Question about the expansion of space.

[Chalnoth]

OK, I'll buy this proposition, but will you allow me to test it first?

The argument, as I understand what you are saying, is;

1) that there is no expansion of space within the physical limits of a gravitationally bound system,
2) that a gravitationally bound system is one in which the matter therein has enough 'gravity' to pull all the matter back, back to within that bounded system, and keep it like that*.

*(notwithstanding any processes that imparts enough energy to particular masses that may cause them to escape the system)

Please help me clarify these statements, or let me know if they are correct (wrt your proposition).

That's more or less accurate.

 

[Chalnoth]

No, you misunderstand. The role of gravity in the two cases is not the same. In that sense it is a confusing analogy, using gravity in both cases, but using them in completely different ways.

Universe:
Gravity is the coalescing force,
cosmological expansion is the expansive force.
The coalescent force easily overcomes the expansive force.
Balloon analogy:
Atomic bonds of copper is the coalescing force,
gravity is the expansive force.
The coalescent force easily overcomes the expansive force.

I am simply trying to point out to cmb that, when there are two opposing forces, one can overwhelm the other such that the smaller one has no measureable effect.

This is getting a bit pedantic, but I don't think it's accurate. The fundamental problem here is that we don't have two opposing forces. We just have one: gravity. I don't think it makes sense to think of the expansion as a force (even though yes, you can write it in as a pseudoforce). I think it makes far more sense to think about the expansion as being due to the initial conditions, and the gravity on the components of the universe determining how that expansion changes over time.

 

[inf. improb.]

It would seem to me that this question really hinges on the nature of the expansion of the universe. As I understand it, that expansion is due to the continued outgrowth of spacetime itself that is the result of the Big Bang. As such, it is not really the space between your finger and the computer monitor that is "stretching", but all space and time is currently expanding at an accelerating rate. That acclerating expansion of space carries all matter and energy along with it.

The apparent cancellation of this expansion that results from gravitationally bound bodies and systems can be explained by the curved geometry that results from gravitational warping of space-time. That curvature is sufficient to reduce the effects of overall spatial expansion within the limits of the curves (i.e. the gravitational influence of the system). Take the rubber sheet example that is so often used to visualize the gravitational effects of a large body like the sun.

If you place a bowling ball in the middle of a stretched sheet of latex, the rubber distorts. Now, if you imagine the edges of this rubber sheet being attached to an expandable ring, and you increase the diameter of that ring mechanicall, the rubber sheet will stretch. Observing this, you'll notice that the flat areas of the sheet stretch much more rapidly than the part of the sheet that is warped by the bowling ball. This would correspond to the easily measurable rate of expansion of relatively empty space between galaxies where the large-scale geometry of space-time is essentially flat.

While this example is limited in the fact that it only expresses a two dimensional analog to the fabric of space time, the principle holds true, I believe. The more drastically the fabric of space-time is curved as a result of gravity, the less the "stretching" of space will affect that area of space-time. If you imagine that fabric stretching to infinity, however, you will quickly see that the curvature is neccessarily flattened over time. This would correspond to the "Big Chill" principle in which gravitationally bound systems and bodies break down slowly in response to the universal expansion of space-time.

 

[The Seeker]

If you imagine that fabric stretching to infinity, however, you will quickly see that the curvature is neccessarily flattened over time. This would correspond to the "Big Chill" principle in which gravitationally bound systems and bodies break down slowly in response to the universal expansion of space-time.

Would this lead to the eventual separation of particles and their constituent particles ad infinitum?

 

[Chalnoth]

The more drastically the fabric of space-time is curved as a result of gravity, the less the "stretching" of space will affect that area of space-time. If you imagine that fabric stretching to infinity, however, you will quickly see that the curvature is neccessarily flattened over time.

This does not follow. In fact, the average spatial curvature does not change with time at all. It does change in relative importance as other parts of the universe do (or do not) dilute as the universe expands. But it remains the same value for all time.

Now, the space-time curvature does change over time, but that's pretty simply-related to the rate of expansion. And the rate of expansion will not ever tend towards zero, in any universe.