I sent this question to Cecil and am awaiting a reply, but I would like answers from others also:
How is it possible that the universe can be expanding in such a way that some regions are receding from others at a speed greater than light speed (for instance, in the inflation following the Big Bang), but the galaxies in these regions cannot be travelling relative to each other faster than the speed of light? I know the usual answer is that it is space that is expanding (more space is appearing between objects), but if the space between two objects expands, isn’t this the same as saying the objects are moving away from each other? For instance, there are galaxies which once were close to us but are now beyond our event horizon (space is expanding between us more quickly than their light can head toward us). What is their velocity relative to us?
I can picture a situation where points on the surface of an expanding balloon are separating. At any given time the surface occupies one portion of 3-dimensional space, and getting from one to another involves moving through this portion of space. At a later time the balloon’s surface occupies a different portion of 3-D space. You can no longer get from one point to another by following the old path, which no longer exists. The two points each only moved a short radial distance from their original locations, but are now two pi times that further apart on the new surface. Is this the type of explanation that applies with galaxies (except going from 3-D to 4-D space)?
IANACosmologist, but my understanding is the expansion of space is an intrinsic phenomenon of space itself, and doesn’t abide by the laws of c like energy and matter do.
My guess is the red shifting we observe of galaxies ever more distant is because this expansion appears accumulative over distance from our POV. But I’ll leave that for a real physicist to explain.
Imagine dots drawn on a rubber sheet. The dots are spaced one inch apart. Now you and a friend start tugging on opposite ends of the sheet, stretching it until the dots are all two inches apart. Say it takes 1 second to stretch the sheet.
Now, what would this look like from the perspective of one of the dots? The adjacent dot went from being one inch away to being two inches away, so it’s “receding” at a speed of 1 inch/second. The next closest dot went from being two inches away to being four inches away, so it’s “receding” at 2 inches/second. A dot that started off 20 inches away is now 40 inches away; it’s “receding” at 20 inches/second. And so on. If the sheet were big enough, eventually you’d reach a dot that “recedes” faster than the speed of light.
But the dots aren’t moving relative to the sheet. They’re still drawn in the same location. They just look like they’re moving because the sheet is stretching.
But of course there is no sheet, no ether and no absolute space. It makes no sense to talk of how fast the dot is “really” moving; you have to pick a reference frame. From Dot A’s reference frame, Dot Z is/has receded FTL. No?
Yes and no.
Consider Dot Y, which is “receding” at slightly less than light speed.
The light from Dot Y will not be Doppler-shifted the way it would if it were moving at a large velocity relative to Dot A. Instead the red-shift of the light from Dot Y is caused by a different process – the gradual stretching of the light during its long transit time through expanding space. These two different types of red shift don’t produce the same experimental results in certain situations.
So, depending on how you’re measuring “movement” the distant dot may or may not seem to be moving.
Yes. You are (mostly) correct. There is no harm in thinking that the sheet is real. You can set a coordinate system up and everything. The problem with analogies is that our only common place from which to draw them is Euclidean space, or maybe a simple shape like a sphere sitting in Euclidean space. It is certainly beyond me, though, to picture a 4 dimensional object not sitting in a bigger dimensional space, and expanding.
Draw a cartesian grid on the sheet, it makes a fine coordinate system. Make each dot from the sheet example an intersection. Stretch the sheet out flat, or stretch it around a some other object, and you still have a coordinate system. Your coordinates might no longer be orthogonal, and you might have to look at just small patches in order to make sense of them at a time, but you still have a coordinate system. (Just don’t put a sharp bend or tear in the sheet.)
The coordinates of a the dots have not changed: they are not moving relative to the coordinate system. Pick any dot to be the origin. A dot that was 3 over in one direction from that dot, and 4 up on the other was at (3,4) and it is still at (3,4). However, the distance between the dots is now some other distance away. If you stretched it out flat, then just use the Pythagorean theorem. If you didn’t, you need to use Riemannian geometry to figure it out. However, two points can recede from each other faster than light. The points aren’t objects, they are geometrical entities. (The intersection of two laser beams can also move faster than light, even if neither the photon nor the source does. An intersection is not an object.)
Reality is more complicated: we assumed a global time coordinate, and that we can label points in space (by drawing dots or lines) but the idea all works. Note that you can not see something moving away faster than light. As two points get far enough away from each other that their apparent relative velocity approaches that of light, the light redshifts. Once the relative velocity hits the speed of light, the redshift is infinite. You can think of it as the light still traveling at the speed of light, as it must, but the distance between grows so fast that it never crosses the distance between the two objects.
Is space real? I remember this being addressed in my old college cosmology course. The thought-experiment was this: you have a universe that contains an earth-like planet ---- and nothing else! Nothing at all! No moon, no stars, not even space dust.
