"Redshift" is a term that astronomers use a lot. This is particularly true if they are extragalactic astronomers or (especially) cosmologists, but even galactic astronomers use it, and it is absolutely central to the method use to discover most of the extrasolar planets known today.
This post is going to be divided into three parts. First, I am going to explain that redshift itself is just a definition of an observable or measurable quantity, without any need to reference what caused it. Second, I'm going to talk about the more familiar source of redshift -- the Doppler shift. Finally, I'll talk about the gravitational redshift-- and, specifically, the cosmological redshift-- that is what astronomers are talking about when they talk about the expansion of the Universe.
The Observational Definition of Redshift
When you take a spectrum of an object, you are breaking its light out into its constituent colors. Many people are familiar with the fact that if you shine sunlight through a prism, you see a rainbow. Indeed, below is a picture of a high-resolution spectrum of the Sun taken at Kitt Peak. Visualize all the horizontal bands put end-to-end to make a really, really long rainbow— that's what makes it so high resolution!
There's something to notice here other than the rainbow: the dark bands. These are called "absorption lines." They are very specific colors — very specific wavelengths of light — where some type of atom found in the atmosphere of the Sun absorbs light. The neat thing about this is that the wavelengths of those lines are set by atomic physics. We can figure them out from calculations, or by making measurements in the lab. (In practice, we need both; some species, such as the Hydrogen atom, can be calculated very well. Other atoms and molecules are harder to calculate, so sometimes the calculations need to be supplanted with empirical determination.)
When we say we observe a redshift, we say that we are observing light whose wavelength has been shifted. For example, in red light, there's a well-known line that comes from the Hydrogen atom at 6563 Angstroms. If we observe a star that has that absorption line, but it shows up at 6567 Angstroms, we know that the light has been shifted to a wavelength that is 4 Angstroms longer. We know from atomic physics that when the light was emitted, it was at 6563 Angstroms, so something has happened between emission and detection to make the observed wavelength different.
We define the quantity redshift — often denoted with the variable z — as the difference in thew wavelength divided by the original wavelength. In my example above, the redshift z would be 4 Angstroms divided by 6563 Angstroms, or z=0.0006. If light shifts to shorter wavelengths, we would call that a negative redshift— or, sometimes a blueshift. (Red light has a longer wavelength than blue light, hence "redshift" being a shift to longer wavelength, although that would term apply even in the case of a shift from the red fo the infrared.)
And that's all there is to it! We can define and measure what redshift is without any reference to what causes it.
So what causes it?
The Doppler Shift
Most of us are familiar with the Doppler shift in sound. When a car goes by you, you hear the characteristiic "...rrrrrrRRRRROOOWWWWwwwww..." sound, with the pitch higher at first as it is coming towards you, and lower later when the car is moving away from you. The same thing happens with light. If I'm looking at you, and you are moving away from me, I will see all the light you emitted shifted to the red.
For low speeds (i.e. a lot less than the speed of light), it turns out that the redshift is just the speed of the emitter relative to the observer divided by the speed of light! Consider the example above. Suppose that you are holding a vapor tube with rarefied Hydrogen in it, and that Hydrogen is emitting light at 6563 Angstroms. If I observe that light at 6567 Angstroms, I would say that's a shift of 4 Angstroms, giving me a redshift z=0.0006 Angstroms, implying that you're moving 0.0006 times the speed of light (or about 400,000mph). (Slow down! Woah!)
If you were coming towards me, I would observe any light you emitted to be blueshifted— that is, I would observe it at a wavelength that is shorter than the wavelength you emitted it at.
Generally, when you think about measuring a speed, you think about looking at something, waiting, looking at it again, seeing how far it went, and determining the speed from how far it went in a given amount of time. In astronomy, alas, even though things tend to be moving very quickly compared to speeds in our everyday lives, things are so far away that often it takes a very long time for the object to have moved enough for us to be able to detect it — and for the vast majority of objects, they're just too far away for us to have been able to detect their motion. Redshift is neat, though; it lets us measure speeds of things moving in at least one direction (i.e. towards or away from us) all in one go.
We can use this, for example, to measure the rotation of a galaxy. If you look at a galaxy and see that all the stars on the left side are blueshifted and all the stars on the right side are redshifted, then you know the galaxy is rotating with the left side coming towards you and the right side moving away from you.
