Expanding Universe, Acceleration, Model
Date: Winter 2012-2013
Is the accelerating expansion of the universe analogous to the fact that, if the radius of a sphere is increasing at a constant rate, two points on the surface of the sphere will move away from each other at an accelerating rate?
You are congratulated for “thinking” about a cosmological problem that has attracted a lot of very sophisticated minds for many years. There are several problems that have escaped resolution, however. One problem is: How do we know that expansion of the Universe is behaving like a “simple” sphere? The answer is: We do not.
Another problem is the geometry of an isotropic sphere may not apply. For example: Given a sphere of radius, R, the volume is V = (4pi/3) x R^3, and the surface area, S, is dV/dR = (4pi) x R^2, and dS/dR (8pi) x R. Rearranging gives: dS / dV = 2/R. This result implies that the change in surface area, dS, DECREASES as the volume INCREASES. It does not increase. That is: dS/dV = 2 / R. So the surface area, that is a measure of the distance between points on the surface decreases as R increases. What this means is that the geometry of a hard sphere does not apply to expansion of the Universe. So some other things are going on. The “answer” remains elusive.
It is analogous in some ways with respect to the two points only. But that may lead a student to think of a constant acceleration. The acceleration is not constant and is not derived from a focal source on a spherical plane.
Please consider the sphere under varying local pressures with unequal gravimetric attractors to and between the points. That sphere is inside a vessel of unequal negative pressures with weaknesses around those two points.
It may seem counter intuitive, but consider the making of a chocolate chip oatmeal cookie. It begins as a blob of no single point on a tin. It is heated. As it expands the dough moves quickly. The chocolate chips and oats move with, throughout and are retarded by the dough. The other oats and chips contribute or slow the expansion of both the dough and the oats/chips. The rates of expansion for the dough, the oats and the chips are not constant and are not constant between themselves.
Space is expanding and the objects in it are expanding with it, under influence(s) with everything else in it.
Hope this helps and if in a classroom, the cookie makes a great demo! Peter E. Hughes, Ph.D. Milford, NH
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Update: December 2011