drwtsn32,
here is a must read for you! it looks as if homer would get satisfied!
If the universe is finite, what is outside it?
When we stand outside and look at the sky, it is hard to believe that there shouldn't be some very simple explanation for what we are seeing. But after a century of delving deeply into the laws of physics, we now know that much of the underpinning is probably destined to remain intuitively incomprehensible. There are no known simple explanations for why nature obeys quantum mechanical laws, why special relativity is the only explanation for the phenomena seen at high speeds. And then there is the universe itself.
Einstein's theory of general relativity is the only existing theory we have that guides us in thinking about physical space. So far as possible, it has been put to a variety of diverse tests and found to give an accurate picture of how gravity operates. But it asks us to also forget about common sense in the particular domain in which it works. General relativity is the premier theory of how gravity works. It says that space and time are a 4-dimensional 'thing' whose overall shape is dictated, nay, defined by gravitational fields themselves.
General relativity shows that if we looked at a spacetime whose 3-dimensional space sections were finite ( the case of our universe as a closed, finite one destined to recollapse in the far future) we would discover that the paths of particles and light rays would be closed curves. If the universe could hold this particular spatial shape long enough as in Einstein's original cosmological model in 1917, a rocket could circumnavigate the universe by always traveling exactly straight ahead. There is no edge to such a space for much the same reason that if surveyors were to map the 2-dimensional surface of the earth they, too, would not find an edge to it ( well, there are of course the Atlantic and Pacific Oceans, but I think you know what I mean). Gravity has distorted 3-dimensional space to such a degree that it has seamlessly folded over itself through the fourth dimension to form a closed spatial universe. This business only sounds strange to us because we have never experienced anything other than life in a 3-dimensional world since we emerged out of the oceans 500 million years ago.
Since the mathematical space in which this finite, closed universe is embedded is outside our physical spacetime, it will never contain events that can be experienced by anyone within our spacetime....ever. This means that since we can never observe this exterior space, it lies outside science. On the other hand, it does not lie outside mathematical deduction since mathematics is controlled by logical necessity not physical testability.
There are many philosophical attitudes that can be taken about this question. None of these can be strictly proven on the basis of hard data since the arena of interest lies outside of our spacetime. The first attitude is that our spacetime, our universe, is absolutely all there is. It extends beyond our visible horizon, there is no 'embedding space' to account for because it simply doesn't exist. The second attitude is that nothing is forbidden in nature so if a mathematician can imagine it, it actually exists. The embedding space is as physically real as our spacetime, and in it, all possible universes exist including ones with drastically different physical laws, particles, forces and dimensionality.
The difficulty in thinking about the embedding space is that we persist in asking "What is happening in it?" and "How do events evolve in time?" when in fact time is only a phenomenon experienced when one of the 4-dimensional spacetimes that inhabit it is sliced in a particular way. Each of these closed universes is like a coconut floating in the vaster ocean of the embedding space. From the perspective of the embedding space, all structures in it are seen from their timeless perspective. They are not in the process of becoming or changing, they simply exist.
If you have trouble visualizing what this embedding space looks like, you are in good company. John Wheeler confesses in his 1990 book A Journey into Gravity and Spacetime that "I confess I have never been able myself to picture directly this mythical, flat, infinite 4-space and the 3-space universe embedded in it...This flat, 4-dimensional space has nothing whatsoever directly to do with our real physical world as spacetime, even though that also is four-dimensional. Almost all of this [embedding] space is totally out of our reach, quite untouchable, pure talk... Only [3-dimensional space] itself is real [to us]".
I know this sounds as if I am dodging the question by playing on the limitations of the human mind, but these limitations seem to be real. The human mind is perpetually puzzled by the rules of the quantum world, the constancy of the speed of light for all moving observers, and a host of other properties of the physical world. According to general relativity, the universe is a 4-dimensional thing which requires us to visualize it as a complete 4-dimensional object. You can never appreciate a sphere by only looking at one of its circular cross sections.
Copyright 1997 Dr. Sten Odenwald
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