Universe Expansion: Understanding the Role of Geometry in the Expansion of Space

[hagendaz]

If the universe is expanding per the inflating balloon example, how come the planets within our own (and every other) solar system aren't spreading further appart.

 

[mathman]

In a word - gravity.

 

[marcus]

If the universe is expanding per the inflating balloon example, how come the planets within our own (and every other) solar system aren't spreading further appart.

Nor is our galaxy spreading further apart. A system of several hundred billion stars orbiting the center of mass bulge.

Things in orbit may have already adjusted for any slight percentage increase in distances. In any case gravitationly bound systems are not pulled apart.

Think of things orbiting imperceptibly farther from center than their orbit speed would ordinarily allow. So that other things being equal they'd have a tendency to fall inwards to orbit closer to center. And it just compensates. Maybe it's an oversimplification but it helps me.

The percentage expansion rate is only 1/140 of one percent every million years.

The general rule of thumb is that distances between gravitationally bound objects don't increase. The only distances that increase, by Hubble law, are between widely separated pairs of objects which have no significant gravitational effect on each other and are not bound.

So even clusters of galaxies just go about business collectively orbiting each other and they are not spread apart.

I understand there are borderline cases where what looked like a wannabe cluster got pulled apart, it wasn't really gravitationally bound to begin with.

 

[ThomasT]

I understand there are borderline cases where what looked like a wannabe cluster got pulled apart, it wasn't really gravitationally bound to begin with.

By "pulled apart" do you mean that there are 'groupings' of individual galaxies that because of the proximity of the individual galaxies they would be expected to behave as a bound system, but are observed to be moving away from each other? If so, is this behavior primarily due to the velocities of the galaxies involved -- or is there more to it?

 

[hagendaz]

Thank you for your response, I have a follow up question...
If two rifles in deep space were fired exactly parallel to each other, but far enough apart that the bullets had zero gravitational pull on each other, would the effects of space expansion increase the distance between the two bullets, or would their forward momentum, as with gravity, be too strong a force for it to overcome? If it is unable to change the gap between the two bullets in the example above, how is it able to expand the distance of objects opposite sides of the universe...

I guess it sounds to me like a wind that can tremendous effect at pushing things forward in the direction they are already traveling and expanding the universe, but is too weak a force push anything sideways.

 

[Chronos]

That depends, if spacetime is flat, they remain parallel and equidistant for eternity. If it is curved, they either more apart, or collide at some point in time [in minkowski space].

 

[v2kkim]

For parallel running bullets, another factor other than the spacetime flatness should be the basic space expansion. Assuming gravitational interaction ignored, they will fall apart at the standard expansion rate of 1/140 % per million light yrs.

 

[Ich]

Assuming gravitational interaction ignored, they will fall apart at the standard expansion rate of 1/140 % per million light yrs.

Not if they were parallel to each other.

 

[v2kkim]

Not if they were parallel to each other.

Ich. I do not agree with you. The space expansion does not matter it is parallel or not, but it affects everything evenly.

 

[Ich]

The space expansion does not matter it is parallel or not, but it affects everything evenly.

Space expansion per se (the first derivative of the scale factor \dot a) does not affect anything at all. It is merely a set of initial conditions, saying that at a certain starting time nearby objects have a (measurable) velocity v=H*d, if "d" is distance.
If we assume the bullets to be low-speed, so that we don't have to care about spatial curvature, they will stay at a fixed distance if there is no such transversal velocity component, i.e. if they're fired parallel. Only if the guns were comoving, i.e. moving apart from the start, the bullets' distance will increase accordingly.
If you add gravity to the picture (\ddot a \neq 0), their distance will change eventually, but not proportional to a if the guns were not comoving.

 

[v2kkim]

What I am saying is the distance between bullets will increase due to space expansion.
But I do not care if you call it parallel or not. Basically the space expansion applies quite fairly to all objects, unless there are disturbing forces like gravitation or electric or other forces.

 

[Ich]

What I am saying is the distance between bullets will increase due to space expansion.

Yes, and what I'm saying is that it will not increase.

Basically the space expansion applies quite fairly to all objects, unless there are disturbing forces like gravitation or electric or other forces.