The Doppler shift, however, is not the explanation for the redshifts we observe as a result of the expansion of the Universe....
The Gravitational and Cosmological Redshifts
While many people are familiar with the idea of the Doppler shift, few are familiar with the gravitational redshift.
Consider the following thought experiment. You are standing at the bottom of a tower, and I'm standing at the top of a tower. We're both at rest, not moving relative to the surface of the Earth. You have your favorite Hydrogen gas vapor tube that's emitting Hα light at 6563 Angstroms. When the light reaches me, however, it turns out that the wavelength is slightly longer— the light has been redshifted! This is clearly not a Doppler shift, since we aren't moving relative to each other. This is what's called the "gravitational redshift." And, yet, there is a redshift. In this case, for a 100m tall tower, it turns out that the redshift will be only about one ten-billionth of an Angstrom, so I'm not going to be able to measure it. However, there are cases were gravitational redshift can be quite significant, as in the expansion of the Universe.
(If you will allow me to briefly lapse into borderline technical language for those few in the audience who know some GR, the gravitational redshift is simply the result of the metric being different at the point of emission as compared to the point of detection.)
One special case of the gravitational redshift is what we call the cosmological redshift. Now, to understand the cosmological redshift, we have to know a little bit about the expansion of the Universe. This is a conceptually difficult topic, so I won't do it justice at the moment. However, let me just say that the expansion of the Universe is not galaxies flying apart from each other, even though you will often hear it described that way. Rather, the expansion of the Universe is just the Universe getting bigger. As the Universe gets bigger, galaxies get farther apart from each other, because there's more space between them. There are lots of analogies to this. Consider, for example, an infinite loaf of raisin bread. There's dough, and there's raisins embedded in it. If you have yeast in the dough and you leave it to rise before baking, everything will get bigger. All of the raisins will get farther apart from each other as the dough expands. The raisins aren't moving through the dough, but they are getting farther apart.
Another analogy is to consider the surface of a balloon, with pennies pasted on the surface of the balloon representing galaxies. I have made a 3d animation that tries to show this analogy to the expansion of the Universe.
Now here's the deal with the cosmological redshift. The whole expansion of the Universe comes out of General Relativity, and is a gravitational thing. The cosmological redshift is the gravitational redshift applied to this specific circumstance. The result you get is that wavelengths of light expand at exactly the same rate as the Universe. Here is another 3d animation that attempts to illustrate that statement.
The cosmological redshift is a wonderful thing. Because light expands at the same rate of as the Universe, measuring a redshift that is the result of this effect means that you have measured exactly how much the Universe has expanded during the time between when the light was emitted and when the light was detected.
Redshift turns out to be a very useful quantity. The Universe is expanding now, and has been expanding since the beginning (the moment of the Big Bang). What this means is that the longer you wait, the more the Universe will expand. Now, think about the fact that the speed of light is finite. What that means is that the farther away something is, the longer it takes for light to reach you from that object. When you look at the Sun, you're looking at light that was emitted 8 minutes ago. When you look at the Andromeda Galaxy, you're looking at light that was emitted 2 million years ago. If you get a telescope and look at the Virgo Cluster, you're looking at light that was emitted 65 million years ago. And so forth.
Because the farther away something is, the more time the Unvierse has had to expand in between when that thing emitted light and when you detect that light, that means that in our Universe, the farther away a galaxy is, the greater its redshift will be. (It turns out for very nearby galaxies, like the Andromeda galaxy, there's a little bit of Doppler shift on top of the cosmological redshift, so this doesn't work very well there. Indeed, the Andromeda galaxy has a blueshift because even though the Universe has been expanding for the last 2 million years since light from that galaxy was emitted, the Doppler shift of the galaxy coming towards us is a bigger effect! For galaxies that are farther away and that show a bigger cosmological redshift, any additional shift due to the Doppler shift becomes insignificant.)
This is why you will often hear astronomers use "redshift" as a stand-in for distance. When we talk about observing a galaxy at a redshift of "z=1", what we mean is that we're observing a galaxy so far away that during the time the light was traveling towards us from that galaxy, the Universe had time to expand so much that we'd observe a redshift of 1. (That means that the change in the wavelength divided by the wavelength is 1, or that the wavelength has doubled. Thus, if we see a galaxy with a redshift of 1— which we do all the time&meash; we are seeing a galaxy from the time when the Universe was half its current size.
