Revisiting the Boundary of Space
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In a previous essay I deduced statements equivalent to the theorem that the word space names a spherically-symmetric entity of finite extent, one whose boundary has no area and expands outward away from each and every point at the speed of light. Now I want to revisit that deduction to see what additional light our subsequent discoveries can shed upon it.
First, I want to prove and verify the proposition that the Universe possesses only one boundary, that the boundary stands before us as a perfectly unique phenomenon. That proposition necessarily entails the statement that space does not contain holes. To put that statement to the proof, assume that space does contain a hole, a region filled with Absolute Nothingness. Again we note that the side of the boundary enclosing that region that faces the non-space side can have no area, so the side of that boundary facing the space side must have zero area. In this case we cannot argue that the boundary appears to surround us: we can only use that ploy once and we have already used it on the boundary of the Universe. Thus the zero area of the boundary of our putative region of non-space must have zero extent. Our description of that region becomes indistinguishable from that of a mathematical point, leading us to infer that such a region does not, can not, exist as a hole in space. If space has no holes, then it has only one, unique boundary.
Second, the boundary has a property that I could have inferred for you in the earlier essay, but chose not to infer there because it would have led us too far from the point that I wanted to make. Now, though, it helps me to tighten the weave that we have made of Relativity into Cosmology. Manifesting the property in question, the boundary of space remains frozen forever in a single instant of time, the instant of the Universe's origin.
We know that two clocks immediately adjacent to each other with no motion between them must count time at the same rate. Suppose that we want to insert the boundary of space between two such clocks. A clock cannot exist in Absolute Nothingness, but we also know that time also does not exist in that realm. By the same reasoning that we applied to deduce the area of the boundary, we infer that a clock placed next to the boundary on the space side never shows the slightest elapse of time.
That inference conforms to what we have deduced before. The boundary moves away from every point at the speed of light, so the phenomenon of time dilation brings the elapse of time on the boundary to a complete halt for all observers. So now we know that the aeternal instant of the Universe's self-creation flies away from us, leaving in its wake a cloud of cosmic fire that cools, releases its trapped radiation, and condenses into new galaxies.
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