Space expansion applies exactly to those objects that are subject to a certain set of initial conditions.
In the absence of disturbing forces, e.g. gravity or a cosmological constant, it is nothing else than good old velocity. If there is relative velocity initially, the distance of objects will incease with time (that's what velocity means). If there isn't initial velocity, objects will stay where they are.

 

[Dusty_Matter]

I thought that the cosmological constant is the same as spacetime expansion, and that it was an ongoing condition. That all objects are under this albeit very small constant velocity force. So while it does not affect objects that are close in distance, or objects that are gravitationally bound to each other, the further apart things are, the more apparent this force becomes.
If this is true, then the two bullets fired in parallel with each other, if they were a million light years apart in distance, would they not feel this 1/140% of cosmological constant expansion, and therefore their distance between each other would actually be increasing with time?

 

[Ich]

I thought that the cosmological constant is the same as spacetime expansion

"expansion" usually means that objects are moving away from each other. They could do so wihout a cosmological constant or gravity.
A cosmological constant will accelerate expansion, gravity will slow it down. If those influences exist, the bullets will not generally stay parallel. But neither will they follow "the expansion", because they were not initially moving away from each other, contrary to the objects which we denote "comoving" with the expansion.

 

[Dusty_Matter]

Okay, let's say that the bullets to be fired are not a million light years apart, but are now 13 billion light years apart, but they are still parallel when they are fired onto their paths. Are you saying that they still will not spread apart along with the expansion of the universe, but will stay parallel with each other?

 

[hagendaz]

So does space expansion only act as a "tailwind", but is unable to expand the distance between two objects lateral to their path of motion? What then if two bullets were fired from opposite sides of the universe directly at each other? Would the expansion of space not increase the distance they would have to travel to hit each other?

 

[Ich]

Okay, let's say that the bullets to be fired are not a million light years apart, but are now 13 billion light years apart, but they are still parallel when they are fired onto their paths.

Whatever "parallel" and "when they are fired" means at these distances. Better stay close, so that the bullets can be described in a common nearly flat frame.

Are you saying that they still will not spread apart along with the expansion of the universe, but will stay parallel with each other?

I'm saying that neither wil happen. They will eventually spread abart, but more slowly than nearby comoving objects.

So does space expansion only act as a "tailwind", but is unable to expand the distance between two objects lateral to their path of motion?

Expansion is unable to alter the distance of any two objects, unless these objects are initially prepared with some relative velocity. (where "expansion" has the meaning I use in this thread.)

Would the expansion of space not increase the distance they would have to travel to hit each other?

Yes, cosmological distance between observers at rest wrt each other would initially increase under some circumstances. But "cosmological distance" is a coordinate construct, not what one would call a "distance" in any realistic operational way.
For example, in flat, empty space, one has a definite notion of two observers moving parallel or being at rest wrt each other. If you apply the definition of "cosmological distance" here, it would still increase with time. Not because the objects are moving away from each other, but because cosmological distance's definition is different from the "normal" one.

 

[Dusty_Matter]

I believe that when they talk about the universe expanding, a lot times they use the example of raisin bread rising in the oven to show how galaxies are spreading apart. They are in motion with space/time which is expanding. The galaxies are not flying apart due to any velocity on their part, but due to the expansion of the universe. If it was due to an intial explosion of some sort, then there would be a central location from which they are leaving. But galaxies are getting farther apart from each other in all directions. In other words the universe is getting less dense. Anything therefore in our universe that exists, is on a ride with the spacetime fabric of the universe which is expanding. Expansion does alter the distance between objects, otherwise they would be fighting against the growth of the universe.

 

[Ich]

I believe that when they talk about the universe expanding, a lot times they use the example of raisin bread rising in the oven to show how galaxies are spreading apart. They are in motion with space/time which is expanding.

Yes, that's an usual picture. I dont'tlike it at all. The picture of space dragging things along with it, or the notion of motion through space as opposed to (and physically different from) motion of space, are awfully inadequate and misleading.

The galaxies are not flying apart due to any velocity on their part, but due to the expansion of the universe. If it was due to an intial explosion of some sort, then there would be a central location from which they are leaving.

