So this means that, say, my computer screen is attempting to “move away” from me at some incredibly miniscule speed as dictated by the Hubble constant because the volume of space between me and my computer screen is getting larger. If my computer screen and I were not “bound” my computer screen would, in fact, be getting farther away from me (and indeed, actually “accelerating” away from me) while remaining in an inertial frame of reference.
However, because my computer screen is bound to me (say, gravitationally), it can’t actually move away from me. To put it another way, the expansion of the universe is causing my computer screen to feel a force, albeit an extremely small force. Have I got this right so far?
Not having studied GR I don’t have an intuitive grasp of this concept.
What is the definition of comoving frames? If they are truly comoving, would they not be correcting for the expansion of the universe? How do you determine that two widely separated frames are comoving without assuming the expansion factor? I don’t get it.
douglips, if I understand Undead Dude, he is using “comoving frame” as shorthand for “a frame comoving with the Hubble flow.” Does that clarify matters at all?
Er, not quite. This is your second warning–I am somewhat out of my depth here, so I might not be getting this exactly right, but I’ll do my best.
The reason that local space is not expanding is because we’re surrounded by lots of mass: planets, stars, dark matter, what have you. Recall from General Relativity that mass warps spacetime–and spacetime is what is getting bigger due to cosmological expansion. Its not the gravitational binding between you and your computer which is preventing it from drifting away, it is the distortion of spacetime by the Galaxy (and all the stuff in it) that prevents spacetime from expanding inside the Galaxy (and even slows its expansion between galaxies.)
I think your intuition is correct, though, that the Galaxy must be doing some work in slowing or halting the expansion of spacetime locally. Maybe Chronos can clarify.
Very interesting. Is it actually known that the entire dipole component of the anisotropy is Doppler shift? Or is this simply assumed? I’m not understanding why the original lumpiness could not have a strong dipole component.
I think I get what he’s saying. He’s saying (I think)
That makes sense to me now - you calibrate your motion to the CMB, and then send a laser at your friend N parsecs away and he measures the redshift.
This then confuses me in other ways. If the CMB has no dipole at comoving frames A and B which are widely separated, but there is a redshift between A and B, then wouldn’t B see CMB in A’s direction as redshifted, thus having a dipole shift in his CMB?
Let me be more explicit:
A detects a uniform (in the dipole sense) CMB. B also detects a uniform CMB. B looks in A’s direction. If there is a “redshift” between A and B, then B must see the CMB coming from behind A as weaker (i.e. more red-shifted) than A sees it. This means that B must see all of his CMB as weaker than A, or it violates the first given (uniform CMBs.)
doug, I think your example makes the assumption that the source of the CMB can be treated as a single reference frame (like a rigid sphere).
While the concept of the source of the CMB is the same for both comoving frames, it isn’t accurate to say that the CMB is coming from any particular place that would be the same for both comoving frames.
I hate to contradict an actual planetary scientist, Podkayne, but I believe Truth Seeker is right: the computer is (attempting to) move away from you. The effect is WAAYY too small to measure, but if we think of it in terms of force, there is a tiny “expansion of the universe force” that should be subtracted from the gravitational force between you and your computer. (Actually, the gravitational force is really tiny too. The computer sticks to the table via electromagnetic forces (friction), as do you to your chair. These forces far outdo the gravitational force, which is why the computer screen doesn’t crash into your face.)
Of course, in GR gravitation is caused by curvature of spacetime. But we can use force concepts when the gravitational interaction is relatively (NPI) small.
You and me both! The fact that you know you don’t know suggests to me that you know more than most people think they know. . . . or something.
**
The problem I have with this is that, if it were true, the universe wouldn’t be expanding at all. This seems to be equivalent to saying “only space where there is no gravity is expanding.” Isn’t all space that we can observe “distorted” by gravity to a greater or lesser extent?
I have trouble buying this for several reasons, not the least of which is that it’s too facile. First, just how “significant” does gravity have to be in order to “turn off” the expansion of space? Is there any theoretical basis for this in GR? AFAIK, our belief that space is itself expanding is based on observation rather than on basic theory. I could, of course, easily be wrong as the math involved in GR gives me nose bleeds.
Second, if it’s not a simple “on-off” sort of thing (and I doubt that it is) one assumes that if sufficiently strong gravity can cancel the expansion of space, stronger gravity would cause space to contract. Do we observe this happening? Remember, we aren’t talking about whether the matter in space gets closer together, we’re talking about whether two theoretical points “fixed” in space are attempting to get farther apart.
Third, even if gravity is preventing space from expanding, the real question is, is space still trying to expand even in the presence of gravity?
