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 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 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.
No – as shown in the conformal picture, more most distant objects we can see (effectively the lumps in the CMB) are *now* 46 billion light years away.
Thanks Geraint, that’s a relief!
My guess is that there are plenty of people (made of ordinary matter 😉 ) out there who just give up on trying understand the universe because of this “lost in translation” situation. I have talked to science journalists about this “46 billion question” (those who are supposed to bring this info to the public) and they are besides “lost in translation” completely “lost in space” as well…
It’s probably a tricky problem to find one or two words that say; The largest piece of universe that we can know anything about is at visual distance of 14 billion light years, which represents an actual present physical position of 46 billion light years away, even if it’s problematical to talk about *now* according to Einstein’s general theory of relativity.
Did I get that right?
> Did I get that right?
Yeah – except the bit of the universe we can ever know something about is given by the event horizon, and is currently at a radius a little over 60 billion Lyrs away.
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?
Er.
You are slamming on me by quoting the question from a blog post that’s written in a “hypothetical questioner and answer” format. I invite you to read the next paragraph after the one that you quoted, in which I explain what’s going on.
And, in any event, talking about the *distance* to very distant objects is troubling, because there are lots of different distances involved… proper distance at the time the photon was emitted, proper distance now, both of those measured by setting the FRW t parameter to constant; or the distance the photon travelled…
When I give public talks, I talk about lookback time, because it’s conceptually a lot cleaner.
The speed of light determines a relationship for a distance and a time locally. There can exist two frames F and F’ where observers in both will see that d = ct works. However, the two frames F and F’ may have their lightcones oriented differently. And the further away an observer on the frame F detects things on frame F’ this deviation may become more extreme. It is because of this with cosmology that as one observes further out the general relativistic physics of particles comoving in a frame becomes significant. The lightcone on the frame of a distant galaxy has an orientation different than the lightcone for your local frame. This corresponds to points on the spatial surface that galaxy is embedded in are being “slid” away. This then can lead to the discrepancy between time and distance (13.7 billion years vs 47 billion light years).
This 47 billion light years is only the distance to the CMB region some 370,000 years after the big bang. If we could get the neutrino telescopes or gravity wave interferometers to peer much further back to the inflationary period of the universe this distance will become far greater. On a local frame the light cone defines the projective space and the local projective Lorentz group. This is naturally defined because of the null property of light rays, ds^2 = 0. Globally, where these local frames “mesh together” on the whole spacetime, this projective spacetime has a more complex geometry, so that the distance “infinity” is parameterized by a finite time interval. That distance “infinity” is, or close to, the initial quantum event giving rise to the observable universe. That might be a quantum fluctuation of some vacuum state, the collision of branes or … , which is infinitely far (or approximately so), but is also the single point from which the universe emerged.
Lawrence B. Crowell
Geraint said: “the FRW “metric” is a coordinate system on the underlying geometry.”
At this point I can only say: “Huh?”
“The important thing is the observables are the same.”
If we are really going to be hard-headed positivists then we should give up all talk about hypothetical objects like “galaxies” and confine ourselves to discussions of optics in telescopes etc. The point of these discussions is to find a way of *thinking about* what we mean when we say “space is expanding”.
Let’s try this. Pythagoras came up with a formula for the distance between two points. Naturally enough it did not occur to him that his formula should include any functions of time. But fascinatingly enough it turns out that he was wrong: the corrected version of Pythagoras’ formula *really does* have an *intrinsic* time dependence. So in order to understand the distance between two objects, it is no longer enough to know where they are and how they are moving: *superimposed* on that, the laws of geometry are dependent on time. This time-dependence of the laws of geometry is what we call “the expansion of space”.
I find that infinitely simpler and more interesting than a tedious addition of infinitely many Doppler shifts etc etc etc. It is just a translation into English of the mathematics of GR applied to cosmology. It has also the virtue of being true.
> At this point I can only say: “Huh?”
You may say huh, but the statement is correct. The FRW metric is a coordinate choice, but there are others that can equally be thrown over the geometry of the universe. In FRW (comoving) galaxies are stationary, in others they are not.
The point is that all of these coordinate systems are equal, FRW is no more “fundamental” or special than any other (like choosing cartesian over polar on a piece of paper – both are just coordinate systems).
I know what I think about “the expansion of space” – if you look at the 3 papers at the start of this thread, I wrote one of them.