Yes, and every observer will think that the explosion happened exactly at his position. It's just a matter of coordinate choice:
In comoving coordinates ("public space"), everything is essentially at rest, and redshift is due to "stretching of space". In observer-centered coordinates ("private space"), things are moving away from the center, and redshift is due to their velocity and gravitational time dilation.
Both pictures cover different aspects of the same universe, and both should be contemplated.
There is a tendency to use exclusively the first set of coordinates, but describe it as if it were minkowskian coordinates. That's the source of a lot of misconceptions and bad wording in cosmology.

 

[bombaglad]

From my understanding, which is very limited, the expansion of the universe began at the moment of the bang. All the continued expansion is a result of the original acceleration. There is not a continued force acting on objects. So, there was a big explosion and the momentum from the explosion caused everything to expand from the center of that explosion in all directions.

Let's say prior to the bang, the planets in our solar system were all clustered together in the orbits that they now occupy. Picture that as a closed system. When that explosion happened it pushes the whole system away at a given speed. It will continue in the path at a given speed forever(excluding friction) but the system will never be disturbed (unless another outside source acts on the system) because of the gravity which held the system in place prior to the explosion.

Like your bullets. if you fire them parrallel they will remain parallel. The only reason objects get further apart over time is they were on a different path originally. There is no continued force... ? From what I understand

 

[Dusty_Matter]

The creation of our universe was not an explosion in space, with space already existing. The BB is the beginning of the creation of everything including the spacetime of our universe. We know of nothing existing before the BB. There were no planets or stars to speak of, before the BB.

Picture the universe as an expanding balloon, and our galaxy taking up a very small point inside it. Do not picture an inflation point. There is no central point from which our universe expands. Picture the air inside the balloon as merely reproducing or multiplying in quantity, in all quadrants within the balloon.

It is this spacetime expansion that is making the galaxies (on the large scale) get farther and farther apart. Spacetime is growing, or expanding which is expanding the distance between distant galaxies and galaxy clusters. It is not really a force that pushes the galaxies apart, but it is the growth of the universe that causes them to become farther apart in distance.

So while the two bullets fired in parallel to each other do not really experience a force that would change their own trajectories, the growth of the spacetime between them would cause the distance between them to increase as time went on. They would not continue parallel to each other. Just as the galaxies are getting farther apart from each other, so the bullets would as well.

 

[bombaglad]

I did not mean to make it sound as if I was saying our solar system existed before the BB. I was only using an example to try and explain an expanding universe and a non-expanding solar system. Sorry for confusion. And if you shot these two bullets now it is not exactly clear that the two bullets would ever be any further apart. Everything is expanding at the same rate granted. But these are two objects that are being introduced into an already expanding universe. It is not as if the universe is "growing" but it is expanding, relative to our location. If you were to shoot two bullets at the time in the same direction and watch them, they would travel as if they were the same object, relative to our location. The way I understand it The "empty" part of space is not growing but the "full" parts are moving away from each other.

And how could space be becoming less dense? If the only thing holding the galaxy together is gravity wouldn't a less dense space cause the galaxy to be changed? In fluid systems, The inside pressure is not affected by the outside pressure but if the pressure outside of the system is lowered the system would expand. And if space is becoming less dense, why would the gravity existing in the galaxies not effect each other? I mean, if two relatively close galaxies with constant gravity, and the density of the only thing that separates them is reduced how would the distance between them grow?

 

[Dmitry67]

Dont think about space as some substance with density.
It is the same no matter how you expland it (even there are some tricky things regarding the negative pressure of space...)

 

[Ich]

All the continued expansion is a result of the original acceleration. There is not a continued force acting on objects.

Not quite, if you count gravity as a force, it will change the rate of expansion.
But essentially, yes, inertial unaccelerated expansion is such a good fit that it accounts for most of the "effects" of expansion. A mere 10 years ago measurements were accurate enough to tell the difference.

Like your bullets. if you fire them parrallel they will remain parallel. The only reason objects get further apart over time is they were on a different path originally. There is no continued force... ?

There is a continued force, but its effect is minuscule, and the bullets will stay at essentially the same distance for a long time, when comoving particles will long have increased their distance measurably. Comoving particles are those which had the proper relative velocity from the start.