Fourth, I assume that the expansion of space is some basic characteristic of space itself. It is true that gravity represents a distortion of space. However, I don’t see any obvious reason why the two phenomena can’t both be occuring simultaneously.
Just to be clear, I’m not talking about the matter in space, I’m talking about the space itself.
I think mebbe we just didn’t give enough details. What you are uncertain about makes lots of sense. Lemme try to add some of those details.
It’s never off. Nothing can prevent space from expanding. The local effects can simply keep objects from moving away from each other.
Think of the balloon analogy. If two coins are sitting on the balloon as it expands, they would normally move away from each other. If we hook them together with a chain, then the balloon needs to slide out from under them.
So gravitation keeps the solar system together. Objects sitting around on the Earth are held together and in their place primarily by electromagnetic forces (including friction). But none of these things actually change the expansion of the universe.
Undead Dude would you then agree with what FriendRob posted?
Remember, we’re not talking about the matter in space, we’re talking about the space. It seems to me that, since mass has inertia, it will stay “affixed” to the “point” in space on which it sits, unless some force is applied to it. If you have two particles which are not bound to each other sitting at points A and B, the expansion of the universe will cause them to “move” apart because, though they remain affixed to the same points in space, the space between them is expanding. It follows that, in order to remain the same distance from each other, two particles must actually be moving towards each other. It also follows, (more or less) that two particles which are “at rest” with respect to each other must be exerting some amount of force on each other and that the force necessary to keep the particles at rest increases the farther the particles are apart.
“It follows that, in order to remain the same distance from each other, two particles must actually be moving towards each other.” – Truth Seeker
In a sense I suppose it would be like that.
“It also follows, (more or less) that two particles which are “at rest” with respect to each other must be exerting some amount of force on each other and that the force necessary to keep the particles at rest increases the farther the particles are apart.” – Truth Seeker
Well, they don’t need to be exerting forces directly on each other, but some sort of force (or local gravitation) needs to be there. To keep me at the same distance from my computer, I don’t need the gravitation of my computer. I am kept at the same distance from my computer (and essentially everything else on the Earth) by friction (which fundamentally is electromagnetic). So with the example of terrestrial objects, you see the distance doesn’t really matter. I stay the same distance from Tokyo because Tokyo is well planted on the Earth and so am I via friction. These electromagnetic forces are way, way, way, way, way stronger than the drag of expanding space.
I picture the pull of expanding space to be a lot like a very weak gravitational well-- as if the mass of the universe as a whole wants to lead you into a comoving frame. But is is very weak-- very easily overwhelmed by local forces and the strong gravitations of nearby celestial bodies.
Let me just add that we really do have a great surplus of force to hold us here. Gravity wants to pull us to the center of the Earth, and as a result we compress materials on the ground. As we compress those materials, they increase in repulsive force, like a spring. With a combination of the attractive force of gravity-- the motion resistant forces of friction and the repulsive force of compressed solid matter, we are kept is a very stable equilibrium which makes the pull of the expansion of the universe look like nothin’.
Um. I was a biophysics major long ago, which sort of makes me a physicist, but probably not enough to keep this from being a dumb question:
Who says you aren’t moving away from your computer? If space is expanding, wouldn’t our senses, our concept of scale, and ourselves and our possessions all expand in a manner commensurate with the expansion of local space, so that you are unable to perceive the expansion of the space between you and your computer?
Nametag, lets think about that possibility for a moment. Suppose our perception of space is changing-- a meter gets bigger as time goes on, atomic forces stabilize with a wider distance, so atoms and molecular structures get bigger.
Well, then two possiblities occur as we work outword-- either gravitation must get weaker to allow the planets and such to orbit at a greater distance, or it would appear that the Sun was getting bigger. In addition, the speed of light would need to getting faster so that our ability to verify distance in that manor remained the same.
So there would need to be a lot going on here to conspire to hide this expansion from us.
There’s no particular reason to suppose that what the comoving frames are doing has any particular relationship to what, say, interatomic forces are doing. And we do know that distant galaxies are definitely redshifted, so the expansion does, in fact, have measureable effects.
Let’s distinguish between the “rules of the game” and the “actors on the stage.” Sorry, mixed metphor! Football has rules, which are the same from one game to the next. Any specific game also has players, however the players can change from game to game.
Relativity is the “rules of the game.” It does not define a preferred frame; it treats all frames equally.
The matter (and energy) in the universe corresponds to the “players” or “actors” and can indeed define a preferred frame. Consider a universe with no background radiation and nothing in it but one atom. Obviously, there is a frame that is different from all other frames–and a location that is different from all other locations.
Another analogy would be the diffusion equation (which tells us how heat moves around) and a set of boundary conditions (which tells us what hot and cold objects we have at the moment).
