Think of it this way: Rub a balloon on your head, hold it to the wall, then let go. It stays there, bound to the wall by electrostatic force, which is simply stronger than gravity.

The reason expansion doesn't affect even galaxies and galactic clusters don't expand is because they're bound by gravity, which is stronger than the miniscule effects of expansion, even over millions of light years. It's only the non-gravitationally bound empty reaches of space which feel the forces of expansion.

Thus, while the galaxies in a galactic cluster don't expand, two distantly separated galactic clusters separated by empty space would feel the effects of expansion and be drawn, along with space itself, away from one another.

__________________
I am Mugs, of the Alien clan of Usa, Nordamerica, a Terran, of Sol.

Mine: "Perception isn't reality. It's merely an abstraction thereof, and quite often not a very good one at that."

Heinlein's: "Staying young requires the unceasing cultivation of the ability to unlearn old falsehoods." "Freedom begins when you tell Ms. Grundy to go fly a kite."

Yes, there are big problems with arguing that space expanded locally while the orbits stayed fixed. In particular, I think it would be detectable within the orbits of the planets.

OK ... this makes sense. I was just wondering if there was a minimum requirement for this ... my understanding ( wont use the word belief ) is that it is for areas where the gravitational attraction is exactly equal to the universal expansion.

Yes... there will be a point from which you could say that you are still. ie; Not being drawn closer to any other body of mass, and that you are not drifting out as part of universal expansion... Finding such a place would be Dependant on the measured force of gravity being non existent. Deep Space.
Is Planet Earth expanding...NO.
Is Earths moon expanding away...NO.
Galactic expansion... NO.
The universe is expanding...Yes.
Continued acceleration observed...Yes.
Gravitational binding of orbiting bodies...Yes.
The binding of atomic structures...Yes.
Cellular binding...Yes.
Electro magnetic binding...Yes.

Do you still have a question...?

.Mark.

Why didnt you just say so in the first place ;-)

Just kidding of course ... I know it has been a long journey but this space stuff is just starting to make some sense.

I think the problem lies in the fact that "space expands" is just a metaphor for the mathematical description of the expanding Universe, in which the proper distance between comoving points increases with cosmological time.
When you look at a gravitationally bound system, like a solar system, the planets have been sprung free of the Hubble flow because they are gravitationally bound to the sun: there is no viscous "space expanding force" trying to disrupt their orbits by shoving them away from the sun. So an appropriate GR metric for thinking about the solar system might be the Schwarzschild metric, which includes no terms that could be interpreted as "the expansion of space".

So applying the "expanding space" metaphor too seriously gets you into tommac's situation, in which you wonder if space is "really" expanding within the confines of the solar system (and being ignored by the planets) or if space is somehow nailed in place by the existence of gravitationally bound orbits. I believe this is a question with no answer, because it arises from a misapplied metaphor.
But of course I'm ready to be corrected by those with a better grasp of GR than mine.

Grant Hutchison

Tommac, I answered this in my original post, and have since pointed this out in another post, as has speedfreek. If you want to learn, you need to read posts. I'll repeat a portion of my initial post:

These links provide the abstracts of the papers, and also links to the full articles, which are available freely from the arxiv e-print links.


You will need a PDF viewer such as the adobe reader (here), which is FREE.

I dont see the link to the article.

Look on the page. Read the text.
There's a bunch of stuff, top left, that looks like this:

· Electronic Refereed Journal Article (HTML)
· Full Refereed Journal Article (PDF/Postscript)
· arXiv e-print (arXiv:0707.0380)

You click on these links to get to versions of the article.

Grant Hutchison

I just get the abstract. now on the right I get issue contents. But then it takes me back to the other page.

Do I need to sign up?

Click on the green arXiv link.
You get an abstract.
Look top right.
Download pdf.

I just did it from the embedded link in my own post.

Grant Hutchison

It took me forever to figure out how to navigate those pages too.

I remember the first time I saw a link to one- I wondered why they linked me to just the abstract-"Where's the article?" I said to myself...

Grant,

There is an indeed an exact solution of a "point mass" against a deSitter (lambda, expanding universe) background, one metric called oddly enough the Schwarzschild-deSitter (SdS) metric. The coordinates here at that of the static deSitter metric with the "black hole" plopped down at r = 0. And I stress this is not in any comoving form, so the typical language doesn't work there.

