# Expanding space

1. Feb 26, 2004

### DW

There is some discussion about the expansion "of space" in a thread that actually belongs to a different topic so I thought I'd start a thread about that with my input here. Consider the Robertson Walker metric in the following form
$$ds^2 = dct^2 - \frac{R^2}{R_{0}^2}\frac{d\rho ^2 + \rho^2 (d\theta ^2 + sin^{2}\theta d\phi ^2)}{(1 + \frac{1}{4}k(\frac{\rho}{R_{0}})^2)^2}$$
Where R is a function of t. This metric represents the expanding universe and specifically what is expanding is the R term. If k = + 1 then the universe is positively closed curved and spacelike hypersurfaces can be taken from this spacetime that are conceivable as balloon like spheres embedded within a hyperspace where R would be the radius of the surface and would then have the interpretation of being the radius of the universe. So, when one talks of the radius of the universe or of the universe as expanding then it is this term changing in time that is being referred to. Some people more convinced that the universe is open curved don't like to think of the universe as having a radius and so call R by scale factor or whatever, but even then R still has the interpretation of the "radius of curvature" of the universe. It is still this radius of curvature that is actually expanding. Now the positions of comoving galaxies are constant with respect to the choice of coordinates expressed in this metric. Their coordinate velocities are zero. The fact that we observe them to be separating is because we are using a rigid ruler extension so to speed of local Cartesian coordinates to describe them instead of the choice of coordinates expressed in this metric. In a sufficiently local limit their rigid ruler velocities are related to the Doppler shift we see by the same formula that gives special relativistic Doppler shifts. So, in a sufficiently local limit saying the galaxies are stationary with respect to a coordinate frame according to which space itself is expanding is equivalent to saying that the galaxies are moving with respect to another coordinate frame according to which space is static. However when one considers the global behavior of the metric and the galaxies one can no longer use the special relativistic Doppler formula, nor the special relativistic metric. One instead finds that the metric in a global description is dynamic according to every frame and so globally speaking it is expanding space and not galaxies separating within space that is the accurate description.

Last edited: Feb 26, 2004
2. Feb 26, 2004

### yogi

Yes - that is the exact conclusion arrived at by Robertson - so what is the issue

3. Feb 26, 2004

### DW

In the abberation thread David was saying that no papers are saying that it is space expanding. I am pointing out that this is exactly what is being said.

4. Feb 26, 2004

### yogi

oh - ok DW - sorry - I didn't look into the history of the post - quite right

5. Feb 27, 2004

### David

Saying that the distant galaxies “aren’t really moving”, is like saying that the galaxies are “stationary” relative to themselves. Everybody already knows that. Just like parked cars in a parking lot are stationary relative to themselves, as the parking lot moves around the sun at 18.6 mps and around the center of our galaxy at 250 mps and through space at whatever.

Now take a group of parked cars on a barge. The barge starts to move in the ocean, and so all of that “local group” of cars starts to move through space. That doesn’t mean “space is expanding”, it means all the cars are moving together. Their distances from the parked cars on land is growing, because the cars on the barge are moving through space.

You seem to assume that our physical universe of galaxies has a boundary beyond which there is a big spherical brick wall, and behind that wall is “no-space”, and you assume that “expanding space” is pushing that brick wall further away from us and is inventing space as the universe expands.

All you have in your growing radius is the expanding radius of a spherical 3-D universe of expanding matter, that is moving through space as it expands. This is the “big bang” theory.

6. Feb 27, 2004

### David

The Robertson-Walker metric describes the expansion of the physical matter in the universe, galaxies separating and moving apart, not the “expansion of space”. His so-called “radius of curvature of curved space” is the radius of the presumed spherical collection of galaxies that are moving apart. The universe of physical galaxies that we see is assumed to be spherical in shape, something like a spherical star-burst fireworks explosion. The galaxies are moving through space. We can say that “the space in between the galaxies is expanding”, but what that really means is the distance between the galaxies is expanding, because the galaxies are moving through greater space. Look at a spherical fireworks explosion. You can say that the “space” in between the glowing particles is “expanding”, but all you are really saying is the distance between the particles is expanding as the particle move through space. Thus, all of “space” is not just what we see in-between the galaxies, inside the spherical radius of the expanding collection of galaxies, but greater space, deeper space, more distant space, is also what the galaxies are moving into as they move apart.

To say that the space inside our universe is truly expanding, you’d have to show us the outermost galaxies of the expanding sphere, and you’d have to show us a big wall, beyond which there is nothing, not even space, and you’d have to show us that that wall is moving outward and away from us. Then you could say our “space is expanding” if you can prove that beyond the most distant galaxies there is some kind of solid wall and beyond it lies “no-space” at all.