Redshift: observationally, it just has a definition that is the change in wavelength divided by the original wavelength. It can result from a couple of things: the Doppler shift, and the gravitational redshift. The redshift we see from the expansion of the Universe is not a Doppler shift from galaxies flying away from us! Rather, the cosmological redshift is a special case of the gravitational redshift, and is a direct result of the fact that the Universe has expanded between when the light was emitted and when it was detected.
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Something that I've often pondered is, where does the space come from? I mean, the space that must be "created" between galaxies as the universe expands? Is it energy from the initial Big Bang? Or am I thinking about it in entirely the wrong way?
You're sort of thinking about it the wrong way. There isn't really energy in spacetime itself. Indeed, energy in GR is sort of a scary thing; there isn't any universal global conservation of energy law. There is a *local* conservation of energy law (the 4d analog of the continuity equation from fluid dynamics).
It's probably not really right to say that "space is created between the galaxies," even though I said that. The space is just getting bigger; the galaxies are getting farther apart.
There used to be a black and white sign on a lab door in the Vandy Physics Dept. that said "Warning: If this sign is blue you are traveling too fast." Is it still there?
No, the sign isn't there any more. I have seen a red bumper sticker that says exactly that.
Redshift - mind-shift!. I am still pondering, but it seems that I have been enthralled by the popular media's uniform coupling of universe expansion with Doppler redshift. Dang, 'Basic Concepts' should not be this convoluted.
I take from this article that there is also, in common usage among cosmologists, more significant gravitational and cosmological redshifts. That gravitational redshift (unexplained and unreferenced although it was implied that it derives from General Relativity) includes the cosmological redshift (General Relativity, again) (better defined but still indistinguishable from the other redshifts (if you think about it too much.)) And, at the 'basic concept' level, it seems that cosmologists don't care to comment on whether the three mentioned redshifts play well together (it somehow seems to me that Doppler would be a (very) special case of 'cosmological' and that, given the lineage of each of them, it may well be insufficient to speak of them as independent effects).
Thanks for an article which provided considerable (yet to be evaluated) information as well as much needed conformation that I don't know it all yet!
So the space between the galaxies is getting bigger, and that would insinuate that the galaxies themselves are getting bigger as well correct? The stars themselves, planets, us, all the way down to a quantum level?
So does the "distance" between galaxies (ignoring any relative movement) really change if measured by something physical, say, a metre stick? If the universe has doubled in size, so has my metre stick.
What implications (if any) does that have on a quantum level? Obviously thinking of atoms and particles as little balls is incorrect (quarks aren't twice as big now as they used to be), but it must all change together otherwise wouldn't we see observable differences in the very nature of the universe as we look into the past?
Sorry if I'm not articulating my question properly.
Oh and wanted to add: I really have enjoyed your blog so far!
So the space between the galaxies is getting bigger, and that would insinuate that the galaxies themselves are getting bigger as well correct? The stars themselves, planets, us, all the way down to a quantum level?
No -- they *would* be, but there are local forces that hold them together against that expansion. With galaxies, it's their own local gravity. With us and atoms and all of that, it's all the other forces.
So as the Universe expands, the galaxies get farther apart, but they don't expand themselves.
An analogy (that's actually really about the same thing) is considering the Earth going around the Sun. The side of the Earth closer to the Sun is feeling a stronger gravitational pull, and so would want to be moving in a faster orbit than the side of the Earth on the opposite side of the Sun. This would tend to stretch the Earth out into a schmear along its orbit. However, the Earth's own gravity holds it together against that.
On the quantum level, there's really no implication :) The other forces are *so* much stronger than gravity that nearly everybody who does quantum mechanics completely ignores gravity. The only people who do feel much consternation, because General Relativity and Quantum Mechanics don't really work well together. That's what the string theorists (at least some of them) are trying to work on, but for most of us-- either we deal with gravity (i.e. planetary orbits, galaxies, the expansion of the Universe), where other forces don't matter (because they are confined, a la the strong force, or because the charges all cancel out, a la the electromagnetic force); or, we deal with the other forces, where gravity doesn't matter (atoms, molecules, etc. -- and gravity's so much weaker than the other forces).
