phinds said:
I thing my problem is that I can envisage the pennies haveing fixed locations relative to a spot on the expanding balloon but what I can't seem to get anyone to tell me is, does the suface of the balloon remain unchanged under the penny as the rest of the balloon expands or does that part of the skin expand as well?
Phinds,
we are using words to translate a math model and my words may not be the right ones for you. If they don't work, sorry. there can be several different translations of something in a foreign (math) language. Try several and choose the one best for you.
My take is this: there is no rubber. Geometry is not a material.
The balloon model is ONLY to help you visualize a pattern of expanding distances.
It is not meant to make you think there is a material called space analogous to rubber. In fact the basic "covariance" principle of GR implies that points of space cannot have objective physical reality.
GR is only about geometry. It describes how geometry evolves with time and in interaction with matter. We have no right to presume that geometry has to be the usual static Euclid setup. In fact GR explains why in our neighborhood it IS NEARLY like that. GR provides a reason why it is almost the usual static schoolbook Euclid setup.
It is both our law of gravity and our law of geometry.
So there is no rubber "under the pennies". There is no rubber. It is all a web of geometric relations. That web can change. It is just information. Not material.
The very simplest version is what is called the Friedmann model which is a simplified universe with uniformly distributed matter. It is a good approximation. In that model the distances that grow are ones between observers who are at rest relative to CMB.
Now I'll take a chance and say something a bit risky. IF the CMB rest criterion were a bit more uniform and precise and stable than it really is we might find that the galaxies in a cluster of galaxies were just a little farther out from the center of mass than their orbital speed would suggest. As if the cluster had been stretched out. As if there really was "rubber under the cluster".
We might even find that expansion of distance in our own galaxy has an effect. Someone will correct me if I'm wrong. We might find (if we could measure that accurately) that the rim stars are just a tiny tiny bit farther from center, given their speed, than they Newtonly ought to be. Their distance has stabilized at a slightly stretched out value.
An observer on a rim star would be able to detect that even after compensating for circular orbital motion he was still not at CMB rest, but was falling in towards Center just fast enough to compensate for the increase of distance from center.
But the expansion effect is only 1/140 of one percent per million years! So this infall speed would be undetectably small. And it would not change his actual distance from Center. It would only be a speed measured relative to CMB.
However in reality the CMB has that random fluctuation element you see in maps of it, so no such very precise measurement could be made. So it is a what-if kind of thing, to take with a grain of salt if at all. In that very limited sense one might want to imagine that there is rubber under the pennies, since you asked