7. Feb 27, 2004

### David

I said there are no papers that give us a physical mechanism and a physical description of how “space” itself can “expand”.

When things move apart, the distance between them expands, but you can’t say the “space” in between them expands. They are merely moving into deeper space, and thus there is more space between us and them, but that doesn’t mean that its the space in between us that is expanding. The objects are just moving through space, that’s all. How complex is that to understand?

8. Feb 27, 2004

### yogi

David - your view is contrary to all interpretations of the metric - if you step down one dimension to a two sphere as the surface of an inflating balloon, dots placed on the balloon will recede from one another - all points on the surface can be described in terms of coordinates defined by the surface - or perhaps better said - the coordinates that define every point need not be related to the center of the balloon or any third dimension - you do not have to consider the balloon a two dimensional surface embedded in a three dimensional space - everything is contained in the metric that defines the surface - there is no volume to consider - the balloon surface is not expanding into something - it is all there is - there ain't no third dimension necessary to regard the expansion as "expanding into" Same is true for the 3d universe - there is no space into which expansion is progressing - it is the existing space that is strething just as the existing surface of the balloon stretches when it is inflated - that is the beauty of the metric description

9. Feb 27, 2004

### Phobos

Staff Emeritus
David - I suppose you reject the idea that infinite (or at least boundless) space can expand. That is part of Big Bang Theory.

Your idea would require that we see galaxies moving away from a central point. That is not the case.

10. Feb 27, 2004

### Staff: Mentor

Yeah, we discussed that in one of the other threads. David is not bothered by our lack of ability to see the edge (or in fact see any evidence that the universe isn't roughly homogeneous on the huge scale). Somehow he sees no problem with assuming the existence of something for which there is no evidence, simply because the alternative is in his words "silly."

11. Feb 27, 2004

### David

Hey, I’ve got Eddington’s original 1932 book in which he invents the “balloon” analogy. He says we live inside the rubber skin of the balloon! LOL! Some of you guys will fall for anything!

Look, contrary to popular belief, we do not live on the “surface” of an “expanding balloon”. We live inside what appears to be an expanding Euclidean sphere galaxies. We do not live inside the rubber “skin” of a balloon. We do not live on the “surface” of our universe, we live inside it.

12. Feb 27, 2004

### Phobos

Staff Emeritus
It's an analogy...a simple way to think about a complex idea. No one is saying that is how it actually is.

No, that would imply a common origin point of the expansion. That does not appear to be the case.

Again, it's just an analogy.
There's also the "raison bread" analogy, but even that falls short of perfection because you can still see a center and edge, which is not what Big Bang Theory describes.

13. Feb 27, 2004

### David

In the 1960s, ‘70s, ‘80s, and ‘90s, the “big bang” theory discussed a specific “point of origin”. I talked to professional astronomers in the ‘90s who discussed a specific “point of origin”. When I interviewed Dr. Robert Jastrow, he specifically told me he thought the “point” was originally about the size of a “basketball”. Eddington in 1932 said he thought it was bigger than that, but something like a small sphere of galaxies. Lemaitre’s original 1927 paper had it as a “point”, what he called a “primordial atom” that sort of exploded outwards. So, all of that describes an expanding spherical universe of matter that is moving apart. When I’ve got professional astronomers from Mt. Wilson and Harvard and other places telling me in the ‘90s it was originally a “point” or a “basketball” sized thing, Ok, so I’ll accept that, as a tentative theory. I didn’t invent that idea, they did.

If you want to call it an “expanding balloon surface” or a “loaf of raisin bread” or “not quite like that” or “something similar but not really like that” or “there is no way to explain it”, ok, then that’s your opinion. I express my opinion and you express yours.

Is our universe really like any of that? I don’t know. You don’t know. Nobody knows. All of us are just speculating. Face it, human beings on earth today are free to speculate, muse, think, and express their own opinions in most countries. That’s all I am doing.

Maybe the galaxies really aren’t moving. Maybe the redshifts are due to the Compton effect or something else. I don’t know, you don’t know, and nobody knows for sure.

Look, only in Fascist and Communist countries (and a few others) are people required to all think alike and all support exactly the same science theories that are approved by their dictators or their governments. We don’t live in that kind of country. So ease up.

14. Feb 27, 2004

### yogi

There is no requirement that everyone think alike - what the members of PF are doing is attempting to convey a concept - we use the 2 sphere analogy because it is something we can all visualize. But we cannot visualize a three sphere embedded in a forth spatial dimension - but we can extrapolate from two dimensions to what three dimensional expansion involves mathematically.

PS ... I have some of Eddington's original publications also - you have misinterpreted what is being said by the authorities - I do not believe that any of the authorities you mentioned would ratify the interpretation you have put upon their statements.