>I find that infinitely simpler and more interesting than a tedious addition of infinitely many Doppler shifts etc etc etc.
Again, the point is that this viewpoint is as valid as anyone elses.
Geraint on Oct 8th, 2008 at 9:39 pm
You may say huh, but the statement is correct. The FRW metric is a coordinate choice,
That is true, the metric is given by a coodinate choice, which underlies the connection coefficients, which in turn are used to compute curvatures. The metric is a tool, and points defined in a particular metric are calculational entities of sorts.
Lawrence B. Crowell
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!”
neophyte “So, what are you saying space is, if it is not some thing?”
Geraint “Nothing”
Oh yeah? Where’s the geometry then?
>Oh yeah? Where’s the geometry then?
It’s a mathematical construct, just like the wave function, magnetic fields and all the other constructs.
i.e. – it’s nowhere.
Before I give up, I have to correct
“You may say huh, but the statement is correct. The FRW metric is a coordinate choice,”
A metric is a particular kind of tensor. It is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.
Likewise the fact that a particular spacetime has the FRW structure is a property of that spacetime’s geometry. It is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.
Everything about FRW spacetimes can be stated without ever mentioning any coordinates. With a few [extremely non-generic] exceptions, namely the ones with maximal isometry groups, one can say definitely whether they are expanding or not. Generically they do expand or contract. This statement is not a coordinate choice, it can be defined without ever mentioning coordinates, and it doesn’t care about coordinate choices.
LB Crowell said “That is true, the metric is given by a coodinate choice”
No, that most certainly is *not* true. See the early chapters of Misner Thorne and Wheeler.
I can try.
At any distance. Comparing velocities at different spatial locations is simply not a valid operation in General Relativity. Doesn’t matter whether it’s a millimeter, a light year, or a billion light years.
Now, then, that said, it is something that you can do in special relativity, which assumes perfectly flat space-time. So you can go ahead and compare relative velocities in different locations as long as the area has an approximately flat space-time.
Therefore, since the curvature of the universe is essentially set by its expansion rate, the expansion rate of the universe determines how far away assuming special relativity works (which is typically as far as the expansion is negligible, so within a megaparsec or so, and also far away from any really dense objects, such as black holes or neutron stars). So as long as you stick with special relativity, and as long as that works as an approximation, you’re golden.
Now, does this mean that in General Relativity there is no speed of light limit? Certainly not! The speed of light limit in General Relativity just means something different: no object with mass can ever outrun a light ray. That is to say, if I use a laser to pulse a beam of light off in some direction, and at the same time launch a rocket ship from that same location, that rocket ship, provided it takes the same path as the laser beam, can never ever catch up to the beam of light, no matter how much acceleration it has or how fast it moves.
Of course, if the space ship was launched before the beam of light, in some special circumstances it is possible for the beam of light to never catch up either. This depends entirely upon the curvature of the space-time through which the ship travels, and it’s exactly why we can see things today that are some 20 billion light years away: when that light was emitted, they were much, much closer than that. But the universe has expanded since then, and they’ve moved so far away in the intervening time that we can no longer ever reach them with a beam of light, nor they us.
Well, no, they’re saying basically the same thing. After all, if there’s no such thing as expanding faster than the speed of light, then it doesn’t make sense for there to be a speed limit on it, does there?
As for why this is, it’s simple: expansion of space is not a speed. Expansion of space is speed per unit distance (or, equivalently, inverse time). The Hubble constant, for instance, is often given in units of km/sec/Mpc. You just can’t compare this number to the speed of light because it’s got the wrong units.
Geraint,
While it may be true that things like wave functions, magnetic fields, manifolds, metrics, etc. are mathematical constructs, mathematics is the most specific and accurate way which we know to describe the universe around us. A “magnetic field” exists in the exact same way that a tree exists. While the mathematical equations that describe the status and behavior of a magnetic field are not in and of themselves the field, they are a description of a real, physical system which we call by the name “the magnetic field”.
H.M. Amir … King of the Yemen. on Oct 9th, 2008 at 5:47 am
LB Crowell said “That is true, the metric is given by a coodinate choice”
No, that most certainly is *not* true. See the early chapters of Misner Thorne and Wheeler.