(If you remember Comet Shoemaker-Levy 9, before it slammed into Jupiter, it did pass close enough to be broken apart by the tidal forces of Jupiter.)
-Rob
AnotherRoy -- yeah, there are other gravitational redshifts. To be honest, I'm not sure how well or how many have been measured. However, the GPS system *must* take into account the gravitational redshift (and gravitational time dilation) due to the Earth; if it didn't, it would be woefully off within a matter of hours. It's a tiny effect, but the GPS needs enormous precision.
-Rob
forgive my ignorance please , but would the redshift from a particular structure be the same , independent of one's location in the universe , at the same point in time .
Good post, Rob. Keep it up.
Rob,
In one reply, you wrote:
Are you discounting dark energy (in whatever form you care to speculate) or are you saying that dark energy is not a property of spacetime?
I guess I would argue that dark energy really is energy in spacetime itself. Is that wrong?
I have a very basic question about redshifted light.
Suppose a photon leaves a distant galaxy at 656.3 nm (isn't that already red?), and the universe expands while it is traveling towards us, so that it arrives at 693 nm. Converting from wavelength to energy, that photon has lost 0.1eV. Where did that energy go?
Also, how is any of this used to find extrasolar planets? Isn't that done via wobbles?
Finally, do real astronomers use diffraction gratings or dispersion media to make their high res spectra?
I'm not sure is this is a naive question or a technical one, but how are you able to recognize that a line at, say, 6567 Angstroms is indeed the Hydrogen line shifted, rather than some other line shifted even further? Does the line itself have an identifying feature aside from the wavelength? Or do you look at relative positions of lines?
but would the redshift from a particular structure be the same , independent of one's location in the universe , at the same point in time .
No. The redshift you'd observe would depend on how long it took for light from that object to reach you.
The redshift is exactly the same as the amount of expansion. How much redshift you get will depend on how long the photon was travelling, which means it will depend on how far away the structure is from the observer. More distant objects will always be seen to have higher redshifts because the light took longer to reach the observer, so the Universe had more time to expand
Are you discounting dark energy (in whatever form you care to speculate) or are you saying that dark energy is not a property of spacetime?
I guess I would argue that dark energy really is energy in spacetime itself. Is that wrong?
The real answer is that we don't know. If dark energy is vacuum energy, then, yes, it is a property of spacetime itself, and then, yes, as you have more space, you have more energy.
Which sound like cheating, but again, GR doesn't have a global conservation of energy law....
On the other hand, it's possible that dark energy is just another thing that's in the Universe, like dark matter or normal matter.
-Rob
Where did that energy go?
:)
Nowhere.
Again, there's no global conservation of energy law. There's a local continuity law, but that's it.
Sometimes in GR you can define the equivalent of what is gravitational potential energy in Newtonian gravity, and losses like the one you mention go there. However, this isn't always the case.
Also, how is any of this used to find extrasolar planets? Isn't that done via wobbles?
Yes. The wobble you mention is the reflex motion of the star as a planet orbits around it. That's observed via a periodic Doppler shift (sometimes of just meters per second, which is tiny compared to what astronomers usually measure) in the star's spectrum.
Finally, do real astronomers use diffraction gratings or dispersion media to make their high res spectra?
Usually diffraction gratings-- reflection gratings, in particular. Sometimes lower resolution spectra use a "grism," which is a combination of a grating and a prism.
-Rob
Or do you look at relative positions of lines?
This is it. It's pattern matching.
There is one other characteristic feature, and that is the strength of the line. You notice in the solar spectrum that some lines are stronger than others. So, it's not just the relative positions of the lines, but also their relative strengths. The relative strengths can vary depending on the composition of the source you're looking at, and on its physical conditions, but some lines generally tend to be stronger than others.
Sometimes with emission spectra you can do OK if there's only one line. If you have a general idea of what the redshift is, there may only be one line that the one you observe could plausibly be. However, in cases like that, there can be ambiguity.
-Rob
Pfft. Pound and Rebka needed only 22m, or thereabouts :P
I've yet to be convinced that there's any meaningful distinction there.