 

[pixel01]

May I ask this question:

The universe is expanding, then how about the size of individual galaxies, say, our Milkyway is increasing in size?

 

[Ich]

The universe is expanding, then how about the size of individual galaxies, say, our Milkyway is increasing in size?

No, object the size of galaxy clusters and below are gravitationally bound, they do not expand.

 

[pixel01]

No, object the size of galaxy clusters and below are gravitationally bound, they do not expand.

You mean galaxies in the universe do not influenced or being influenced gravitationally?

 

[George Jones]

You mean galaxies in the universe do not influenced or being influenced gravitationally?

Homogeneous, isotropic models of the universe predict expansion. On large scales, our universe is homogeneous and isotropic, but at the scale of galaxies, our universe clearly is not homogeneous. Expansion happens over large scales, but not over smaller scales.

This is discussed in simplified models in

http://arxiv.org/abs/gr-qc/0508052.

 

[v2kkim]

You mean galaxies in the universe do not influenced or being influenced gravitationally?

My understanding is that a galaxy does not expand, even possibly contract due to gravitation.
However the space expansion is quite universal, so applys to each space in a galaxy. But in a galaxy after each tiny expansion between objects, they adjust their motion due to gravity, and we know in this case gravity influence is much much greater than space expansion in a galaxy distance. Therefore we can ignore space expansion within a galaxy.

 

[Wallace]

My understanding is that a galaxy does not expand, even possibly contract due to gravitation.
However the space expansion is quite universal, so applys to each space in a galaxy. But in a galaxy after each tiny expansion between objects, they adjust their motion due to gravity, and we know in this case gravity influence is much much greater than space expansion in a galaxy distance. Therefore we can ignore space expansion within a galaxy.

Sorry, but your understanding is unfortunately quite misinformed. The 'expansion of space' is nothing more than a metaphor describing in simple terms the result of the uniform motion of galaxies that follow a Hubble law behaviour, which is a simple consequence of matter simply continuing to move apart following the initial kick given by inflation. Let me be very clear, the expansion of space is not a causal force that 'does' anything. It is not at all universal, it is only thus is everything is following a Hubble law in the first place.

I pose a question. If a ball drops from your hand to the floor, does it do this because space is falling, dragging the ball down? No. Using 'expansion of space' in the way you are above makes just as much sense.

 

[marcus]

... continuing to move apart following the initial kick given by inflation. ...

I see, you picture it as "continuing to move".
In which direction did this initial kick point?

 

[Wallace]

I see, you picture it as "continuing to move".
In which direction did this initial kick point?

Marcus, you surprise me. I thought you were beyond this! It is elementary physics to realize that the spherical symmetry of the FRW model requires that the forces are also spherically symmetric as well. Let me explain more fully though;

Imagine a very large (possibly infinite) blob of dust of uniform density. Let it start completely from rest. What will the blob do? Because of gravity, all bits of the dust will be attracted to every other bit and the blob will start to contract, in the sense that everything gets closer to everything else (thus even if it is infinite we can still say that is contracts). Now, if you do the sums you will see that the material in the blob will be following Hubble law contraction (same as Hubble flow, but contracting). We don't need any funky relativity here, this thought experiment is entirely Newtonian. If you want, you could describe this situation as 'contracting space' as long as you knew that you were just inventing a metaphor, not describing physics. You could derive co-moving co-ordinates and all the rest.

Now, imagine that we turn gravity OFF after a small amount of time. What happens? Does everything stop moving? No, of course not, the dust blob continues to follow a Hubble law contraction and space continues to contract in the invented metaphor. The second derivative of the contraction rate would go to zero, but the contraction would continue.

So, in this situation, in which direction was the kick that was applied before we turned gravity off? Easy, every particle can say they every other particle received a kick towards it. All kicks are inwards to every point. This is an inevitable consequence of Gauss's law and the homogeneity of the material. It is Aristotelean to suggest that motion requires something to perpetuate it, so let's get with the Renaissance and realize that mass has momentum and we are done.

Now, how do we go from this thought experiment to our Universe? Easy. Inflation was (we think) driven by some inflaton field that had negative pressure. This means that it acts as a kind of 'anti-gravity'. For some reason the inflaton field turned off after a small period of time, and ever since* the expansion has been simply due to momentum originally given by that kick. You just need to go back to the original though experiment and apply anti-gravity in the beginning. You still get the same answer, all 'kicks' can from each point be viewed as going outwards in all directions.