And another tricky thing is the coordinates don't correspond to any observer and that trips a lot of people up. In static deSitter alone, r = 0 is the location of a co-mover coordinatizing with his own tanget ruler. But in Sds, r = 0 is the singularity. In Schwarzschild alone, the coordinates correspond to an observer at r = infinity. But in SdS, the local frame of the far away observer is not the Sds coordinates.

But it's an r with a clock that you can sort of see how it works, and can certainly plot the geodesics and everything else SdS is nicely static and perfectly spherically symmetrical itself. The magic metric factor neatly is just the sum of deSitter and Schwarzschild:

g_00 = 1/g_11 = (1 - R/r - k*r^2)

Here R is the normal Schwarzschild --BlackShield, I love that -- radius. So Lambda interestingly does not change the event horizon (that holds only for lambda -- other types of "dark energy" models, such as the Big Rip stuff, tha behave differently that "pure" lamdba do indeed perturb the event horizon).

k is the same deSitter alone factor that depends on lambda. IOW, SdS just simply sums the two terms from both. These coordinates sandwich us between two event horizons. There is the regular one at r = R, and then the cosmological horizon at k*r^2 = 1.

There is a balance point, call r0, at the maximum of the g_00 which is the maximum stationary clock rate, where a test particle would hover stationary, with the gravity of the point mass and lambda just cancelling.

There is another interesting result. The lambda part completely cancels for the null geodesics, and they are exactly the same as Schwarzschild alone. This had led many to *erroneously* conclude that the cosmological constant has no effect on gravitational lensing. Wolfgang Rindler, of Rindler metric fame, wrote some recent papers about this. It's a simple coordinate error by assuming the local ruler and clock of a "far away" observer correspond to the coordinates as they do with plain Schwarzschild. They don't here -- a far away observer is different, very different if r is approaching the cosmological horizon, and the lamdba does indeed affect the observed lensing.

Rindler went on to show that distant cluster lensing results were consistent with this effect for the currently accepted value of Lambda.

-Richard

thanks grant ... I think that was harder to figure out than the ant and the rope thing. was it like a test to see if someone is smart enough to read the doc?

I agree with tommack post 1. Some locals are bound, perhaps nowhere are things totally gravity unbound, so there are lots of grey volumes where expansion should be occurring at a rate inversely proportional to how near to totally unbound it is. One or zero seems improbable to me. Expansion is analog and variable. Neil

The important question in the context of this discussion is, I think, whether this metric is actually applicable to objects as strongly bound as planetary systems and galaxies, or if it finds its usefulness only at the scale of clusters and superclusters. I'm not suggesting I know the answer . But Rindler, in his Relativity: Special, General, and Cosmological (his second comma, not mine!) seems to come down quite firmly for a non-expanding metric at the planetary scale.Grant Hutchison

Grant,

I'm certain Rindler wrote that before the Cosmological Constant came back in the forefront of the cosmological consciousness. What he says is certainly true for a non-Lambda expansion, the "regular" FLRW (if I got the order right) expansion.

However, add Lambda in, and you get SdS. In that paper about lensing and gravitational lensing, Rindler uses SdS for his calculations and does mention that the time-like (non-null) geodesics are perturbed by Lamdba. It's just the null ones that are the same in the coordinates as they are in Schwarzschild.

So I think we can take Rindler himself using SdS for calculations of the effect of lambda on distant gravitational lensing as evidence that Rindler agrees SdS is the one to use when Lamdba is afoot.

The component of 'g' due to Lamdba is vanishingly small on the solar system, and even galactic scales. It's only ~10^-25 m/s^2 at 1AU.

The Newtonian limit paints a picture of space being filled with a repulsive negative mass density proportional to Lambda. So for the solar system, you imagine everything immersed in the ever so small negative mass density "soup".

Without Lambda, there is no local "negative mass soup".

-Richard

I called deSitter an "expanding universe". Well, it is, but is a Lamdba driven expansion. Very different from a non-Lambda Big Bang scenario. So I'll be sure to make that clear from now on. DeSitter and SdS and related are about Lamdba driven behavior.


-Richard

Could the cosmological constant be the coeficient of friction for light?
i mean not literally ... but could the cosmological constant be similar to a force ( I know not a force but something providing resistance ) to the infinite travel of light?