The balloon analogy (please critique)

[GeorgeDishman]

If the balloon surface is uniform, distances between galaxies grow at a rate which is proportional to their separation. That is the Hubble Law and that law holds for comoving distances, the distance measured by the orange arc.

That's a nice observation regarding CURRENT distance measures...since the Hubble constant varies over time. It's obvious, but I did not think of it...thanks!

That's not quite the point. For any given cosmological time, the Hubble Law is a linear relationship, rate of recession equals the constant times a distance. That is also true of separations measured on the surface of the balloon. If you use other distance measures (luminosity distance, angular size distance, etc.) for the analogy, the relationship will not be linear so it would no longer match the balloon.

What I wondered in the article is whether such potential well 'detours' of CMBR photons require or deserve any correction in CMBR observations??

The EM emissions from the galaxies themselves are generally greater so "foreground features" have to be removed. However, we can use the effect to learn about the galaxies since the CMBR is so well defined.

 

[Ich]

#4: My last issue is the earlier posted point from Wallace regarding acceleration not velocity [or rapidity if your prefer] as the determining factor in separation. The balloon analogy does NOT capture that but how to explain in simple terms why is not yet clear to me...

What he meant by "velocity" is \dot a, the time derivative of the scale factor. It corresponds to the radial velocity of the balloon surface. (It is its proper velocity rather, not bounded by c therefore.)
The acceleration is \ddot a, here the proper radial acceleration of the balloon surface.

Now if you put two dots at rest wrt each other on the surface (i.e. not comoving), their relative acceleration is proportional to \ddot a, not \dot a. That holds in FRW coordinates as well as in the analogy.

I'll open another thread for the distance definition subtleties, that doesn't belong here.

 

[Naty1]

Ich, George,,,thanks for the feedback...appreciate it...

will reread your explanations tomorrow and be back then...

But not until I walk my Yorkies...after all, this is JUST science...!

Idea of a separate discussion on distance is good... look forward to that!

 

[Naty1]

George's Ned Wright link posted above did not 'click' for me after an initial reading so I was doing some background reading and came across this Wikipedia discussion which seems to support my own incorrect interpretation... not what George claimed for Wright...but in all honestly, Wright's explanation link and this one below are not really clear to me yet:

http://en.wikipedia.org/wiki/Comoving_distance#Uses_of_the_proper_distance

...It is important to the definition of both comoving distance and proper distance in the cosmological sense (as opposed to proper length in special relativity) that all observers have the same cosmological age. For instance, if one measured the distance along a straight line or spacelike geodesic between the two points, observers situated between the two points would have different cosmological ages when the geodesic path crossed their own world lines, so in calculating the distance along this geodesic one would not be correctly measuring comoving distance or cosmological proper distance. Comoving and proper distances are not the same concept of distance as the concept of distance in special relativity. This can be seen by considering the hypothetical case of a universe empty of mass, where both sorts of distance can be measured. When the density of mass in the FLRW metric is set to zero (an empty 'Milne universe'), then the cosmological coordinate system used to write this metric becomes a non-inertial coordinate system in the flat Minkowski spacetime of special relativity, one where surfaces of constant time-coordinate appear as hyperbolas when drawn in a Minkowski diagram from the perspective of an inertial frame of reference.[4] In this case, for two events which are simultaneous according the cosmological time coordinate, the value of the cosmological proper distance is not equal to the value of the proper length between these same events,(Wright) which would just be the distance along a straight line between the events in a Minkowski diagram (and a straight line is a geodesic in flat Minkowski spacetime), or the coordinate distance between the events in the inertial frame where they are simultaneous...[/QUOTE

Maybe this is better saved for a subsequent discussion on distance...I did want to post it for future reference.

I assume I am the one that is 'mixed up' and will continue background reading...

 

[Ich]

Sorry for the delay, I'll start the other thread tomorrow (I hope). Again, it will go along the line of Ned Wright's arguments.
For the time being: a spacelike geodesic is not the same as a geodesic of space. The former is a geodesic of spacetime which is, well, spacelike. The latter is a curve of extremal distance in some subspace of spacetime, which is necessarily spacelike but not necessarily also a geodesic of spacetime.