* Note in fact that the expansion has slowed of course due to gravity, and is now once again accelerating due to dark energy, which like the inflaton has negative pressure. The point is that forces operate on the second derivate of motion, not the first and the symmetry of the Universe means that all forces and radial and isotropic from every Hubble flow observers viewpoint.

 

[v2kkim]

Marcus, you surprise me. I thought you were beyond this!

* Note in fact that the expansion has slowed of course due to gravity, and is now once again accelerating due to dark energy, which like the inflaton has negative pressure. The point is that forces operate on the second derivate of motion, not the first.

Some people may say I am wrong but I like to post my opinion of the expansion rate. Hopefully it helps us to have a better perspective of our universe.

The expansion rate does not accelerating but decreasing in a sense that the expansion rate means the rate of length change for a unit length. Its unit could be %.
But when we monitor actual objects like very far away galaxies their recession speed is accelerating, which is not surprising considering that the recession speed goes up with distance.
In my option, we 'd better use the expansion rate (%) when talking of acceleration universe.

 

[Wallace]

If expansion was simply units changing then we would not see it, since everything we measure with would also change and we would simply see the Universe as static.

We do not observer any individual objects to be accelerating. To do this requires measuring 'red-shift drift' which would take a 42 metre telescope 10 years of continual observations to measure (our biggest today are 10 metres). Instead we infer acceleration by measuring, effectively, the distance vs redshift of a range of objects at a single instant (in cosmological terms data we take over human lifetimes is an instant).

 

[marcus]

... continuing to move apart following the initial kick given by inflation. ...

I see, you picture it as "continuing to move".
In which direction did this initial kick point?

...
Imagine a very large (possibly infinite) blob of dust of uniform density. Let it start completely from rest. What will the blob do? Because of gravity, all bits of the dust will be attracted to every other bit and the blob will start to contract, in the sense that everything gets closer to everything else (thus even if it is infinite we can still say that is contracts). Now, if you do the sums you will see that the material in the blob will be following Hubble law contraction (same as Hubble flow, but contracting). We don't need any funky relativity here, this thought experiment is entirely Newtonian. If you want, you could describe this situation as 'contracting space' as long as you knew that you were just inventing a metaphor, not describing physics. You could derive co-moving co-ordinates and all the rest.

Now, imagine that we turn gravity OFF after a small amount of time. What happens? Does everything stop moving? No, of course not, the dust blob continues to follow a Hubble law contraction and space continues to contract in the invented metaphor. The second derivative of the contraction rate would go to zero, but the contraction would continue.

So, in this situation, in which direction was the kick that was applied before we turned gravity off? Easy, every particle can say they every other particle received a kick towards it. All kicks are inwards to every point. This is an inevitable consequence of Gauss's law and the homogeneity of the material. It is Aristotelean to suggest that motion requires something to perpetuate it, so let's get with the Renaissance and realize that mass has momentum and we are done.

Now, how do we go from this thought experiment to our Universe? Easy. Inflation was (we think) driven by some inflaton field that had negative pressure. This means that it acts as a kind of 'anti-gravity'. For some reason the inflaton field turned off after a small period of time, and ever since* the expansion has been simply due to momentum originally given by that kick. You just need to go back to the original though experiment and apply anti-gravity in the beginning. You still get the same answer, all 'kicks' can from each point be viewed as going outwards in all directions.
...

We are potentially talking to newbies (newcomers). There are pedagogical issues.
You speak of a kick. I picture a kick as having a direction and resulting in ordinary physical momentum, with a direction.
In which direction is the kick?

If it has no direction then perhaps a different bunch of words?

I think we are trying to describe the Friedmann-Lemaître model, the classic 1920s model that cosmologists have always used.
"Inflation" is an unproven mix of scenarios that were proposed starting when? Around 1980? It's typically thought of as involving superluminal rates of distance-increase. Correct me if I'm wrong.
It sounds like you are invoking inflation as your "kick".

