I hope these puzzlers are thought-provoking. "Problems" deserve many thanks
in science, since they stimulate it to grow.
The way the universe expansion and deceleration (at least, before negative
energy/cosmological constant) was very elegant when thinking of little
particles on the surface of an expanding balloon, etc. However, I have
always wondered about consistency problems if the universe is filled with
hard balls and in a state of contraction. (Our universe is not going to
reverse expansion and contract into a "big crunch" due to combination of
factors such as Hubble"constant" and dark energy, but it is logically
possible and "could have" turned out that way if this or that was
different.
In any case, this serves as a proper "what if" problem for general
relativity as a theoretical construct.) What happens when the balls touch
each other? They should scrunch up together and just sit there, but then
we
have strange problems trying to apply the pseudoNewtonian approximation.
For
example, any point in the center of a ball can imagine that light
propagating from itself loses energy traveling up through successive
spheres
of matter (the radii of which are always just wherever the photon is,
since
the stuff beyond that cancels out.) So, the receiver should get a red
****ft, but the receiver could imagine himself at the bottom of the same
self-defined spherical region etc. and expect a blue ****ft.
Then there's the issue of what happens to little bodies inside bigger
spheres: By simple extrapolation of the incoming motion of the little
bodies
as seen by any given observer, they should continue moving toward that
central observer until the smack into the sides of whatever sphere they're
in. But again, this does not provide a consistent picture because it
produces contradictory preferred central observers in every place.
Sure, GR is not Newtonian gravity, but then what *would* happen if our
universe was filled with hard spheres with contents, sending light signals
to each other, when the spheres scrunched together?
I already suspect that Doppler ****ft is going to continue to be based on
relative scale factor, and presumably motion of contained particles would
be
correlated with that, etc. However, it starts getting sticky so to speak
if
a region of space has bodies clump together before the rest of space over
a
wide area does: then, to what extent and under what rules does such a
local
region act like an isolated Newtonian or small GR system (where the test
bodies in the centers of larger spheres keep moving towards the
extrapolated
contraction point, gravitational Doppler ****fts depend on local
distributions of mass, etc.) versus acting consistently with concepts
properly applying in GR to "space as a whole"?
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