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.
eraint, glad that you are “back”! 😉
[Several of my posts did not appear – hope I haven’t upset someone so am now moderated :/ ]
I’m pretty sure that you are *not* moderated by Cosmic Variance, same thing has happened to me several times.
I know more about programming than physics, and it seems to be a problem of “transaction handling” (i.e. what do you do when two or more users are trying to do the same thing at the same time), but I don’t know if Cosmic Variance uses a back-end database (probably they do). Anyhow this is what you do:
How-To Avoid “Pseudo Moderating”
1) Always write you comment in an editor, if it’s long (and you don’t want to lose it).
2) Copy and paste the text in the reply-form and hit Submit.
3) Always check that it worked OK.
4) If Murphy’s Law decides that you have too much spare-time (and therefore sends your text to Cyberspace), repeat No. 2-> 3.
5) If you get an error message (after No. 4 -> 2 -> 3) saying “This comment is already saved” (or similar). Change one character and repeat No. 2-> 3.
And you are OK!
(Lawrence, I’ll be back)
(G)eraint,
6) Also remember to copy the first character in the text! 😀
The idea of space expanding can of course be removed. We can consider the whole spacetime, or look at local light cones in spacetime, without any direct reference to space expanding. So the notion of space as some “rubber sheet” which stretches or contorts is not needed. That picture of things only comes about if one looks at the spacetime as a foliation of spatial surfaces linked by lapse and shift functions. How one considers this folation is a matter of coordinate condition one imposes of course. Of course one normally does so with respect to the Hubble frame. Each spatial surface is linked to the other by the diffeomorphisms of general relativity, which we identify (with some subtle issues I am ignoring for now) this with a temporal evolution of spatial surfaces. In this sense the spatial surfaces of a cosmology can be said to be stretching.
This picture is of course coordinate dependent. There is something in gauge theory called the elliptic sequence. So a system of one-forms or connections are mapped to the field two-forms through an intermediate set of form which “mod-out” group actions or diffeomorphisms. This might be seen as
$latex
Omega^{1}(ad~g)~^Mrightarrow~{tildeOmega}^{1}(ad g)~^Drightarrow~Omega^{2}(ad g)
$
where the map “M” takes connection terms on the left hand side and maps them to
$latex
M:A~rightarrow~A/diffeo(g),
$
and defines a moduli space. This is done by imposing gauge conditions on the problem, where each gauge condition is a “moduli” in the moduli space.
The problem with focusing too much on pictures such as rubber sheets expanding, twisting or in general evolving is that one is focusing a lot on a particular coordinate condition and not on the more general problem. So in that sense focusing too much on this is problematic. It is not so much that it is “wrong” to look at GR according to moving points or shifting spaces, but rather one is best not to focus exclusively on this aspect of the problem.
Lawrence B. Crowell
Lawrence B. Crowell, just a short question:
Do you think that it is ever possible to translate the elegant equations that explain the geometry of the Universe, in to a 3D movie (and export in to a Flash on web for the public)?
(I’ll be back with more questions later)
Clarification: We saying *3D movie* – I mean using a 3D software where you have vertices that can be manipulated and visualized in a 3D space (x, y, z), and using animation in the 3D software you get the fourth dimension of spacetime.
I am not sure, and it must might be a movie of expanding space! The big issue I was driving at is with moduli spaces. There has been considerable mathematical work in this arena. Interestingly the moduli space for general relativity, due to the hyperbolic nature of the connection one-forms, is non-Hausdorff. This makes things very interesting, for it means that sequences of gauge connections may not converge as Cauchy sequence.
I wrote elsewhere recently about my sense that technology makes us stupid. Call it “Amusing Ourselves to Death.” It seems to me that our multi-media world is taking the place of that inner visual-auditory system in the brain or mind. As a result I have growing suspicions that it kills imagination and reasoning. I sometimes wonder if technology is self-limiting, for at some point you end up with people who are information rich, but reasoning poor and thus incapable of sustaining the technological trajectory. Of course you can combine that with resource depletion and planetary ecospasm, and — well you get the picture.
People should maybe exercise the discipline to use that marvelous multi-media machine we have had from our evolutionary roots.