So you visualize inflation as giving ordinary physical momentum to matter. Familiar-type motion thru space. And that is how you imagine starting off the Friedmann universe?
Maybe you would repeat and spell it out in a little more detail.

I want to be sure you are talking about ordinary real momentum and not some curious kind of metaphorical momentum. I'm trying to grasp this a newcomer to PF might.

 

[Wallace]

We are potentially talking to newbies (newcomers). There are pedagogical issues.
You speak of a kick. I picture a kick as having a direction and resulting in ordinary physical momentum, with a direction.
In which direction is the kick?

Please read my post. As I explained, the kick is radially outwards from every point. Yes, I am talking about ordinary physical momentum. You don't ask why a ball keeps moving after you give it a kick do you? Why do so for galaxies then?

If it has no direction then perhaps a different bunch of words?

Please read my post. As explained, the kick is radially outwards from every point. That is a direction.

I think we are trying to describe the Friedmann-Lemaître model, the classic 1920s model that cosmologists have always used.

Right, and the most important thing about easy explanations is that they should reduce the familiar when possible. Relativity also goes to Newtonian in various limits, and you can understand the expansion of the Universe perfectly well without any relativity. The 'expansion of space' appears when you do an equivalent Newtonian treatment. The problem is that the way it is explained people think it is some strange effect of relativity, it is not, it is a metaphor deriving from one non unique co-ordinate system.

Physically it is far easier to think of the expansion of the Universe in familiar Newtonian terms. If you do the sums Newton and Einstein disagree for very distant galaxies, but the qualitative behaviour is the same.

"Inflation" is an unproven mix of scenarios that were proposed starting when? Around 1980? It's typically thought of as involving superluminal rates of distance-increase. Correct me if I'm wrong.
It sounds like you are invoking inflation as your "kick".

You are wrong. We know SOMETHING got the expansion going. At some point the Universe began expanding. In the standard model this happened in a particular way which we call inflation, so that is what I used in my explanation. However, ever since the 1920's when the FRW model was formulated it was known that something needed to provide an initial impetus to expand, that's why we have the name 'the Big Bang', in any version the theory something goes bang, push, shove or inflate in the beginning. It doesn't necessarily have to happen in the e-folding kind of way from inflation, but every bit of motion has to start somewhere.

So you visualize inflation as giving ordinary physical momentum to matter.

Yes

Familiar-type motion thru space.

There is another kind of motion??

And that is how you imagine starting off the Friedmann universe?

I didn't imagine it, Friedmann did.

Maybe you would repeat and spell it out in a little more detail.

Please read my post. There is sufficient detail there. My may have to unlearn some of the peculiar notions you've picked up, but if you come at it with a fresh mind (just think of the blob not as a universe, forgot any ideas about expanding space, just think Newtonially).

I want to be sure you are talking about ordinary real momentum and not some curious kind of metaphorical momentum. I'm trying to grasp this a newcomer to PF might.[/QUOTE

Yes I'm talking about real momentum. What other type of momentum is there?

I really think from reading some of the recent discussion around here that this whole issue has been made unnecessarily complicated.

 

[marcus]

So every dust grain has been given a kick in a direction which is away from all its neighbors.

As you said in earlier post, it can be a finite dust cloud. And the assumption in cosmology is uniformly distributed matter---isotropic homogeneous. So the dustcloud fills space.
And it's finite volume, so let's say space is a 3-sphere.

In what direction, in that 3D space, is the ordinary motion and the ordinary momentum?
Pick a dustgrain and let's say.

To take a simpler 2D analog as example, I'm having trouble understanding you because on the 2D surface of a sphere I find it impossible to imagine a point moving (in a direction along the surface, which here represents space) which is away from all the other points on the sphere.

I don't wish to argue with you personally, Wallace, but your finite dustcloud universe with each grain given a kick seems likely to lead to a pedagogical trainwreck. It is too full of contradictions which newcomers will stumble upon. Also it is atypical---runs counter to the usual balloon model that one gets, for example, at Ned Wright's cosmology tutorial.

 

[Wallace]

Okay, this is going to sound harsh, but I think you need to be shocked out of some mental rut you've gotten into.

Your problem is not understanding cosmology or Einsteinian relativity, it is simple Newtonian physics and Galilean relativity that you do not understand the basics of.