I was going to say the same about dark matter and/or energy and/or flux capacitors but David Heddle beat me to it. Given that we really don't know what Dark X is, or really where it is (under the couch?), it seems to me that you can't ultimately say that space is or isn't created/expanded. Far be it from the realm of science possibility to announce next week that the expanding universe is actually creating dark matter/energy as it goes. I recently read a list of things "we" don't know, and it seems the answer that best sums up many of those things is, "reality is an illusion." Not terribly satisfying, I guess. If only someone on the Blogosphere would come along and tie it all up with some sort of scientific-religious take on it all...
I too confused Doppler and Gravitational, so many thanks (I oughtn't to add that I still fail to see why the redshift isn't evidence for an ether).
I've yet to be convinced that there's any meaningful distinction there.
How about an observational difference, at least in a thought experiment? This one comes from Sean Carroll's GR book.
Consider a Universe that is static -- neither expanding nor contracting. GAlaxy A emits some light towards Galaxy B.
While the light is on its way, the Universe expands by a factor of two, but then stops.
The Universe is static again when the light from Galaxy A reaches Galaxy B.
There will be no Doppler shift if galaxies are just "flying apart" -- because Galaxy B is at rest with respect to Galaxy A at both emission and absorption. However, if instead of galaxies flying apart, redshift comes from the gravitational (specifically cosmological) redshift due to the expansion of spacetime, there will be an observed redshift.
They really are different things.
I've yet to be convinced that there's any meaningful distinction there.
Actually, I'd answer it this way. In the case of the galaxies flying apart through otherwise empty space (as opposed to what we believe, that to first order they are at rest but space is expanding) if you run tape backwards you arrive at some preferred location in empty space--a sort of center of the universe where the big bang occurred.
In the present view, with space expanding, by running tape backwards you just get a smaller universe, back to a time when the big bang occurred--everywhere, not at a special place.
That, I would argue, is a meaningful distinction.
That's not relevant. There will be gravitational redshift in either case, since the metric is time-dependent. The density of the Universe is decreasing in either case. The thought experiment establishes that cosmological redshift is not simply a Doppler effect (though it can be considered an aggregate of infinitesimal Doppler shifts along the photon's path). It does not establish that gravitational redshift requires anything other than galaxies "flying apart," that I can see.
Another point to consider: the same metric which describes the expanding Universe can also be used to describe the interior of a collapsing ball of pressureless dust. Is that a compression of spacetime, or can we think of it as things just moving together?
That would only be the case if you were considering a finite ball of galaxies embedded in a void.
So the space between the galaxies is getting bigger, and that would insinuate that the galaxies themselves are getting bigger as well correct? The stars themselves, planets, us, all the way down to a quantum level?
No -- they *would* be, but there are local forces that hold them together against that expansion. With galaxies, it's their own local gravity. With us and atoms and all of that, it's all the other forces.
Alright, I see what you mean. In the common balloon analogy then, it's not so much galaxies drawn on the surface of the balloon, it's more objects resting on the surface of the balloon then.
In my mind I had things like subatomic particles as being part of or secured to the "fabric" of the universe, which is incorrect then.
I blame the videos of vibrating strings attached to space-time I've seen on various physics TV series :D
MartinM,
That would only be the case if you were considering a finite ball of galaxies embedded in a void.
No, I don't think so. I think it would be the case as long as you assume nothing more than a big bang. It is a very simple argument: a big bang in a large (or infinite) non-expanding universe implies a preferred location. I don't see how you get around that. A big bang in an expanding universe means no preferred location. That's my point--the distinction is huge.
In a spatially infinite distribution of galaxies, all flying apart from one another, where exactly is the preferred location? It can't possibly be that running the tape backwards would result in convergence on a single point in finite time, since that would require arbitrarily high speeds for distant galaxies. So to where, if not a single point, are the galaxies converging?
In fact, running such an infinite Universe backwards will result in divergent density at every point.
Martin M,
I don't see why--but perhaps so if there was no big bang--if you are talking a steady state universe. But if there was a big bang in a large, non-expanding universe, then the motion of the galaxies, or rather the resulting matter in the universe, via the conservation laws, would contain the memory of the big bang's epicenter, i.e. of a preferred location.
"...the big bang's epicenter, i.e. of a preferred location...."
No, the center (naive 3-D concept here, not applicable to dynamic 4-D) is everywhere.
