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Name: Ian
Status: educator
Grade:
Location: Outside U.S.
Country: Australia
Date: Fall 2012


Question:
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?

Replies:
Ian,

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.

Kyle Bunch


Ian, 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 Physics Instructor Illinois Central College


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