I thought of this the other day, but since I just got back from visiting family over Christmas I haven’t had a chance to research it yet. I figured, why not just put it on here anyway? :-D
Imagine a record in a frictionless environment (or, if you prefer, a CD–although the example is easier to “see” if you imagine the record, since it’s bigger and spins slower). Put a mark near the center of the record, and another mark near the edge. When the record turns one revolution, the mark nearer the center has gone less distance than the mark on the outer side; yet both have gone this revolution in the same time.
Therefore, we know that the mark near the edge of the record is moving at a higher rate of speed.
However, from the viewpoint of either of the marks looking toward the other mark, neither mark has moved at all (this is assuming observers at the marks cannot “see” the world beyond the edge of the record). The distance between the two marks is identical, all the space between the marks remained in the same location, etc.
But now imagine that this record is a lot larger. Suppose that the first mark is 1 mile away from the center of the record; the second mark is 10,000 miles away from the center of the record. Thus, there is 9,999 miles distance between the two marks.
The record spins one revolution in 1 minute. The first mark has a radius of 1 mile. The circumference of the circle the mark describes is 2r*pi, or 2 miles * 3.14 = 6.28 miles.
The second mark has a radius of 10,000 miles, and therefore travels 20,000 miles * 3.14 = a circumference of 62,800 miles.
While the first mark traveled at a rate of 376 mph, the second mark travelled at a rate of 3,768,000 mph.
However, as in the first example, the rate of speed of these two points when observed internally to the record is 0 mph. Neither appears to be moving at all.
Let us now apply Einstein’s relativity here.  If such a record actually existed in real life, would time move slower for the second mark because it is travelling so much faster from an outside reference than the first mark; or would time be the same rate for both points because both points are moving at 0 mph from the internal reference?
Obviously, this becomes important as we can expand this from a record to a spinning sphere with the same results; and furthermore we can easily transcribe the sphere to the universe as a whole. If we are internal to the universe, we cannot observe if it is spinning like a kicked soccer ball (since we cannot “see” beyond the edge of the universe, and if there is no friction beyond the edges then we couldn’t observe drag either).
How would such a concept affect General and Special Relativity?
Just a question :-D