That is ok - again, you are free to misinterpret things in the light of your own convictions - God knows we have all been guilty of that. I suggest, however, that if you really think about the issue objectively rather than defensively, much will be revealed.

Its ok to be wrong sometimes - Once when Lincoln was accused of doing an about face he commented: "I don't think much of a man who isn't smatter today than he was yesterday."

15. Feb 27, 2004

### David

Where is the observational evidence that the universe has 4 dimensions of space?

What the observational evidence reveals is us inside a 3 dimensional universe in which the distant galaxies are moving apart with time. What does a 4th spatial dimension have to do with this?

Why are you trying to convey a certain “concept” about the universe, and exactly what is that concept?

16. Feb 28, 2004

### yogi

There is no evidence of a forth dimension per se - but if you ask questions like what exists beyond the 3 dimensional expanding universe - or alternatively, what is our three dimensional sphere expanding into - you imply the existence of a 4th dimension in which the bounded three sphere is embedded. But if you say the three dimensional Hubble sphere is all there is, then the RW metric totally describes the universe as a three dimensional surface without reference to anything beyond.

Think about how a two dimensional being on the balloon would describe his universe - there is no center to the 2 sphere - no volume - no interior and nothing exterior ... the surface is all there is - and it can grow larger unto itself - one can always argue that a two sphere requires a three dimensional embedding-space - and that is of course the real world because we don't have a two dimensional laboratory in which to construct two dimensional cosmological models. Every real two sphere can only exist in three dimensions, but the address of any point on the sphere relative to any other only requires a 2 dimensional coordinate groundform.

17. Feb 28, 2004

### David

Whatever is “beyond” our own outer-most galaxies (assuming there are outer-most galaxies in our system) could very well be more “empty space”. In fact, for all we know, there could be dozens of other physical universes also expanding spherically into greater “empty space”. There is no need to evoke a 4th dimension of space.

Of course we can not see beyond the radius of our own current sphere of observation, but anyone at all should be free to speculate about what is out beyond what we can now see. I don’t understand why there must be some kind of formal “official” view about what might be out there. If science adopts a rigid “official view” about anything, that discourages speculation and creative thinking. It discourages imagination and discovery. It discourages new ideas in science. It makes everyone have to conform to an “official” point of view, just as people in Europe had to conform to the church’s “official” point of view back in the middle-ages.

Geez! We are not two dimensional beings living on the surface of a sphere!

18. Feb 28, 2004

### yogi

I fully agree with your philosophy about conformity - a bit of a rebel myself - but there are some interesting differences that arise between the notion of an exterior space into which the galaxies are moving, and a finite space that is swelling - one concerns how or why the totality of cosmic energy can be zero, another concerns the notion of whether the properties of the vacuum can be explained by expansion, another involves how matter might be created from the notion of an expanding false vacuum (inflation either previously or contiuing) ...or why the velocity of light has the value it does, or how a transverse wave can exist in medium (this can happen if the medium is under tension i.e., a false vacuum). In other words, if space is just a static nothing that has existed eternally, we forfeit perhaps some opportunity of relating certain cosmological mysteries to known physics. In my opinion, physics has already boxed itself in with ideas like "Planck units" and other common assertions expressly or impliedly endorsed by all present writers - the notion of a dynamic expanding medium leads to a lot of answers as to why things have the value they do. Interestingly, the notion of expansion does not necessarily imply a finite age for the universe.

As for the two dimensional sphere to which I referred - it is only metaphorical - but if a two dimensional universe can be finite, so also can a three dimension universe - we can't visulaise it any more than the two dimensional being can comprehend up or down on this balloon universe - but he could write an equation that would be descriptive of its finite-ness ....as we can with the RW metric

19. Feb 28, 2004

### David

Tell me a little more about this “expanding medium” and the “tension” in it. Lorentz wrote something about “tensions” in the medium in his 1895 book. He called it “Spannungen im Aether”.

20. Feb 28, 2004

### yogi

Back to you David: There are a number of ways of modeling a medium in tension - one simple picture is to consider space as a plenum of three dimensional vortices - for an example of something we already know of, consider the neutrino - nearly massless, yet it carries an angular momentum h bar/2 (same as proton, electon etc) - so the angular momentum cannot be tied to any particular mass, but rather to a spatial vortex ... now vorticies exist because the pressure is less in the center - so space might be considered a sea of quasi-static neutrinos - each having a center of negative pressure - ergo there is a tension between adjacent vortices - when space expands the tension is increased.. if you consider a filament of space under tension, and you know the average cosmic density per unit length (consider the universe as having a critical mass), you can apply the classical formula for the velocity of a wave in a stretched string under tension. Using Newton's formula for the reactionary force developed by the expansion of a uniform sphere, and a gausses law, you have all that is needed to calculate the free space velocity of a wave - not surprisingly it is c