Lawrence B. Crowell
> Personally, I think “expanding space” is an extremely useful concept. My universe will keep expanding.
Hi Sean – We arn’t saying that the universe isn’t expanding, just that you have to be careful with talking about expanding space – thinking about the universe as a rubber sheet can lead to problems.
“rubber sheet” is a bit of a straw man don’t you think?
Although it’s probably closer to the truth than saying space is nothing.
> .Although it’s probably closer to the truth than saying space is nothing.
No – it isn’t. Did you read any of the papers at the top?
Geraint, do you have any comments on momentum and the mass of photons?
>> It’s completely new to me that all photons carry momentum, fascinating! But it’s also weird since momentum the product of the mass and velocity of an object (p = mv), and photons don’t have any mass??
p – mv is momentum in classical physics – in special relativity there is a relation between energy, momentum and mass
E^2 = (mc^2)^2 +(pc)^2
for photons, m =0
So they carry momentum and have no mass.
(actually – em radiation carries momentum in classical physics).
Lawrence B. Crowell, I guessed that it wouldn’t be that easy. It’s a little “sad” though that the “sexiest thing” there is for the non-mathematical public to visualize our expanding universe is this raisin bread…
It might be impossible to simulate real spacetime since the four dimensions are (obviously) connected (by speed of light) in a way that is never(?) possible in a 3D software.
I agree in much of what you are thinking about new technology. But I think it’s a never ending story in evolution of society. Take the hunter-gatherer society 10,000 years ago. If they saw us now – sitting inside an office, writing weird stuff on paper or hammering on a keyboard – they would think that we had lose it all, the deeper knowledge and feelings about the nature is gone.
But we got other knowledge and skills that are not all bad, and the best I think we can do is to make the right choices to push civilization in the right direction, using all tools available to make it happen.
We can’t go back to slide rule or hunter-gatherer, except if we find some way to change the direction of time.
Ok, thanks Geraint! I have to go to bed it’s 02:50 here and it’s work tomorrow. But I shall be back.
I guess what I’m saying, Geraint, is that when you say “empty” space is nothing, you couldn’t be more wrong.
In any case, it’s absurd to suggest that GR says that “empty” space is nothing. You don’t need a differentiable manifold to mathematically model nothing.
I read Sean’s book on GR. If “empty” space were nothing, then Sean’s book would only need to be zero pages long.
>I guess what I’m saying, Geraint, is that when you say “empty” space is nothing, you couldn’t be more wrong.
In any case, it’s absurd to suggest that GR says that “empty” space is nothing. You don’t need a differentiable manifold to mathematically model nothing.
I read Sean’s book on GR. If “empty” space were nothing, then Sean’s book would only need to be zero pages long.
I too have read Sean’s book – where in there does it say space is a thing in GR? The “manifold” describes the action of gravity in the presence of mass – it is not a property of “empty space”.
I have an idea for a very simple interpretation of the cosmological redshift. This interpretation does not rely on “space itself” expanding nor on the special relativistic Doppler Effect.
To set the context, we know that cosmological redshift follows the relationship:
?o/?z = a(o)/a(z) = (z+1),
where ? is wavelength and a is the scale factor. We also know that:
Do = De*(z+1),
where Do is the distance to a galaxy at the time of observation and De is the distance at the time of emission of a photon we see now. For example, a photon with redshift z=3 was emitted from a galaxy which is now 4 times as distant as it was then.
I believe that the cosmological redshift effect is simply a Doppler-like reconciliation of the net MEAN velocity of the photon as measured in the observer’s reference frame with the MEAN velocity as measured in the emitter’s reference frame.
In the observer’s rest frame, a photon is emitted at z=3 from a distant galaxy which is moving away from the observer at about 1.6c (in the LCDM model with Ho=71). The photon initially moves away from the observer (figuratively climbing upstream AGAINST the decelerating Hubble flow), and only at about z=1.5 begins closing on the observer. The observer measures the “net” travel distance as De, about 5.3GLy. (“Net” as distinguished from the “gross” travel distance of the photon moving first away from the observer and then doubling back past the original emission distance.)
