Relativity, Cosmology, and Shape of Universe
Location: Outside U.S.
Date: Fall 2012
General relativity says matter curves space and this is what we experience as gravity. No problem. Cosmologists say the universe is flat (or very close to it) rather than closed or open. I take that to mean: ignoring the local dents made by matter, the overall shape is flat - whatever "flat" means in 4D space-time. My question is: How can a flat universe not have an edge? How can there not be planets that are so close to the edge that some nights there are stars in the sky and other nights there are no stars?
Sometimes the analogies used to describe the universe get us trapped
in what seems to be a paradox. If, for example, we view the universe
as a balloon and talk of existence only on the surface, we have
something akin to a two-dimensional analog of the universe. Our
natural tendency in this case is to think of ourselves standing
outside the balloon and to begin speculating about "edges" and
"boundaries." It is not, clear, however, if there is "another place"
other than our universe in which a higher-dimensional being could
view the shape of the universe. Given that, the balloon analogy is
not too bad in that anywhere you are on the surface, you do not
encounter an edge or ending. It is a curved surface, however.
Current thinking has the beginning of the universe as though it were
a deflated balloon with all of matter confined to a single point (a
singularity). Again, there is no "outside" the universe in this
case, and near the beginning, space would be closed. Early on, it is
thought that the universe went through an enormous expansion (called
"inflation") in which space stretched to such an extent that it
caused much of the vast size we see today. Further, the rate of
expansion happened so rapidly that space itself stretched much
faster than the speed of light. In other words, if you were to place
two dots on our analogous balloon and blow it up rapidly, the
distances between the dots would have moved apart faster than the
speed of light. This rapid expansion does not violate the speed of
light limitation of relativity, as it is not matter traveling
through space faster than the speed of light, but space itself that
is stretching faster.
The inflation model, while it may seem fantastic, does fit the
observed behavior of the universe. First, the flatness of space
observed is explained by a huge expansion of our balloon. If you
could blow up a balloon to the size of the earth, you could perceive
it as flat much like ancient people thought the actual earth was
flat. Now blow up the balloon to the size of the sun, the size of
the solar system, the size of the galaxy, and so on, and it becomes
apparent that the universe will appear flat. It also explains the
apparent uniformity of matter distribution on enormous scales in all
directions (locally, of course, matter is not uniform as we see such
things as galaxies, stars and such).
Another interesting consequence comes out of inflation theory,
however, and that is the rate of expansion which causes space itself
to outrun light. Assume your two dots on the balloon were actually
people shining flashlights at each other. The light is confined to
the surface of the balloon in our analogy. The expansion of the
balloon surface would outrun the ability of light to keep up with
this expansion. The two people would stop seeing each other because
the light coming from one flashlight would not outpace the expansion
of the balloon. The balloon universe would quickly become a lonely
place as all points on the balloon would become disconnected from
every other place, unless of course the expansion stops (or slows
sufficiently), and allows light to catch up with the expansion of
the balloon. In our universe, the inflation period did stop. Now,
however, we are only be able to see as far as the distance over
which light could travel from the time of the start of the universe
to present. Inflation has stretched much of the universe so that
light from those sections of the universe has not reached us. In
other words, what we can see is not the entire universe, but a
constantly expanding one. Much of the universe is effectively hidden from us.
Now back to the original question. Given inflation, it is obvious
that the universe appears on the whole "flat." While we may
(theoretically) see an end to the universe, this edge is merely what
we would see given that it is the only the farthest light that could
have reached us since the beginning of the universe. If we were to
travel as fast as possible in any direction, we would see an
ever-expanding universe (as we do now), but we would not see an edge
where the stars do not exist.
One difficulty that many have with the "shape" of the universe involves the image of space and time. Many view the universe as a structure within space and time. Latest theories view it just the other way around. Space and time are within the universe, part of it. In fact, time works just like the other three dimensions of space. We just perceive it differently. While moving along a dimension of space, we can look forward and backward. While moving along the dimension of time, we can only look sideways: we can only perceive where we are in time. This may be just a limit of our senses.
As for slowing down, some current research shows that the rate of expansion is actually speeding up. We don't know why or how. The difficulty with imagining this theory deals with time. Is time expanding as well? If so, what does it mean to our perception? We would not be able to measure the expansion directly, because we cannot look forward in time. If both expand, what does it mean about the speed of light? String theory currently requires eleven dimensions. Some can be so small that we cannot perceive their presence. The math works, and the data agrees. Without a better understanding of how to perceive and measure such things, experiments are quite difficult to develop.
As for relativity, the best I have come up with is a set of dots, a square pattern at integer points of a 3D coordinate system. Connect the dots by "horizontal" and "vertical" lines, something like an old-style "jungle gym". Near a very heavy and dense object, the dots move toward the object. This makes the distance between the dots near the massive object increase. In reality, it is no better than the two-dimensional picture. Still, it does give a 3D introduction to "dips" in space.
Dr. Ken Mellendorf
Illinois Central College
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Update: November 2011