Theologists argued this, as well as scientists, for centuries.
Nicholas of Cusa [1401-1464] wrote the celebrated dictum: God is a sphere "whose circumference is nowhere and whose center is everywhere"
Jonathan,
Perhaps you didn't read all the posts. MartinM an I are speculating on the distinction between a universe in which the galaxies are flying apart through empty space, as opposed to the one we believe we have, in which space is expanding between ~motionless galaxies. I am arguing that a difference would be that in the hypothetical case of galaxies literally flying apart, there would be an epicenter. I understand that in the present model, there is not.
Or maybe I simply misunderstood your comment.
I should probably write another "Big Bang" thing, but for now I will point you to this one on my former blog :
http://brahms.phy.vanderbilt.edu/~rknop/blog/?p=68
David: you're right, I'm wrong. I didn't read your comment carefully enough to see that you were intentionally creating a straw man argument to compare to the argument that we favor. Sorry.
Also, It was semi-trollish of me to give a citation of what I call "Theophysics" or "Theomathematics."
Well, let's start at the beginning. Do you agree that in a spatially infinite Universe, there cannot be a time in the finite past at which all galaxies were at a single point?
I saw one argument there that we haven't already covered here:
Which is simply wrong. No galaxy is required to recede faster than an outgoing photon at the same distance. The apparent contradiction derives from attempting to compare 4-vectors which inhabit different tangent spaces.
Let me know if there's something else on that thread I missed.
MartinM,
No I don't agree, I can easily speculate of an infinite, empty universe in which a big bang suddenly occurs. (Of course, not like the "real" big bang, but an ordinary explosion of matter, like many people imagine the big bang to be.) In this case, in an infinite universe of preexisting space (which we have to have, if space is not allowed to expand) all the galaxies started at a point.
I would a agree with your statement if we are talking about an infinite, nonexpanding universe of ~uniform density. But as I said earlier, that would be a steady state universe. I agree that a steady state universe could a nonexpanding universe without a preferred location. However, in that case the galaxies would not all be receding from our location--at least I don't think so. It would seem that in that case, on average, galaxies would be coming toward us as often as they were moving away.
So, since they are moving away (the night sky is dark) the only way, it seems to me, to avoid a preferred location is with expanding space--you can't do it with galaxies flying through empty space (and all receding, as we observe.)
I don't think I'm begging the question, but perhaps I am.
MartinM,
Rob is indeed right. But, you are not very wrong either, if what both of you said is properly interpreted.
1) To ask whether Galaxies move or not or to ask how much of the observed redshift is doppler and how much of it is gravitational is NOT a reference-frame[1] independent question[2].
2) This does not mean, however, that the two kinds of redshifts are the samething as MartinM seems to think. The two kind of redshifts are more like electric and magnetic fields - how you split them depends on your reference frame, but to assert that there is no distinction between electric and magnetic fields is ,at best, a very confusing way of saying that they are frame dependent.
2) Consider the expanding universe first- In the co-moving frame (defined by say the isotropy of CMBR ), the Galaxies are at rest(or nearly so) - their 3-velocities are (approximately) zero.
If you write down Maxwell's equation (or say equations of Ray optics) in this frame, you will notice that the change in frequency is entirely due to the "gravitational fields" aka the connection coefficients in this reference frame. This is the gravitational shift. Since the source of light(Galaxies) are at rest, in this frame, there is no Doppler shift.
Now you can define other frames in which the 3-velocities of the co-moving galaxies are no more zero (that is the galaxies are moving), you can even make them "accelerate"[3] by choosing frames where there are "gravitational fields"/"connection coefficients" accelerating them. In this frame, the observed redshift is due to a combination of gravitational and doppler shifts.(i.e, if you actually look at Maxwell's equations written in 3-vector notation, the frequency change of the detected light is due to both the motion of the source and the way the gravitational fields/connection coefficients enter the Maxwell's equations via covariant derivatives.)
3) Consider now a flat spacetime. Take an inertial frame(which exists globally if the spacetime is flat). Consider galaxies moving away from a particular point. In such a case, we will observe a redshift which is the standard doppler shift.
