as a perturbation on top of an expanding space-time, and see how orbits behave.

I don’t like encouraging people not to think of the possibility that space can expand between say atoms. Strictly speaking you can only make a manifold flat around some epsilon.

The point is a general manifold (not necessarily FRW) can and does feel this expansion, via tiny tidal forces, which are suppressed by many orders of magnitude.

The reason I insist on making that point, is that this can be important in understanding the role of the cosmological constant. If its too big, gravitationally bound systems will find it difficult to form. Theres a bit of a word game here with what we mean by expansion (a FRW concept) vs negative pressure density, but thats semantics.

The point is, this sort of game is what allowed people to put anthropic bounds on the size of the CC, and its a very real effect.

You have to first solve the appropriate gravitational equation, i.e. the appropriate GR field equation and then comment on it using an analogy to communicate what this means with ‘joe public’, your students and yourself.

For example, Peacock in his “A Diatribe on Expanding Space” uses the Schwarzschild solution to show that ‘expanding space’ is an inappropriate analogy for the cosmological solution and that space therefore does not expand.

However as the Schwarzschild solution is that of a static spherical mass embedded in Minkowski space-time, i.e. non-expanding space, I find this criticism unconvincing.

What happens if the Schwarzschild solution, such as that describing the gravitational field of the Sun, is embedded in expanding cosmological space? Would not the solar system, and by extension the galaxy, not expand with it?

Garth

Perhaps it is time for a general audit of some of the outstanding interpretations in theoretical physics.

Off-topic: The 2008 Nobel Prize in Physics goes to

Yoichiro Nambu, “for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics” and toMakoto KobayashiandToshihide Maskawa“for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature”.Congratulations!

Expanding Space: the Root of all Evil?No, no, no, that’s all wrong. It is

Love ofexpanding space that is the root of all evil.See this article:

Solar system effects in Schwarzschild–de Sitter spacetime