Forgot about your fancy analogies and try some real physics, some very simple intuative, Newtonian physics. The problem with what you advocate is that not only is it wrong, but it is more complicated that the right answer!

So, let's try and understand a self gravitating cloud of stuff. Forget Ned Wright and all the rest, if you can't understand the physics behind this you will not be able to really know what is going on with cosmology. How you choose to relate cosmology to 'newbies' is up to you, but until you yourself understand the physics, you are going to continue making a tangled mess even worse. I'm not suggesting that the explanation below (or above) is the ideal way to teach newbies, that is something that still eludes me, but it has to be better than teaching something that is wrong.

Right, so first thing to remember is that the only force operating in our cloud is gravity, which is a non-inertial force. You don't feel gravity pulling you down if you fall of a building, you only feel the force of the ground pushing up when you reach it. Actually techincally you don't really feel that either, what you feel is each bit of your body pushing the next, but I digress. So, gravity being a non-inertial force each dust grain will not feel the tug of the others the way you feel a car accelerating. Therefore imagine you are sitting on such a grain, you can be getting all kinds of acceleration but because it is all gravitational you feel nothing.

We can choose to define any individual grain as the centre of some co-ordinate system. In this system, we can use Gauss's law to infer that a dust grain at distance R from us will be accelerated towards us by a rate given by Newtons law of gravity, placing all the mass in a sphere of radius R at the origin. You should derive the expression for the second time derivative of R. What you will see in a few lines is that you have just derived the exact second order Friedmann equation (with no relativity required!).

Anyway the derivation is not so important, but it should convince you that cosmology really is pretty much just Newtonian physics, no mystical expansion of space required. Now, you still seem to be mystified by the 'direction' of the 'kick' each particle gets. If you use simple Galilean relativity, we can instead move our origin by a distance R to a new dust grain. What we find now is that our original origin is now accelerated towards the new one instead of the other way around. This is no more complicated than asking which of two astronauts on a space-walk is moving if they are drifting closer to each other. Clearly you can define either or both as moving, depending on where you place the origin. Take our two astronauts. They are moving towards each other, but 'in which direction' is the momentum? If you define one as moving and the other stationary and then vice versa you will apparenetly change the direction of the momentum in the system! This will only trouble you if you don't realize that momentume is frame dependant (Galileans frames, just simple linear shift in the origin, no relativity).

The same applies for our dust cloud. If we let gravity get everything moving then turn it off, clearly at any origin you choose you can define the momentum of every other particle as being directed towards that origin. Turning gravity off means that the second derivative of displacement goes to zero, but the first derivative (that gets you momentum) clearly does not go to zero just because the 'kick' has been turned off. Momentum is conserved and the cloud drifts together. The 'direction' of the momentum of any individual dust cloud depends on your reference frame because velocity is always relative. You seem to be demanding that if momentum exists then it must have an absolute direction, when clearly from high school physics we know that all motion is realtive.

The simple symmetries of the cloud however permit the simple result that the momentum on any particle is always radial with respect to any chosen origin.

Your comment "I'm having trouble understanding you because on the 2D surface of a sphere I find it impossible to imagine a point moving (in a direction along the surface, which here represents space) which is away from all the other points on the sphere." saddens me greatly. You seem to not be grasping to most basic message of the analogy that you hold so dear. The balloon analogy is nothing but a demonstration of the fact that the motion of all points is always radial with respect to every other point. Draw any two dots on the balloon and as it inflates or deflates the motion is always radial, the points don't change their angular orientaion, regardless of which points you choose.

The point is that the balloon analogy gives the bogus idea that it is the rubber that is doing something. In fact we can see that expansion is simply due to momentum, everything is moving away from everything else because it was so in the past. Let me put it more simply, the Universe expands because of Newtons first law of motion, inertia. Why oh why do people keep wanting to invoke some kind of mechanism, like expansion of space, to explain why expansion occurs when the truth is as simple as why soaps slides across a wet floor.