Now, transform to a frame where the galaxies are at rest - basically, choose your tetrad such that the unit timelike vectors at any event is aligned with the four-velocity of the galaxy at that event. The gravitational fields/connection coefficients in this frame are non-zero. In particular,the space is expanding in this frame[4].In this frame, the same redshift has to be interpreted purely as a gravitational redshift, since the galaxies are at rest in this frame.
This example makes it clear that whether something is a gravitational redshift or not is relative. Whereas the case here is similar from the case before , note that in a curved spacetime, the expansion is homogeneous(a point Heddle made above) and there is no frame in which gravitational redshift can be completely gotten rid of[5] (which justifies what Rob says about the redshift not being just a doppler shift).
[1] A tetrad of orthonormal four-vector fields define a reference frame.
[2] Another way of saying the same thing is that there is no sense in comparing vectors from two different tangent spaces before giving a specific mapping from one to another.
[3] "accelerate" as seen in this reference frame. Of course, they are all moving
[4] Expansion, as it is usually defined for a time-like congruence, is just the trace of the covariant derivative of the four-velocity field. The expansion of space that we see in a given frame can be calculated similarly using the unit time-like vector field with that frame.
[5] This basically follows from the fact that in a curved spacetime,almost by definition, there exists no frames in which "gravitational fields"/connection coefficients are everywhere zero.
Which is simply wrong. No galaxy is required to recede faster than an outgoing photon at the same distance. The apparent contradiction derives from attempting to compare 4-vectors which inhabit different tangent spaces.
Exactly. This is why I don't like the "flying apart" picture. It breaks down at great distance.
The derivative of proper distance to that galaxy with respect to our t variable is greater than the speed of light -- but, as you say, speed and velocity only have meaning when defined locally.
-Rob
Which would be the "finite ball of galaxies embedded in a void" mentioned earlier. Sorry, I should have been clearer. I meant a spatially infinite Universe with homogenous matter distribution.
Apologies for snipping most of the post, but...no, that's not what I think. Indeed, I said precisely the opposite. Hopefully my next post will clarify.
IMO, it only really breaks down if one tries to make comparisons that aren't valid.
And I'll raise the pressureless ball of dust again. Can we think of the collapse of such a ball as simply the aggregate motion of each particle within it, or are we compelled to discuss it in terms of shrinking spacetime?
While I certainly don't claim that describing the expansion of the Universe in terms of expanding space is wrong in any way - indeed, I claim that the two pictures are precisely equivalent - I do think that it comes with conceptual issues of its own.
We're used to describing the Universe as an entity, in bulk terms. We average the mass distribution and derive a simple metric for an idealized model. Then we can decompose the motion of any object into two parts; a 'global' part due to the ideal metric, and a peculiar velocity due to local departures from that ideal. The 'expanding space' picture strongly implies that these are two fundamentally different phenomena. It's from there that questions such as Jason's arise. Once you realize that the Hubble flow is just a useful abstraction, cobbled together from local motions so that we can talk in global terms, the answer to such questions is trivial.
IMO, it only really breaks down if one tries to make comparisons that aren't valid.
The real problem is language.
"Galaxies flying apart" really does only work for local galaxies.
"Space expanding," yes, has conceptual problems of its own, but works everywhere.
I find the latter description a much closer and better way to describe the actual mathematics of the F-R-W metric.
The former implies galaxies moving through a flat background spacetime, which gives real observational differences from what the F-R-W metric gives.
-Rob
MUCH THANKS for the fix
Besides, Sean Carroll claims that "it's only true that the distance between any two widely-separated points is increasing. Here in the Solar System (or in the galaxy), the expansion rate is strictly zero (on average), not just very small. In fact there are exact solutions to Einstein's equation that model this situation. [...] The spherically-symmetric expanding universe outside has precisely no effect, in the same way that the electric field inside a sphere with charge on the boundary will be precisely zero."
So, is the spectra from a reflection grating similar to the one you get from a compact disk? (e.g. http://lablemminglounge.blogspot.com/2007/02/high-resolution-improvised…) I assume they have either more expensive gagets, or less shaky hands.
With doppler planet finding, how does one differentiate between expansion and contraction of the star and back-and-forth wobble? for example, can astronomers see the doppler imposed by Jupiter on the Sun, without getting it mixed up with the similar length sunspot cycle?
This is seriously jumping ahead of this article, but doesn't "dark energy" just smell like fudge?