In the emitter’s rest frame, the emitting galaxy at z=3 is at rest and the observer’s galaxy initially recede away at the same 1.6c. Viewed in this frame, the photon never moves away from the observer. The photon always moves away from the emitter in a motion rather like “surfing WITH the wave” of the receding and decelerating Hubble flow. The photon begins at a travel speed in the range of hundreds of c in this frame, and its speed decelerates smoothly over the length of the trip. The photon finally overtakes the receding observer at about 21.1Gly. This is exactly 4 times the net travel distance measured by the observer.
Despite their disagreement about the net distance traveled, the observer and emitter agree on the same elapsed time between emission and reception, because clocks tick at a uniform rate for all comoving galaxies in the FLRW metric. Thus, the observer measures a mean net travel velocity which is 1/4 that measured at the emitter. At any given wavelength, the observer calculates that 1/4 as many wave cycles (peak-to-peak) will fit into the travel distance as the emitter measures. Therefore the observer measures 1/4 the frequency and 4 times the wavelength as the emitter measures. This is a Doppler-like pseudo-time dilation.
Although its nature is Newtonian, this is not the classical Doppler Effect, because the latter measures the discrete velocity differential between the emitter and observer at the instant of emission. Instead, cosmological redshift is generated by the total (= mean) velocity over the total net travel path, because photons are either accelerating or decelerating (depending on you frame of reference) dynamically over the entire travel path.
Why don’t we observe a combination of the mean-velocity Doppler Effect I describe and the classical Doppler Effect? I believe we would, except that the redshift of the classical Doppler Effect is exactly cancelled out by the gravitational blueshift caused by the cosmic gravitation field. If the observer pictures herself at the center of a homogeneous cosmic sphere with the approaching photon at the surface, Gauss’ Law implies a gravitational acceleration force on the photon in the direction of the observer at the center. In other words, cosmic gravity applies an acceleration force to the photon like it does to the galaxies in the Hubble flow that the photon passes along its journey. This is the gravitational blueshift effect that Prof. Peacock describes in his “diatribe” and which Matt, Geraint, Luke and Berian allude to in their recent radar ranging paper.
This also is not the SR Doppler effect. I think SR is entirely inapplicable at cosmological distances in a non-empty GR universe, first because there is no global inertial frame, second because the photon passes every local galaxy at exactly c, and third and most importantly because there simply is no place in the FLRW metric to arbitrarily insert an SR time dilation factor which aggregates a quasi-infinite set of infintesimal local time dilations. As stated previously the local clocks of comoving galaxies in the Hubble flow keep identical time, regardless of any choice of reference frame in the Hubble flow. I am puzzled why Prof. Peacock expresses strong confidence that cosmological redshift is related to SR Doppler Effect, with a sort of double-doppler fudge factor stirred into the mix. In the mean-velocity Doppler model, the blueshift acceleration experienced by the travelling photon is essentially the same contractive gravitational acceleration experienced by the galaxies in the Hubble Flow, so the photon does not experience any gravitational time dilation which differs from the underlying time dilation inherent in the FLRW metric.
Finally, in case it isn’t clear, here is an example using tosses of a ball to show why the observer and emitter agree on the photon’s travel time even though they disagree on the travel distance. Imagine that you and a teammate are standing together on the field, and you start running away from him at a constant 3m/s. When you cross the 10m mark, you throw a ball to him at a speed of 5m/s (measured in your rest frame). The ball approaches him at a net 2m/s and he catches it after an elapsed time of 5s.
Next, the same example, except he throws the ball to you as you cross the 10m mark running away from him. You will catch the ball at the 25 meter mark (from him) and the elapsed time will be the same 5s. The time equation is t = De/(Vo-Ve), where De=10m, Vo=5m/s, Ve=3m/s, and V(net) = 5m/s-3m/s = 2m/s. Do = t*Vo = 25m. If the units are changed to c and ly’s, the cosmological redshift in this non-realistic example is z = Do/De-1 = Vo/V(net)-1 = 1.5.