Can the planet rotate? If space itself, while empty, is still real, still has a meaningful metric, then, yes, the planet can rotate, with respect to space itself. If space isn’t real except as a measurement between objects, then the planet cannot rotate, as there is nothing it can rotate “with respect to.”
So…then…the inhabitants of the planet launch their first space probe…
Are you sure you’re remembering this gedankenexperiment correctly? Because it seems like in the scenario you propose, Coriolis forces would still be in effect, and a Foucault pendulum would still precess … .
Isn’t rotation angular momentum? Mass would still have inertia, even if all other matter and energy were removed. Yeh?
Wait, I can’t tell if we slipped into Wooshville… I’m on my 3rd Sam Adams.
Thoough when talking about expansion you are talking about what happens in one particular frame of reference,not what happens in an arbitary frame of reference.
What particular frame of reference, and what’s the difference?
Short answer - no, it’s not the same.
Speed is motion in space, and is limited to c. Expansion of space isn’t motion in space, and is not limited - because it’s not motion.
Yes, it feels unintuitive. That’s the universe for you!
The frame in which space looks homogenous and isotropic, aka the CMB rest frame.
Changing the frame can introduce anistropies in several different ways.
Not unlike The Reader. Aren’t we on our 2nd or 3rd Cecil Adams?
Take the last train to Whooshville…
I think The Hamster King is more or less right. I suppose the universe is thought of as a three-dimensional (or 4, if you include time) manifold whose geometry is constantly changing consistent with a general expansion (increasing distance between points with time). At any given moment, each object such as a galaxy has a specific velocity (less than light speed) with respect to each other object. This velocity does not take the expansion into account, since it is based on the geometry at that given moment. If objects are fairly close together, and not moving very fast, in measuring this velocity we can essentially ignore the expansion, which will be a small distance over, say, a second, and just look at the change in distance over the change in time. For an object at a great distance, which will be expanding away at a great speed (possibly even greater than light speed), we have to use things such as Doppler shift to measure the instantaneous velocity relative to us. We still have to take the expansion into account. For instance, if a galaxy was 10 billion light years away when it emitted some light and the “average” expansion rate over the time since then is 0.7c, and the observed Doppler shift is 0.72c, then we conclude the instantaneous velocity of the galaxy relative to us at the time the light was emitted was 0.02c. There then could be objects so far away that the expansion speed is/was greater than c, and we will never see any new light emitted by them.
A nitpick: As I mentioned above, the red shift of distant galaxies is NOT a Doppler shift, i.e. it’s NOT caused by them having a large instantaneous velocity relative to us. Instead the red shift of distant galaxies is caused by the gradual stretching of space during the billions of years the light traveled through it to reach us. The LACK of a significant Doppler shift is one reasons we can say that distant galaxies are stationary with respect to us … for a particular definition of “stationary” … . 
I understand your point. What I meant was, we have to consider the observed change in frequency of the light, subtract off the portion due to the elongation of the waves due to expansion, and then consider the rest as the true Doppler shift. For instance, if an atomic emission wavelength which would be 1000 Angstroms at rest in the lab is measured at 2000 Angstroms coming from a distant galaxy, this would imply a relative velocity of .5c. However, if we know that objects at that distance, on average, expand away from us at .49c, then we know the relative velocity of the galaxy in terms of the geometry at the instant the light was emitted was .01c. I was using “Doppler shift” loosely in the sense of the total frequency shift of the light, including the shift due to expansion and the shift due to instantaneous velocity.
I believe astronomers generally speak in terms of using the “Doppler shift” of a galaxy to calculate how far away it is, and Hubble determined from “Doppler shifts” that the universe is expanding. Perhaps we should speak more precisely of frequency shifts due to expansion vs. those due to motion, but it seems to me that astronomers generally just speak of “Doppler shifts.”
Technically, there is a “cosmological redshift” and a Doppler shift. However, the popular press tends to call both Doppler shifts, because both involve a velocity, I suppose. (One is due to the velocity of the expansion, and one due to the velocity of an object.) There is no way to tell them apart, when looking at just one object, nor can you tell either from the gravitational redshift due to climbing out of a well. Instead, you have to do things like look at nearby objects and determine the average redshift for a region.
As far as whether or not spacetime is a real thing, that is more of a philosophical question with subtly different answers. A scientific theory is a descriptive explanation of facts. The General Theory of Relativity models the universe as a mathematical set. The set has particular properties that make it a manifold. Is a mathematical construct real? There is some distance between objects, does the thing you use to measure distance exist? Does the fact that it has properties and changes shape due to physical objects means it exists? You’d get a different answer from Bohr than you would from Einstein. And quantum field theory makes that question even murkier.
I should have said “predictive and descriptive”, if you require precision.