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What is invariant is the interval ds^2 = g_{ab}x^adx^b. However, for a particular spacetime problem how one assigns coordinates is given by a coordinate condition or a gauge-like choice.
Lawrence B. Crowell
Jason Dick, thanks a lot for taking time! I must let this sink in to my little brain 😉 this is not easy stuff for a layman.
Geraint, thanks and I’ll be back with some questions about – Expanding Space: the Root of all Evil?
Rob Knop, sorry man. It was not my intention to slam on *you*, just to “stir the pot” of language confusion. The real nutcase here is *me*, not understanding. Physicists are my heroes!
Yes, FRW is a coordinate choice on a particular geometry. There is nothing special about the choice.
I disagree on the magnetic field statement above – The classical “magnetic field” of Maxwell is not observable, only its consequences. Is it “there” filling space with little red field lines (with little blue field lines of its friend, the electric field)? I suggest you have a read of a little Feynman and the development of QED on that one.
The question might be asked whether the electric or magnetic field in quantum mechanics are Hermitian operators. Of course they are not being of the form
E ~ int dk a^*e^{i@} + a e^{-i@}, @ = kx – omega*t,
and so the matrix elements are off diagonal. Strictly speaking an observable in QM is determined by a Hermitian operator.
I indicated yesterday how the global relationship between distance and time can be seen according to projective geometry of null rays. One is from there free to hang the spatial surfaces on this framework as one want (shift functions) and how they foliate together (lapse functions).
Lawrence B. Crowell
“Everything should be as simple as it is, but not simpler.” — Einstein
Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?
> Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?
No – you can’t “see” the magnetic field – you see an interaction – in QED the “magnetic interaction” is mediated by photons, which, in the large number limit, looks like a “classical magnetic field”. If there were no iron filings there, there would be no photons mediating the magnetic interaction and hence no classical magnetic “field”.
Jason Dick:
Well, no, they’re saying basically the same thing. After all, if there’s no such thing as expanding faster than the speed of light, then it doesn’t make sense for there to be a speed limit on it, does there?
As for why this is, it’s simple: expansion of space is not a speed. Expansion of space is speed per unit distance (or, equivalently, inverse time). The Hubble constant, for instance, is often given in units of km/sec/Mpc. You just can’t compare this number to the speed of light because it’s got the wrong units.
No, it’s not the units that’s the point. At a large enough distance (added up successive “steps” of concatenated local separations) that still generates a separation rate of c, and farther away the rate is even higher. You’re just hiding the separation velocity itself under a rug (making the ration seem to be the point.) There is no limit because we are talking about the rate of change in total distances between various galaxies in a case with no true physical edge (no place where anyone can’t see yet more galaxies in all directions) nor is there a small-enough closed universe (e.g. hypersphere.) Like I said, you imagine this as a “realist” thinking that those galaxies exist and next to one far from us is another one, and from them yet another, and so on – even if we can’t see all of that and never will.
You just have to get out of thinking in terms of SRT and being able to compare local objects that can move *right past* each other. Yes, it is like a “rubber sheet” because as the whole sheet expands, the bumps on it separate accordingly in a classical-type way (I mean, effectively in context, don’t go thinking I meant it literally is a classical process.) Of course this has to be thought of in terms of “cosmic time” to make sense. I am surprised not to hear more about CT in this discussion, do you guys appreciate its significance? Check out the Wikipedia piece:
Cosmic time
From Wikipedia, the free encyclopedia
Cosmic time (also known as “time since the big bang”) is the time coordinate commonly used in the Big Bang models of physical cosmology. It is defined for homogeneous, expanding universes as follows: Choose a time coordinate so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). Measure the passage of time using clocks moving with the Hubble flow. Choose the big bang singularity as the origin of the time coordinate.
Cosmic time is the standard time coordinate for specifying the Friedmann-Lemaître-Robertson-Walker solutions of Einstein’s equations.
Ehhh… I’m not sure what you are talking about here Jason Dick, Geraint and Lawrence B. Crowell, but surely the magnetic field could be observable with a little aid?
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A charged particle will move according to
F = g(E + vxB)
in the presence of an electric and magnetic field. This does not tell us that these fields are “real” as such. They might just be ways in which we organize things to account for the motion of charged particles.
This is one of those frustrating things about physics. A lot of what we use as tools, methods and mental images and constructions might not have quite the hard reality we would like them to have.
Lawrence B. Crowell