Recognition of this scenario becomes subtle when neither party can tell who is moving and who is standing still. In cosmology, each party tends to simplify his/her own calculations by assuming he/she is the one standing still. Therefore he/she will calculate that the ball always travels further and faster when he/she is the thrower than when he/she is the catcher. At cosmological distances, we calculate that the proper speed of contemporaneous photons is always much faster when moving away from us than when approach us. This leads to other interesting consequences.
Jon
Jon Corthell, this is absolutely brilliant!!
This is what I’m talking about, to get the public a chance to understand and visualize the problem:
“Finally, in case it isn’t clear, here is an example using tosses of a ball to show why the observer and emitter agree on the photon’s travel time even though they disagree on the travel distance. Imagine that you and a teammate are standing together on the field, and you start running away from him at a constant 3m/s. When you cross the 10m mark, you throw a ball to him at a speed of 5m/s (measured in your rest frame). The ball approaches him at a net 2m/s and he catches it after an elapsed time of 5s.
Next, the same example, except he throws the ball to you as you cross the 10m mark running away from him. You will catch the ball at the 25 meter mark (from him) and the elapsed time will be the same 5s. The time equation is t = De/(Vo-Ve), where De=10m, Vo=5m/s, Ve=3m/s, and V(net) = 5m/s-3m/s = 2m/s. Do = t*Vo = 25m. If the units are changed to c and ly’s, the cosmological redshift in this non-realistic example is z = Do/De-1 = Vo/V(net)-1 = 1.5.”
On this one could even make a very instructive 3D animation on what’s going on in the universe!!
Speedy Gonzalez wrote: “Take the hunter-gatherer society 10,000 years ago. If they saw us now – sitting inside an office, writing weird stuff on paper or hammering on a keyboard – they would think that we had lose it all, the deeper knowledge and feelings about the nature is gone.”
This is absolutely true. Now to be fair they would be unaware of the fact a mathematician or scientist might be working on deep relationships they could not fathom. However, for every person doing that you have dozens tapping away on keyboards as telemarketers and accountants. We might live longer than our Pleistocene ancestors, but I think on balance “life for life” they had it better than your average modern person today. Which seems more fun?; stalking a herd of bison or mastadons in the wilderness or driving to to your office building, logging onto your computer and spending 8 hours managing other people’s accounts?
—————————-
Jon Corthell wrote:”I believe we would, except that the redshift of the classical Doppler Effect is exactly cancelled out by the gravitational blueshift caused by the cosmic gravitation field. ”
The cosmological expansion, again to use the “root of all evil” the idea of the expanding spatial sheet, means that distant galaxies are comoving with their local frames away from our position, and indeed every position will observe the same thing. Further, a photon will reflect this in its redshift. This redshift can be seen in this expanding space perspective as well. If space is expanding then so too is any volume. We might think of that volume as being a sort of virtual resonance cavity, for every photon which enters the volume is on average compensated for by a photon which exits. So if the volume expands so does the average wavelength of these photons. So the cosmological redshift can be modelled according to an expanding space.
Lawrence B. Crowell
Lawrence B. Crowell, LOL this is really good!
“Which seems more fun?; stalking a herd of bison or mastadons in the wilderness or driving to to your office building, logging onto your computer and spending 8 hours managing other people’s accounts?”
Well, if Sean could have a Self-Driving Car & Sexbot, he would choose the office, and so would I! 😀
No seriously, this is one of the weirdest and most troublesome questions ever in the history of human. We have marvelous machines and a material status then never before (i.e. 12% of us), but are we happy? Well, the consumption of Prozac and alcohol hasn’t directly reduced since Pleistocene.
Many of us are not the masters of our own life, but slaves in the rat race for (more) money.
So of course, our Pleistocene ancestors lived a freer and healthier life, but the rules where much much tougher. If you got seriously ill, you were dead. (= no health insurance)
Oops, here are two corrections to my post on cosmological redshift:
1. I was wrong when I said “The photon begins at a travel speed in the range of hundreds of c in [the emitter’s frame]. The initial “instantaneous” travel speed of a photon emitted at z=3 is about 4c in the emitter’s frame. I accidentally looked at my spreadsheet cell for the instantaneous speed of a photon emitted at z=1023, which is greater than 1000c in the emitter’s frame.