If you don't like inflation then just thing of the Big Bang as an explosion. This seems like an anathema because we are always told NOT to think of this. But it is only wrong if you think of a finite stick of dynamite exploding inside a larger space. However, if you imagine an infinitely large stick of dynamite, or at least one that is big enough you have no hope of seeing the edge from where you are, then this perfectly describes the Big Bang. The pressure generated by the dynamite going off produces a force that from each point in the dynamite is directed radially towards every other point. After the explosion, clearly the momentum imparted by this kick does not dissappear, instead everything moves away from everything else, only being slowed by the gravitational pull of everything towards everything else. In any chosen reference frame there will be no net force at any point. The initial kick pushes everything away from you and the subsuquent gravitational effects slow them down.

The spherical symmetry of the universe means that you can always just think about how two point behave. If you understand that then you will understand how the whole expansion goes.

The whole expansion of space analogy mixes up first and second derivates in a very clumsy way, and this is precisely why it causes trouble when people ask the obvious question 'why don't galaxies expand with space?'. They would not ask the question if they realized that they can just use everyday intuituion about momentum to see that because galaxies aren't in the process of expanding then they simply have no reason to start doing so (Newtons first law! Really it's that simple. You don't ask why your toaster doesn't spontanteously jump upwards when no force is applied do you?). Instead we hear that 'galaxies are so small that the expansion of space on that scale is negligable' or 'the gravity of a galaxy overcomes the expansion of space'. Both of these statements explicately equate first and second derivates as if they were the same. This cannot be the basis of a satisfactory understanding, no matter how seductive it may seem.

 

[marcus]

That's enough of this, I think.

 

[v2kkim]

I see two different point of view on far away galaxy expansion:
(1) Space expansion point of view : space is expanding everywhere.
(2) Continuing expansion motion of objects : a kind of simple Newton inertia.

One common result is Galaxies will expand continuously each other if there is no disturbing factors like gravitation. And the 2 theories will result in the same mathematical formula -- continuous expansion. But they show quite different picture in dealing with within galaxy motion.
Here, one problem of the 2nd theory might be the redshift explanation, because when we use the word motion then people tend to associate relativity. However remote galaxy redshift calculation does not use special relativity but use only space scale factor.

 

[marcus]

I see two different point of view on far away galaxy expansion:
(1) Space expansion point of view : space is expanding everywhere.
(2) Continuing expansion motion of objects : a kind of simple Newton inertia.

Here, one problem of the 2nd theory might be the redshift explanation, because when we use the word motion then people tend to associate relativity. However remote galaxy redshift calculation does not use special relativity but use only space scale factor.

You can calculate the redshift using special relativity and the SR doppler formula, but it is complicated and clumsy. You imagine a chain of observers and the whole expansion history is involved.

The simple direct way is just what you said: use the scale factor.
1+z = scale(now)/scale(then)
or however you want to write it.

=================

Vakkim, if you want my perspective, what I like to do is stick close to conventional cosmo language practice and coordinates, so there is as little confusion as possible.
Cosmologists use Hubble Law and they use Friedman Model.

In practice that means using coordinates (like so-called comoving ones) where stationary objects are at rest relative to
1. the CMB (no doppler hotspot ahead of them)
2. the expansion process itself
3. the ancient matter of the universe, if you want to think of it that way.

It is a natural idea of rest and coordinates like that are natural to use in cosmo.
Other special purpose coordinates are normally defined in terms of them.
And the Hubble Law is expressed in terms of the corresponding distance.

So as far as I can see there is no issue! There is no good alternative way for a beginner to get a solid introduction. Hubble Law and Friedman model have to come first. Scalefactor. The idea of comoving---being at rest relative the expansion process or the CMB. That gives the universe timescale that works in the Friedman model. It all hangs together.

=======================

The one thing you have to remember when approaching things the standard cosmology way is that space is not a substance. When we talk about expansion we are not actually talking about a material space expanding, we are talking about geometry---distances are expanding.
I think you are sophisticated enough about this that even if you might sometimes talk about space expanding you have something more abstract in mind.
I feel confident that you aren't thinking of a piece of rubber!
In the balloon model, people should concentrate on the geometry of the pattern of white dots painted on the balloon. They should not concentrate on the rubber. It is the geometric pattern that obeys Hubble Law. The balloon is only there to "carry" the geometry. If we could de-materialize her and still keep the white dots we would