Universe Expansion and two tennis balls Clear the universe of all matter except for two tennis balls.  Place the two tennis balls in the same inertial frame 1 Mpc apart.


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*Are the tennis balls getting further apart?

*Will the tennis balls remain in the same inertial frame?


EDIT: Don't assume the balls are massless, but please ignore the gravitational attraction two tennis balls separated at 1 Mpc would exhibit on one another. (Previously, I had asked to assume the tennis balls were massless.  I couldn't switch to a strike out font, so I just removed it entirely.)
 A: In the abscence of dark energy, yes (and ignoring the balls' infinitesimal gravitational attraction).  The background of the universe will then be special relativity, which predicts that the two geodesics traced by the balls will remain forever parallel.
A: After pondering this for a day and reading http://en.wikipedia.org/wiki/Metric_expansion_of_space over and over again, I think I know the answer to my questions.


*

*Are the tennis balls getting further apart? - Yes

*Will the tennis balls remain in the same inertial frame? - Yes


Conceptually, let's say that the universe is not expanding at all.  We place the two tennis balls 1 Mpc apart, both stationary to one another.  The momentum of the system is zero.
Now instantly, we change the Hubble Constant to 67.8 km/s/Mpc.  The two tennis balls are now moving away from one another at 67.8 km/s (and of course, as they move away from one another that rate increases with distance).
Theoretically, the momentum: p = mv is now not equal to 0.  But, momentum has always been a relative notion and in the context of space expansion I suspect p = m(v-HD) and so in this case still equal to 0.
If we now switch the Hubble Constant back to 0, even though the two tennis balls were moving apart at 67.8 km/s, they would instantly stop moving relative to one another.  Their momentum remaining 0 throughout the experiment.
When I was thinking about this one thing that was perhaps helpful was thinking of the universe as a checkerboard.  My tennis balls are checkers on opposite ends of the board; checkers that aren't moving from their current space.  In this scenario, "expansion of the universe" means to decrease the size of the spaces of the grid on the checkerboard.
When I start out, I can ask how many spaces apart are the checkers, which could be 7 for example.  Now I divide each space into 4 sections.  The checkers haven't moved, but they are now 14 spaces apart.  I divide the spaces again and now without moving the checkers are 28 spaces apart.
They are getting further apart, not because they are moving but because of the "metric expansion of space".
At any rate, if any and all of this is wrong please let me know. All comments greatly appreciated.