2. I was wrong to characterize Prof. Peacock’s diatribe reference to SR being related to cosmological redshift as a “double-doppler fudge factor.” I meant for this to refer to the SR cosmological redshift equivalence equation in Tamara Davis’ excellent contribution in Appendix A to the recent paper “Time Dilation in Type Ia Supernova Spectra at high redshift” by Blondin et al, 4/08.
Prof. Peacock combines an integration of SR redshift and gravitational blueshift. I think that’s the most reasonable approach for applying SR, but I think it is incorrect to apply SR to cosmological redshift at all for the reasons stated in my post.
One conceptual point to consider is whether the geodesic of a photon emitted by a galaxy in the Hubble flow is properly categorized as purely “peculiar motion”. I submit that it is not. We know that a particle’s peculiar motion “decays” as the universe expands, causing the photon’s motion to eventually be sort of “absorbed” into the Hubble flow, i.e. indistinguishable from it locally. That effect never happens to the photon, which continues to “skate across” the ever-changing local Hubble flow at a constant rate of c, in perpetuity. Conceptually then, the geodesic of a photon emitted by a galaxy in the Hubble flow is fundamentally governed by the same FLRW metric that governs the geodesics of the galaxies the photon passes. This reinforces the point that any geodesic incorporating an element of SR time dilation would be incongruous at cosmological distances in an FLRW universe.
Jon
Jon Corthell, I have been thinking about the “throwers” point of view:
“The initial ‘instantaneous’ travel speed of a photon emitted at z=3 is about 4c in the emitter’s frame”
… and …
“Therefore he/she will calculate that the ball always travels further and faster when he/she is the thrower than when he/she is the catcher.”
But, you can never throw a “ball” faster than 1c (the speed of light), can you?? The thrower must always see the “ball” leaving at maximum 1c … or??
Hi Speedy,
Yes you are correct, the photon can’t initially be moving at 4c from the emitter. The instantaneous speed of the photon compared to the emitter starts at exactly 1c of course, but then it accelerates rapidly as the photon “surfs away” with the receding Hubble flow. The AVERAGE speed of the photon is about 2.7c over the travel leg starting at z=3 and ending at z=2. As compared to an average speed of about 5.44c if it started at z=7 and ended at z=3.
In the emitter’s frame, the Hubble flow moves faster as a function of distance away from the emitter, but the entire Hubble flow also decelerates as a function of time, which somewhat correlates to the photon’s distance from the emitter as well since the photon is moving constantly away. The resulting geodesic nets the two effects.
If you are interested, here are the figures from my spreadsheet for a photon’s AVERAGE travel speed away from the emitter on each individual segment of its path starting at z=1089 (the CMB surface of last scattering) and approaching the observer:
z1089 => z1023: 1048c
z1023 => z511: 686c
z511 => z255: 346c
z255 => z127: 174c
z127 => z63: 87c
z63 => z31: 44c
z31 => z15: 22c
z15 => z7: 11c
z7 => z3: 5.4c
z3 => z1: 2.7c
z1 => observer: 1.4c
These are calculated simply as travel distance divided by elapsed time for each segment. Note that (z+1) for each segment represents a halving of the redshift compared to the segment above it on the chart, except for the z1089 leg. The average photon recession speed also roughly halves during each successive segment; but this relationship is not exact in a universe with a cosmological constant dark energy.
Jon
Groan…
I’m not sure I’m with you here Jon…
“then it accelerates rapidly as the photon ‘surfs away’ with the receding Hubble flow”
Ehhh, how can the photon “surf” and on what? And doesn’t the “Hubble flow” have a “slowing down effect” all the way from start up to my nose??
Jon Corthell, I think you’ve missed an important part on the ball field.
Let’s put 3 guys on the field:
A are standing still
B are running
E(instein) is watching from beside
B is throwing a ball to A. Initially it would look like this:
A :
E
B will throw the ball after running 10m at 3m/s.
B will see the ball leaving at 5m/s.
A will see the ball approaching at 2m/s.
A will catch the ball after 5s, when B has been running another 15m
B will get confused since he was able to run another 15m before A catches the ball, and he should only have been able to run another 6m??
E smiles secretly because he knows that the clocks for A & B are not synchronized…